In this paper, we examine the effect of reserve creation due to the Federal Reserve's Large-scale Asset Purchase programs on bank lending and risk-taking behavior. In particular, we test the existence of a risk-taking channel that induces banks with higher reserve accumulation due to the Fed's policy to increase the share of riskier loans. Exploiting the heterogeneity in the exposure to such asset purchase programs, as measured by relative mortgage-backed securities holdings in the banks' portfolios, we use difference-in-differences analysis to study the effect of the Fed's policies on the supply of total loans and the share of riskier loans such as real estate, commercial and industrial, and consumer loans. We find that the first and third round of Quantitative Easing (QE) policies led to an increase in both the total loans and the share of riskier loans within the banks' portfolios, supporting the risk-raking channel. The second round of QE on the other hand, had no significant impact on banks' lending behavior. The effectiveness of such policies has been a topic of debate over the past decade as central banks in developed countries continue to implement the QE policies. Hence, a more complete understanding of how such policies are transmitted to the economy is necessary. There is rich theoretical literature studying the effects of reserve accumulation due to the Fed's policies on the banking sector. Empirical studies analyzing the effect of reserve accumulation due to the QE policies on banks' portfolio decisions are rare, however. Studies analyzing the effect on banks' risk-taking behavior are even rare.In this paper, we study the effect of the increase in the reserves due to the QE policy on the banks' risk-taking behavior. To do so, we study the effect on the share of risky loans issued by the commercial banks. Studying the effect on the share of risky loans helps us understand the banks' risk taking tendencies due to the increase in reserves. Changes in these loan categories as a share of total loans helps assess the riskiness of banks' marginal lending. We study the effect on real estate loans, commercial and industrial (C&I) loans, and consumer loans. These categories of loans have relatively high delinquency rate. In addition, these loans carry regulatory risk weights of at least 100%.1The study is significant for a number of reasons. First, Banks are directly affected by the QE policies as an increase in the bank reserves is the defining characteristic of such policies. Banks play an important role in facilitating economic activity and a shock to the banking sector can have a major impact throughout the economy. Hence, it is essential to understand the impacts of such policies on the banking sector. It offers valuable insights into how the Federal Reserve's monetary policies affect bank lending and risk-taking behavior. These are crucial factors that impact the stability and growth of the economy. Second, the paper explores the existence of a risk-taking channel, which has important implications for financial stability. If banks respond to the Federal Reserve's policies by taking on more risky loans, it could increase the likelihood of defaults and lead to greater instability in the financial sector. Third, the paper's findings can be used by policymakers to inform their decisions about the effectiveness and potential risks of their monetary policies. If these policies have unintended consequences, such as encouraging risk-taking among banks, policymakers may need to adjust their approach to ensure financial stability.An increase in reserves accumulation forced by the Fed likely induces banks to seek investment in other assets such as securities and loans at a higher rate. Indeed, Friedman and Schwartz Studying the effects of QE poses a significant challenge, overcoming the endogeneity of banks' reserve holdings to other portfolio decisions. While the supply of total reserves is fixed by the Fed, the distribution of the reserves is determined by the individual banks. Hence, relating bank-level outcome to their reserves balances poses an endogeneity problem. To overcome this, we exploit the cross-sectional variation in the mortgage-backed securities (MBS) holding in the banks' portfolio and employ a difference-in-differences identification strategy as in Rodnyansky and Darmouni We find significant effects of QE1 and QE3 on banks' lending behavior. There is evidence of increased lending due to the increase in reserves among the banks with large MBS holdings relative to their counterparts as in Rodnyansky and Darmouni The results suggest that QE2 did not have a significant impact on bank lending as QE2 primarily focused on Treasury securities, rather than MBS, which are sparsely held by commercial banks. Such findings indicate that the effect of the Fed's policies work through a narrow channel that affect the prices of the targeted asset solely and not through a broad channel that affect all long-term rates when targeted at a particular asset such as MBS.bank lending channel as in Kashyap and Stein net-worth channel as in Bernanke and Gertler liquidity channel where QE infuses liquid asset (reserves) in exchange for MBS by the Fed, or via secondary market, without significantly altering the balance sheet of the banks. Such infusion of liquidity allows banks to expand lending. Fourth is the signaling channel as in Bauer and Rudebusch There are various channels through which LSAPs affect banks lending behavior. First is the Most studies thus far focus on understanding the macroeconomic effect of QE policies, such as the effect on long-term interest rates and inflation expectation, or yields on widely traded financial assets as in Gagnon et al. Despite the prevalence of theoretical studies on the reserve creation due to monetary policy, empirical studies linking the reserve accumulation as a result of QE to banks' investment decision remain scarce.8Understanding the effect of reserve accumulation due to the QE policy on banks' lending behavior is essential as banks play an important role in facilitating economic activity. This paper analyzes the effect of the QE policy on banks' risk-taking behavior by studying the effect of the policy on the share of risky loans issued by the banks. We find that QE1 and QE3 raised the share of risky loans issued by the banks, indicating an increased risk taking by the banks due to the policies. We do not find any significant impact of QE2 on banks' lending behavior. The findings contribute significantly to the literature as studies analyzing the effect of the QE policy on Banks' risk-taking behavior are rare.The remainder of the paper proceeds as follows. Section 2The dataset used for the analysis is the Consolidated Reports of Condition and Income, FFIEC 031 and FFIEC 041 regulatory filings, commonly known as Call Reports. All commercial banks with insured deposits must file Call Reports every quarter. Call Reports include detailed information on the composition of banks' balance sheets, income statements and off-balance sheet items. We construct a set of dependent, independent and control variables used in the analysis from Call Reports for the sample period of 2008Q1 to 2014Q1. The summary statistics of variables used in the analysis is presented in the appendix.In contrast to the approach commonly used in the empirical literature using Call Reports, we do not aggregate the data at the holding-company level. Many banks are part of multibank holding companies and non-bank subsidiaries are not included in the Call Reports. The reasons for using bank level data instead of holding-company data are twofold. First, as demonstrated by Rodnyansky and Darmouni 9Next, we present the difference-in-differences empirical methodology used in the analysis. Then, we present the findings on the effect of QE1, QE2 and QE3 policies. To test the robustness of the findings, we conduct two additional tests in the Robustness Tests section. We then conclude the paper with a brief summary of the finding.3Exploiting the heterogeneity in the sensitivity to QE programs across banks, represented by cross-sectional variation in the MBS-to-Securities ratio, we use Difference-in-Differences strategy to identify the effect of QE programs. The dependent variables used are natural log of loans, loans as a share of total loans and log difference of loans, where loans studied are total loans, real estate loans, C&I loans and consumer loans. The baseline specification we use is given by,treatment effect. A positive The coefficient of interest is We use STATA software for the estimation. In particular, we use Difference-in-Differences package to estimate the parameters.13One of the main challenges in assessing the impact of QE programs, particularly QE1, is the presence of confounding factors related to the Global Financial Crisis. As banks that specialize in real estate mortgages may have been disproportionately affected by the sharp decline in MBS prices, it can be difficult to separate any positive effects of QE programs from the negative effects of the crisis. This poses a challenge for disentangling the specific impacts of the QE programs on bank lending and risk-taking behavior from the broader economic conditions during the crisis. In particular, there are three potential limitations of the approach. First, the estimation approach assumes a parallel trend between the treatment and control groups in the absence of the treatment. The limitation of the difference-in-differences estimation approach is that we are unable to observe the trend of the treated group in the absence of treatment. Second potential concern that is closely related to the first concern in this case is the endogeneity of exposure. The MBS-to-securities ratio may be endogenous to bank lending and risk-taking behavior. Banks that are more willing to take risks may have intentionally held more MBS, anticipating the policy effects. Alternatively, banks with higher MBS holdings may have been more likely to receive LSAPs due to their size or relationship with the Federal Reserve. Given that QE programs were implemented to provide a general support to the housing market and improve financial condition, and considering the legal restriction governing assets purchases by the Fed, the cross-sectional variation in the MBS-to-Securities ratio is likely to be uncorrelated with the pre-intervention lending rates for each bank. Specialization in real-estate lending by some banks implies that the distribution of MBS-to-Securities ratio is unlikely to be random. However, while the levels of lending are different across banks with high and low MBS-to-Securities ratio throughout the sample period, the trend in lending is unlikely to be altered absent the Fed policies. In other words, the parallel trends assumption in lending across banks with different MBS-to-Securities ratios before the Fed policies is likely to hold. To further provide support to the parallel trend assumption and alleviate the concern of endogeneity, we analyze the trends in average lending-to-asset ratio across banks in the treatment and control groups. In addition, the literature studying the QE policies document a narrow channel of the policies that affect the prices of the targeted asset solely and not through a broad channel that affect all long-term rates when targeted at a particular asset such as MBS, further providing support to the identification strategy.Another limitation of the study is the generalizability of the findings to the overall financial system. The study focuses on commercial banks and may not be generalizable to other types of financial institutions. Nonetheless, understanding the effect on banks' behavior is an important finding.There is a concern of borrower-level shocks still that could potentially affect the bank-level outcomes. For instance, banks with relatively high MBS holdings may experience higher credit demand growth due to improvement in their borrowers' financial health around the policy periods. To alleviate the concern, we refer the reader to Rodnyansky and Darmouni 4Until the Great Financial Crisis, the Fed relied on conventionary monetary policies that resulted in relatively modest increases in excess reserves in the banks' balance sheets. The QE policies implemented in response to the crisis and subsequent recession resulted in unprecedented increases in reserve balances held by banks. 4.1We present the findings in chronological order, starting with the first round of LSAP. QE1 began on November 25, 2008 when Federal Open Market Committee (FOMC) announced a program to purchase MBS with a stated goal of providing support to the housing market and improve financial condition more generally. By the end of 2010Q2, the program purchased a total of $1.25 trillion in agency MBS, $175 billion in federal agency debt issued by Fannie Mae, Freddie Mac and Ginnie Mae, and $300 billion in long-term treasury securities.The estimated coefficient of interest  only. This is to test if the main results are driven by the size effect. Second, we further test the validity of the methodology by estimating the baseline specification for quarters prior to QE3 policy. If the main results are biased, we expect the effects on lending behavior from the set of test should also be significant. Below, we present the results of these tests.5.1While the baseline regressions control for the size of the banks, there's a possibility that the control is inadequate, perhaps due to nonlinearities. In order to alleviate the concern that the main findings are due to size effect, we restrict the sample to include banks in top 50% by total assets. Such restriction significantly reduces the size differential across banks and any potential size effect in the findings is reduced.The estimates are similar to those of the baseline case. The findings suggest that the results are no different whether smaller banks are included in the analysis or not, ruling out the size effect explanation of our baseline results. The findings also suggest that there's no significant difference between large and small banks in lending sensitivity to the QE policy.5.2The set of tests aim to provide further support to the empirical methodology used in the paper. The biggest concern when estimating the effect of QE policy is that of endogeneity. In particular, some pre-existing trends might be driving the results as treated banks could have expanded lending prior to the QE policy relative to untreated banks. To alleviate such endogeneity concerns, we perform tests that make repeated observations of the banks over time. For brevity, we present analysis on QE3 only as the concern is most relevant to this round of QE.The estimated coefficients are not significant for any quarters prior to QE3 while they are positive and significant after the implementation of QE3. The findings suggest no significance difference in lending behavior between treated and untreated banks before QE3 was phased in, and the treated banks expanded the loans relative to untreated banks after the adoption of the Fed policy, implying the causal effect of QE3 on banks' lending behavior. The findings provide further support to the identification strategy used in the paper.In addition, there are evidences to show that the effects grow over time, indicating an increasing rate of shift towards riskier loans.6The paper explores the effect of bank-level reserve accumulation as a result of QE policies on bank lending and risk-taking behavior. Reserve creation by major banks has increased significantly on the onset of the Fed's response to the Great Financial Crisis, raising the question on role of such reserve accumulation on transmission of the QE policies. Despite rich theoretical literature on the role of reserve creation due to QE policy on bank lending behavior, empirical studies on such role is scarce. This paper contributes to the literature by studying the effect on banks' risk-taking behavior.Exploiting the cross-sectional variation in the MBS holding in banks' portfolio, we employ a difference-in-differences identification strategy to estimate the effect of the QE policies on bank lending and risk-taking behavior. Each bank's exposure to the QE policies is captured by the MBS as a share of total securities in the bank's portfolio prior to the implementation of the policies. There's a significant heterogeneity in the MBS-to-securities ratio among the commercial banks and hence, their exposure to the QE policies.We find that reserves created as a result of QE1 and QE3 led to banks with a relatively large fraction of MBS on their balance sheet to expand lending more aggressively when the Fed targeted those particular types of securities. Based on our findings, QE2 had no significant impact on banks' lending. The findings suggest that the transmission of QE works through a narrow channel that affect the prices of the targeted asset solely and not through a broad channel that affect all long-term rates. In addition to increased lending, the QE policies also led to an increase in the share of riskier loans in the banks' portfolios, supporting the existence of risk-taking channel.There exist strong evidences that the overall efficacy of QE on banks' lending behavior depends on the types of assets purchased. The increase in reserves leads to an expansion of bank lending and shift towards riskier loans.Saroj Dhital; Chandler Dixon; Eddie Evanczyk: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Laminotomy has been introduced in surgical practice to reduce complications of laminectomy after surgery of tumors in the spinal canal. However, the posterior ligament complex, which is routinely interrupted to remove the laminoplasty segment and gain access to the spinal canal, has a tendency not to heal and can lead to progressive kyphosis and collapse.A 5-month-old boy affected by a thoracolumbar extradural tumor extending along seven spinal levels was operated on. The tumor was exposed and completely resected by a one-piece laminotomy with preservation of the integrity of the posterior tension band at both extremities. After 1-year radiological examination ruled out spinal deformity.The technique herein presented, which we named in situ laminotomy, allows to fully preserve the posterior tension band without reducing the exposure of the spinal canal in multilevel tumors. Additionally, the technique makes also the reconstruction of the spine elements very easy and rapid. However, longer follow-up is necessary to prove the effectiveness of this procedure in preventing long-term deformity and instability. Laminotomy has been conceived and introduced in surgical practice to reduce complications of laminectomy after surgery on tumors in the spinal canal .Although bone structures are repaired, the risk of medium- to long-term deformity still exists because other factors concur with this complication, in particular, younger age and extension of the tumor . Thus, tOn these grounds, superiorly-based laminoplasty has been conceived aiming to preserve the integrity of posterior tension band at least at its cephalad extremity .In the present case, we moved a step forward, aiming to preserve the integrity of the posterior tension band at both extremities. The technique herein described, which we named in situ laminoplasty, warranted a complete exposure of the spinal canal, allowing to resect a huge thoracolumbar extradural tumor extending along seven spinal levels in an infant. The technique made also the reconstruction of spine elements very easy and rapid. The obvious advantages for the restoration of spine integrity and function should be confirmed by a larger experience and longer follow-up.A 5-month-old boy complained a 2-month history of inconsolable crying and progressive lower-limb weakness. Spine MRI showed a voluminous spinal extradural tumor  extending from D10 to S1 . This instrument allowed us to achieve the largest lateral exposure of the spinal canal along with careful preservation of facet joints since the thin tip allows a micrometric osteotomy that is tangential to the medial aspect of the facet [The supraspinatus and interspinous ligaments were fully preserved, as well as the flavum ligaments. Standard laminotomy after this step would consist of section of these ligaments rostrally and caudally to the level included in the laminotomy.In the present case, only the flavum ligament was sectioned with a 1-mm Kerrison punch at those levels, thus preserving the supraspinatus and interspinous ligaments. Then, the laminoplasty segment was lifted with curettes and retracted laterally on one side or another, thus allowing full exposure of the spinal canal and dural sac.Under microscopic view, the tumor was carefully dissected away from the dural sac and completely resected. The neural roots were freed of the tumor at the conjugation foramina.After epidural hemostasis, the laminotomy segment was brought back in place. Reconstruction was made easy by the preservation of the posterior tension band. Burr holes on the laminae and receiving bone edges were performed by means of a 1-mm high-speed drill. Laminae were fixed with 5.0 prolene sutures, and minimal bone gaps were sealed with fibrin glue.Then, the paraspinal muscles were re-approximated to the laminae and sutured to the deep interspinous ligaments, and the surgical wound was closed in a standard fashion.Intraoperative neurophysiological monitoring was unchanged from baseline.Intraoperative pictures and schematic drawings of the procedure are presented in Figs. The postoperative course was characterized by a prompt improvement of the preoperative neurological deficits. Spine MRI confirmed the radical resection of the intraspinal component of the tumor with small residual extraspinal tumor extending out of the foramina.Pathological examination confirmed the diagnosis of neuroblastoma, and the extraspinal residual tumor was resected by a pediatric surgeon.One-month follow-up CT scan and spine X-rays performed 6 months after surgery confirmed the correct realignment of the laminae. CT scan after 1 year ruled out any spinal deformity or other complications Fig. .Fig. 43DLaminectomy has been long time used to gain access to the spinal canal. However, the risk of deformity and instability in the immature spine of a child uniformly affects over one-third of patients .This risk recognizes several factors and is in part ascribed to the presence of a higher content of cartilage, to a more horizontal alignment of facet joints, to the more flexible ligaments, to the growth of the spine, and to the disease process itself.Thus, laminotomy and laminoplasty have been conceived to overcome the limits of laminectomy  and are On one side, the split laminotomy, first proposed by Bognar et al. in children , may minOn the other side, variants of traditional laminotomy have been proposed. Indeed, laminotomy aims to preserve the bony elements, but the posterior ligament complex is routinely interrupted to remove the laminoplasty segment and gain access to the spinal canal. An effort to partially preserve this functional structure has been proposed by sectioning only the ligaments at the caudal extremity of the laminoplasty segment and reflecting it rostrally .The present surgical technique allows to almost fully preserve the posterior tension band without reducing the exposure of the spinal canal since the laminotomy segment is lifted almost completely away from the exposed spinal canal in its median portion Figs.  and 3. TObviously, this technique is not feasible in a single-level approach, and we may not draw a definitive conclusion about the minimum number of levels required to perform this technique. We may speculate that the possibility of using this technique to approach a tumor of the spinal canal is related to the age of the patient and the extension of the laminotomy.Although we may not know in advance if this technique may warrant adequate mobilization of the laminotomy segment in order to adequately expose the spinal canal, we think that is worth attempting this option in the pediatric population before moving forward to traditional laminotomy.As a result, in multiple-level laminotomy, we propose a step-by-step approach aiming to preserve the functional integrity of the spine.As the first attempt, we try to approach the intraspinal tumor with in situ laminotomy. If the retraction of the spinal flap does not allow to gain adequate access, superiorly based laminotomy, as proposed by Meyer et al. , is perfIn conclusion, the present case proves the feasibility of removing the intraspinal tumor with in situ laminoplasty, although longer follow-up is necessary to prove the effectiveness of this procedure in preventing long-term deformity and instability.


In the realm of injection-molded parts, small length scale deformation defects such as sink marks often pose a major challenge to the aesthetics or functionality of the parts. To address this problem, we present a comprehensive thermoelastomechanical approach that calculates the deformation of injection molded plastic by solving the elastic problem at each time step. In our methodology, two treatments of the molten core are considered: one as a liquid and the other as a rubbery state. Our results suggest that the rubbery state treatment provides higher accuracy in predicting the deformation results, as it maintains the displacement of the localized thermal shrinkage in its vicinity. The validity of our method is supported by empirical measurements on produced parts from the existing literature as well as on samples that we molded independently. Injection molding of thermoplastic polymers is a widely used production process in which molten plastic is injected at high temperature into a metal cavity and cooled until it solidifies into a functional part. This process is essential to the mass production industry due to its scalability and low unit price, which keeps production costs manageable. Considering the low profit margins and high capital intensity associated with acquiring steel molds for plastic injection molding, it is critical to avoid costly mold and part design mistakes. Broken molds or visually deficient parts can have a devastating impact on profitability, which has led to the emergence of slogans such as “right on the first try”. To consistently achieve such production goals, simulation of the injection molding process is required. This involves solving the relevant partial differential equations for a given part geometry, considering appropriate boundary conditions as well as material models, and generating results that predict part moldability and quality. The prediction of warpage, i.e., the deviation of the shape of the produced part from the intended shape, is the pinnacle of modern simulation software ,2,3.In addition to warpage, there are many other defects that can occur in injection molded parts, and the goal of simulation is to predict as many defects as possible. One particular defect that occurs in injection molding is a “sink mark”, an undesirable depression on the surface of the part caused by localized high shrinkage of the material. Typically, sink marks occur in areas of the part that are thicker and cool more slowly, causing the surface to shrink away from the cavity wall more than adjacent areas. The local thickness is best defined as the diameter of a maximum sphere contained locally in the part, as shown in The aim of this work is to show that both global warpage and local depressions are due to the same cause, namely, thermal contraction during cooling and solidification of the plastic under pressure. Although this interpretation has been suspected in the literature, it has not yet been clearly established. The exact elastomechanics of the solidified layer in at least two dimensions throughout the production cycle must be calculated to show that sink marks and warpage are the same deformation manifested at different length scales. Furthermore, this work aims to broaden the definition of “sink marks” to include both depressions under a typical rib, as shown on the far left in An excellent historical overview of the academic field of injection molding simulation is provided by Peters Kennedy’s book , which sWith the increasing popularity of computer-aided design systems (CAD) in the 1980s, midplane shell models emerged. It became possible to solve the relevant equations using the finite difference method over the thickness of the part and to propagate them over the entire component using the finite element method ,11,12,13In the 1990s, CAD systems evolved to produce three-dimensional models. Full three-dimensional simulation using the “volume of fluid” method gained traction , but comOpen source software for injection molding simulation was virtually nonexistent until the early stages of development were begun in . The resDuring the injection molding process, the plastic is exposed to significant temperature and pressure changes as the phase boundary between solid and molten plastic progresses. Already-solidified layers prevent newly formed layers from freely changing shape, as they are all subject to elastomechanics as an integral domain. Early attempts to model shrinkage of injection molded parts relied only on thermodynamic (pvT) characterization of density  to prediSink marks were first discussed by Marchewka in 1974 . In theiLater, Naka et al.  of what In the late 1980s and early 1990s several influential doctoral studies were carried out in the Department of Mechanical Engineering at Ohio State University. The first thesis by Ramachandra  involvedThe research was continued by Mahesh Gupta of Michigan Technological University, who used the commercial software C-Mold  to simulSubsequently, several experimental studies were conducted using methods such as design-of-experiment and genetic algorithms ,40,41,42All the studies mentioned above start by calculating the deformation of the solidifying plastic when the pressure at the point of interest reaches the atmospheric value and show that such an approach can correctly predict the depth of the sink marks. However, by disregarding the exact pressure history of the filling and packing phases, the large-scale warpage is conceptually decoupled from the small-scale deformations of the parts. Moreover, all of these studies employ fairly complex elastomechanical material models such as elastic-perfectly plastic ,36,37,38z-axis. We assume that plastic flow occurs only in the direction of the z-axis, so that the cross section under study is filled instantaneously at time zero. This assumption eliminates the need to model the flow. Flow-induced residual stresses are not modeled in this study. As established by Baaijens [We have developed a method for predicting the local deformation of injection molded parts by dynamically calculating the displacement and stress fields of the solidifying plastic. Plastic parts are typically sheet-like, which means that some of their geometrical features can be adequately represented numerically by a two-dimensional cross-section, as already shown in Baaijens , they arAs soon as the cross-section under investigation is filled with hot plastic melt, heat transfer to the colder mold with homogeneous temperature begins, initiating the evolution of the temperature field of the plastic z-direction exists in the molten During the filling and packing phases, a hydrodynamic plastic flow in the z-direction disappears and the flow through this cross-section is completely stopped.In the packing phase, the flow through a cross-section compensates for the thermal shrinkage of the downstream plastic. For a given cross-section, the packing phase ends when the hydrodynamic pressure at that cross-section drops to zero (the ambient pressure of the vented mold). This occurs when the packing flow at the set packing pressure can no longer accommodate the downstream thermal shrinkage due to the large cooling-induced viscosity increase of the upstream plastic. At this point, thermal shrinkage prevails and the pressure at this cross-section begins to drop. When it reaches the ambient value, the pressure gradient in the z-direction. The hydrodynamically isolated molten core continues to shrink thermally together with the solidified plastic, while there is no pressure that would prevent the solidified plastic from detaching from the mold walls.In the final hydrostatic cooling phase, the pressure connection to the molding machine is interrupted and there is no longer any transport of the melt in the In this phase, we treat the molten region uid melt ; r=t we are dealing with a separate elastic problem defined only during a short time interval t. Similarly, in the rubbery core treatment of the cooling phase we are dealing with an elastic problem defined only in the time interval t.The plastic, already solidified at a given time, undergoes elastic deformation caused by the changes in the time-dependent stress field due to thermal shrinkage and/or the changes in the time-dependent pressure The result of the elastic problem in the time interval The crucial implication is that both the final stress state and the final shape of the cross-section generally depend on the specific time course of all relevant variables, i.e., of the fields The heat equation  and the z, and consequently no heat flux in this direction. The temperature-dependent density The evolution of the temperature field A homogeneous initial condition culation .h [h is widely discussed in the literature [Due to the imperfect contact between the polymer and the mold walls, the heat transfer through this interface must be modeled with a heat transfer coefficient h , which iterature ,52, we uterature  with speK and G are the bulk and shear elastic moduli, respectively, and K are extracted from the pvT relation  encloseThe global bending deformation seen in z-direction, it has a large When a part has cooled to a uniform temperature, it no longer deforms. As long as it remains in the mold with restricted displacement in the z. The calculated displacement field increment This is accomplished by solving another elastomechanical problem, analogous to the previous problems for each time step, with the boundary condition according to Equation  as beforement Δu  is addedThe deformation that occurs when a part is removed from the tool is commonly referred to as warpage. Commercial software usually calculates this type of deformation only once at the end of the production process. While the stress field required for this is not accumulated over the multitude of elastic problems of individual time steps, as in our thermoelastic method, it is an effective stress field constructed by various methods from simple to more sophisticated. One of the simplest is the linear shrinkage approach; this uses an isotropic stress field that, when released, causes the same local volumetric shrinkage as local cooling :(11)σij plastic Makrolon 2405 with three constant packing pressure settings of The molding process was simulated with Autodesk Moldflow software to calculate the time-dependent pressure  section a. The coWe can conclude that the agreement between the calculated and measured data is good. Due to the long packing phase, the molten core is localized under the rib, which makes the liquid approach suitable.In this study, we have introduced and applied a method to predict the deformation of injection molded parts. Our approach advances current research on sink mark formation by incorporating both the filling and packing phases of the injection molding process. We establish that global part warpage and localized deformations such as sink marks are due to the same cause, namely, thermal shrinkage and local pressure within the molten core.By adopting a dual perspective of the molten core, treating it as both a liquid and a rubbery material according to previous studies ,37,38, wAlthough the limitations of the liquid approach are evident, it remains a valuable conceptual tool. It naturally describes the buildup of negative pressure in the molten core that leads to the formation of voids. Furthermore, by studying the outcomes of this simulation model, practitioners can develop an intuitive understanding of where sink mark risks might be apparent when examining the cross-sectional shape of the molded part. This understanding is aided by the identification of stiffer and weaker regions of the solidified shell in relation to the negative pressure load of the molten core.Viscoelastic relaxation: with this modification, the value of elastic parameters could be adjusted locally based on the material history. Material parameters for such an approach are increasingly common.Variable heat transfer coefficient: during the cooling phase, the heat transfer coefficient could be updated at each time step based on the local distance between the plastic and the mold.Evaluation of local detachment: the condition for detachment from the mold walls could be evaluated locally, implementing the boundary conditions for the displacement accordingly. The numerical stability of such an approach remains an open question for further investigation.Looking ahead, several refinements could be incorporated into the thermoelastic method, including:The true utility of this method lies not in its theoretical demonstration but in its potential for practical implementation in commercial software, which would make it accessible to the plastic design community. Advances in computing power have made such an implementation feasible within existing three-dimensional simulation procedures. Warpage calculation of predefined critical areas with a limited number of discretization points could be improved with such a method. Future validation procedures would reveal the extent to which the filling and packing phases are already adequately addressed within current procedures and whether the primary benefit of this method does indeed lie in its capability to incrementally calculate the displacement of solidified plastic during the cooling phase.


Spectrum sensing in Cognitive radio (CR) is a way to improve spectrum utilization by detecting spectral holes to achieve a dynamic allocation of spectrum resources. As it is often difficult to obtain accurate wireless environment information in real-world scenarios, the detection performance is limited. Signal-to-noise ratio (SNR), noise variance, and channel prior occupancy rate are critical parameters in wireless spectrum sensing. However, obtaining these parameter values in advance is challenging in practical scenarios. A lifting wavelet-assisted Expectation-Maximization (EM) joint estimation and detection method is proposed to estimate multiple parameters and achieve full-blind detection, which uses lifting wavelet in noise variance estimation to improve detection probability and convergence speed. Moreover, a stream learning strategy is used in estimating SNR and channel prior occupancy rate to fit the scenario where the SU has mobility. The simulation results demonstrate that the proposed method can achieve comparable detection performance to the semi-blind EM method. With the rapid development of mobile intelligent terminals, wearable devices, and industrial monitoring in 5G applications, the amount of mobile data traffic is growing exponentially . To ensuGenerally speaking, different detecting techniques require different amounts of wireless environment information. According to the amount of prior information required, spectrum sensing methods can be divided into un-blind detection, semi-blind detection, and full-blind detection. The likelihood ratio test (LRT) based on the Neyman-Pearson criterion is currently known as the optimal detection method, which requests a known distribution of the received signal that is generally related to the PU information, the noise variance, and channel statistic characteristics. Therefore, the LRT is an un-blind detection method . ConversOwing to the intricacy of the full-blind approach, several studies employed a semi-blind approach. The semi-blind detection method expects knowledge of certain parameter values such as noise variance, PU information, or channel occupancy. Energy detection (ED) is widely used in spectrum sensing due to its easy implementation. However, the detection accuracy is susceptible to noise uncertainty, as the noise variance should be known to calculate its threshold value . In addiCompared with full-blind detection, semi-blind detection has the advantage of being easy to implement and relies on the assumption of known noise variance. In practical scenarios, it is difficult for semi-blind detection methods to obtain real-time noise variance values, which makes semi-blind detection face challenges in practice where noise uncertainty exists. The semi-blind detection method with known noise variance can availably serve as a full-blind detection method in spectrum sensing when noise variance estimation is conducted. In noise variance estimation, some special channels for noise variance estimation can effectively avoid interference from the PU signal, but this estimation method sacrifices spectrum utilization ,20. MoreDue to the limitations of path loss and multipath fading, local spectrum sensing performance may be affected. When reusing the licensed spectrum, it is usually hoped to minimize the impact on the PU, which relies on highly reliable spectrum sensing techniques for global sensing of the wireless channel. Cooperative spectrum sensing (CSS) using spatial diversity among SUs is a good solution to achieve highly reliable spectrum sensing . In CSS,In this paper, we investigate full-blind cooperative spectrum sensing based on the classical optimal LRT. In order to eliminate the coupling between the unknown parameter estimates, we independently discuss the noise variance estimation problem and combine it with the EM estimation algorithm to achieve fully-blind detection. The main contributions are: (1) in un-blind optimal likelihood ratio detection, many parameters need to be known in advance. Traditional full-blind detection approaches are hard to use in practice as they have high computational complexity. When the parameters are unknown, the detection problem becomes a composite hypothesis. In order to achieve full-blind spectrum sensing with multiple unknown parameters, the EM algorithm is used to estimate the noise variance, SNR of the received signal, and channel prior occupancy rate. (2) Besides, a simple noise variance estimation method based on the lifting wavelet transform is used in the EM algorithm to further shorten the detection time and improve the detection performance and fitness for actual scenarios with noise uncertainty. (3) Finally, the stream learning strategy based on historical information is used in estimating SNR and the channel prior occupancy rate, making the proposed method adaptable to the scenario where the SU has mobility.The remainder of this paper is outlined as follows: The corresponding system model and the optimal detection problem are described in J SUs, which is shown in It is assumed that the cognitive radio network consists of one PU, one FC, and j is defined as [j is denoted by m-th sampling point of the PU signal, which follows a Gaussian distribution with a zero mean. j with variance According to Neyman-Pearson criteria, the spectrum sensing problem can be modeled as a binary hypothesis test, and the received signal sample at the SUfined as (1){yj, the probability density function (pdf) of The detection statistic, SNR, and noise variance for all SUs in the entire network are denoted as According to the likelihood ratio detection principle, the decision expression based on the log-likelihood ratio function for the whole work can be written as (9)Lℋ1(TBy substituting (5) and (7) into (9), the decision expression can be simply described asAccording to (10), the decision can be made if the SNR and the noise variance for each SU are known. However, these parameters usually vary in a dynamic environment. In order to determine the state of the channel, it is necessary to estimate the SNR and the noise variance of each SU. The unknown parameter vector is defined as Since the channel occupancy is unknown when SUs acquire the detection statistic of ariables . In the n-th detection, the n-th detection statistic for the j-th SU. According to Bayes’ rules, In the The conditional expectation of (8) given the posterior probability of the channel occupancy state of n-th round of detection are obtained by maximizing the In the M-step, the corresponding estimation parameters of From (15), the conditional expectation By substituting (18) into (15) and let the Finally, we compute the The detailed solution to the optimization problem is given in According to the above derivation, this multi-parameter estimating method using the EM principle is denoted as a fully Blind-EM estimation and detection method.Because the estimated values of noise variance and SNR are coupled with each other, the performance of multi-parameter estimation will be affected in fully Blind-EM estimation and detection. Consequently, we consider decoupling the two estimates. Since the noise variance in the received signal is mainly concentrated in the high-frequency part and the wavelet transform can realize the variable resolution decomposition of the signal, the noise variance value can be estimated by using the high-frequency coefficient decomposed by the wavelet transform.The dynamic environment caused by SU mobility puts forward a higher demand for detection delay; a shorter detection delay will help the fusion center estimate and track the changes in various parameters promptly. The traditional wavelet transform relies on the Fourier transform and has complex operations, so it is not suitable for dynamic scenarios. The lifting wavelet can realize the specific wavelet function by designing different prediction operators and update operators, which has the advantages of fast decomposition speed and small memory consumption and is completely equivalent to the traditional Mallat algorithm . A low-cp-th layer is shown in k represents the number of prediction times.The decomposition process of the Similarly, p = 1 is considered, the db2 wavelet transform can be achieved by performing two predictions and one update, and the corresponding operator can be written asIf the case of The specific calculation process is as follows:In the end, by multiplying the normalization factors by the final wavelet factorization coefficient, the following can be obtained:The noise variance can be estimated using the high-frequency coefficients obtained from the current period’s decomposition .(27)σ^jThe noise variance estimation conducted in the Blind-EM algorithm is replaced by the estimation through the lifting wavelet, which is called the lifting wavelet-assisted EM iteration joint estimation method (WEMJD), which performs estimation of other unknown parameters by setting Compared with batch learning, which needs to wait until all the observed data are obtained, online learning is better suited for scenarios where data arrives continuously . The parBy replacing (19) and (21) with (29), the final estimating expression of SNR and channel prior occupancy rate can be expressed, respectively, asAs the noise samples are independent of each other and do not have a correlation, it should be noted that historical learning is not suitable for predicting and tracking the irregular changes in the noise variance. Hence, only the sliding window is used to smooth the noise variance estimation results.Due to the sensitivity of the EM algorithm to the initial values, reliable initial values can help the EM algorithm converge to the global maximum and greatly reduce the iteration time of the algorithm. Since the PU activity status is independent of the noise variance and SNR, it is assumed that the probability of the channel being occupied and unoccupied is equal at the initial time, therefore To evaluate the performance of a detection method, its ability to correctly detect the presence of a target signal can be determined by using the false alarm probability and detection probability.The ability of the detection method to correctly detect the presence of a target signal can be described by using the false alarm probability and detection probability. The detection probability Based on the Neyman-Pearson criterion, the threshold value should maximize the detection probability with constraint d degrees of freedom forms like In general, the exact distribution of the weighted sum is difficult to obtain, So we approximate R=αχd2+β ,41,42. TLet the first three cumulative moments of The approximate distribution of The value of Refer to J SUs, M sampling points, and N detection times. At FC, for WEMJD, Semi-blind EM and GLRT have the same computational complexity is M is the same size as N, while J is usually smaller than M and N, so the proposed method has a lower degree of complexity. At SUs, we assume that the length of the prediction operator is p, the complexity of the noise estimation part is The algorithm complexity is evaluated under the case of In this section, the simulation results under different settings are shown. To make the results more realistic and reliable, we performed j.In the network, due to the random distribution of SUs, differences in geographic location also bring about differences in received SNR. Therefore, we define the global average SNR asn-th detection is defined asIn order to evaluate the estimation performance of the proposed algorithm, the mean squared error (MSE) is used as the evaluation metric. The MSE for the To discuss the convergence of the method, it is first assumed that the secondary users are stationary and have the same nominal noise variance of The setting of the false alarm probability is related to the threshold value. From By taking account of the scenario of changing channel conditions, it is assumed that the SUs exhibit mobility, which means that the received SNR at the SUs changes over time. In the presence of To observe the sustained performance of the method, the simulation parameters are set as To observe the performance of different estimation and detection methods with noise uncertainty. It is assumed that the noise variance follows a uniform distribution within a certain range, It may be noted that the false alarm probability of the proposed method fluctuates around the set value as the global average SNR is varied, which is shown in As it is often difficult to obtain accurate wireless environment information in real-world scenarios, the estimation and detection methods of cooperative spectrum sensing in dynamic environments are studied in this paper. Based on the LRT theory, it is required to estimate the noise variance, the signal-to-noise ratio, and the channel prior occupancy in the blind scenario with varied channel conditions. A lifting wavelet-assisted EM joint estimation and detection algorithm is proposed to estimate multiple parameters and achieve full-blind detection. Moreover, the lifting wavelet technique is applied in noise variance estimation to improve detection probability and convergence speed. At the same time, a stream learning method is used in estimating SNR and channel prior occupancy rate to fit the dynamic environment. The simulation results demonstrate that the proposed full-blind method can achieve comparable detection performance to the semi-blind EM method. It can adapt to mobile scenarios where the SNR varies over time and exhibit a certain robustness against noise uncertainty.


A novel approach coupling the finite volume method code Pyro2 and the smoothed particle hydrodynamics code PySPH is introduced and applied to one-dimensional shock problems. The finite volume mesh models the bulk of the system, while regions with discontinuous fluid values are identified and populated with PySPH particles to model the fluid around shocks. The approaches are coupled with boundary cells and ghost particles, with linear interpolation used to extract fluid properties at each timestep in the respective boundary regions. Results from three shock problems using Pyro2, PySPH, and a hybrid approach are presented. The hybrid approach preserves accuracy and computational efficiency in strong shock problems. Additionally, the coupling approach provides a potential avenue for including SPH functionality in FVM simulations, including modeling complex geometries and fluid-structure interaction. The preliminary investigation of the hybrid approach in one dimension highlights the potential efficiency gains of applying coupled FVM-SPH methods to larger blast simulations in two and three dimensions. •A novel FV-SPH approach is introduced and applied to 1D shock problems.•SPH particles model the fluid around shocks while FV cells model the bulk fluid.•Linear interpolation couples fluid properties across FVM and SPH zones.•The hybrid approach accurately models strong shock simulations while preserving computational efficiency. The predictive capability of models used to describe shockwaves is vital to understanding the relevant physics and, in many cases, pertinent to the safety of industrial processes. Shockwaves propagate through a medium supersonically and are characterized by a significant jump in fluid properties such as pressure, density, and internal energy. The discontinuous nature of shockwaves makes analytical treatments difficult in simple cases and impossible in most applications.The difficulty of modeling shockwaves arises from the extreme gradients across fluid properties. Computational methods of simulating fluid or solid media typically involve spatial discretization of the problem and solving the relevant equations at the each point. The medium can be discretized in several ways, including using meshes, cells, particles, abstract mathematical elements, or spectra. In each discretization method, a fine resolution must be taken around the shockwave to accurately resolve the shockwave features, either in space or, in the case of spectral methods, the number of approximation terms.c is the fastest fluid component across all grids or cells. With many spatial cells and a small timestep, the simulation of shockwaves can quickly become computationally expensive. Adaptive mesh refinement allows using varied cell sizes to include fine resolution cells only where needed and dynamic adjustment of cells as the simulation progresses Limiting the scope of discussion to grid- or cell-based methods, the fine resolution leads to a small timestep via the Courant-Friedrichs-Lewy (CFL) condition, which dictates the necessary timestep for the stability of a solution Meshless methods are a class of approaches that do not rely on a traditional form of spatial discretization for a problem. Unlike mesh-based methods, meshless methods have no fixed connection between discretization nodes that can move throughout the domain. Interactions are computed between neighboring nodes at each timestep. Smoothed Particle Hydrodynamics (SPH) is a meshless method developed by Gingold and Monaghan In a typical SPH simulation, the number of interactions per particle per timestep is higher than in grid-based methods. For a regular 2D mesh or particle distribution, SPH particles, on average, interact with 21 particles compared to 9 grid points used in a second-order mesh solver Various approaches are used to enhance grid-based methods for modeling shockwaves, including higher-order methods, reduced-order methods, and even predictive machine learning 22.1f for the cell at point i with a volume of ΔV. Derivative operators in the FVM can be converted into surface fluxes through the divergence theorem. The gradient operator can be expressed as:s iterates over each surface of a cell volume, In the Finite Volume Method (FVM), the domain is discretized into cells or volumes with fluid properties averaged for each enclosed volume. Differential equations for a given system are modeled through the approximation of fluxes across each volume boundary. The FVM employs a structured or unstructured mesh for discretizing problems ρ is the density, E is the total energy. E can be further broken down into internal energy e and kinetic energy:p and close the system of equations. In this investigation, the gamma-law equation of state is used:For compressible fluids, the Euler equations describe the conservation of mass, momentum, and energy. Written generally in conservative form without source terms, they appear as In one dimensional planar geometry, Equations 2.2x is tethered to a particle's size rather than the size of a mesh cell.Smoothed Particle Hydrodynamics is one of the most common meshless approaches to hydrodynamics. A collection of simulated particles is used to define the field variables and compute interactions needed to evolve the simulation in time. The meshless approach to SPH creates some key differences from mesh-based approaches. SPH must still abide by the CFL condition described in equation The implementation of boundary conditions in SPH varies significantly from grid-based methods and includes many unique challenges. Periodic and reflective boundaries can be implemented with ghost particles, while inlet and outlet boundaries require careful consideration. h is the characteristic length scale of the kernel, also termed the smoothing length. Functions describing fluid values can be approximated using the kernel function f is evaluated. Note that as j is an index referring to neighbors of a given particle i. The spatially discretized integration volume has been inserted using In SPH, the domain is discretized through discrete particles whose shape is described by a kernel function j is an index that refers to all particles that lie within the range of the kernel function In SPH, the Euler equations are discretized for each individual particle. Given the Lagrangian nature of SPH, it is helpful to construct the equations in terms of the material derivative. In one dimension, the density of each particle is given by 33.1The shock simulations were performed in python using two frameworks to implement a finite volume method and smoothed particle hydrodynamics, respectively. For the FVM implementation, the Pyro2 framework was used The standard compressible Pyro2 solver utilizes a two-dimensional NumPy array to store conservative mesh variables, including density, internal energy, and x- and y- momenta, and has built-in conversion functions for finding primitive variables: density, pressure, and x- and y- velocities. The python package Numba 3.2PySPH is an open-source python framework for implementing SPH methods PySPH contains custom data structures for particle arrays compatible with NumPy and accelerated through Cython The ADKE scheme is one of the two schemes investigated for one-dimensional test problems. Monaghan and Gingold The GSPH scheme utilizes a Riemann solver for accurate solutions to shock problems. Riemann solvers have been used extensively in grid-based methods for resolving shocks. The Godunov scheme uses the solution to the Riemann problem for every cell interface to find the numerical flux between each cell. The GSPH scheme incorporates the same principle but instead uses the solution to the Riemann problem for every particle pair 4SPH simulations are, in general, less efficient than mesh-based simulations because the number of particle-pair interactions that must be calculated is greater than the number of neighbors needed for each mesh cell calculation. In shock problems, a large number of particle interactions are computed for particles that are located well past the interaction range of the shockwave. The spatial resolution provided by these particles is unnecessary until the shockwave travels within range. By incorporating the SPH method as a type of subgrid modeling on a finite volume mesh, the SPH particles are only included around the regions of discontinuous fluid. Additionally, since the discontinuous regions around shocks are simulated with SPH, a coarser FVM grid can be used to achieve the same resolution as a finer FVM without SPH particles.SPH has previously been used in conjunction with other methods to realize the unique benefits of SPH without its disadvantages. A common application of hybrid SPH approaches is the modeling of fluid-structure interactions. SPH is very capable of modeling deformable or fracturing solids and, as a result, is typically used for structures in hybrid fluid-structure interaction simulations The steps used in the novel FVM-SPH algorithm are displayed in A timestep begins by advancing the FVM mesh forward one step in time. Pyro2 allows for an adaptive timestep size, but for simplicity in coupling with SPH, a fixed timestep is used in each problem. After every timestep, the FVM mesh is scanned for discontinuities by calculating the derivative of each variable and flagging regions with a derivative greater than a predetermined threshold. Two sets of zones are defined by the location of flagged discontinuous regions: an active particle zone, where SPH particles will be used to model the local fluid, and ghost particle zones, where SPH ghost particles are placed to serve as boundary particles for the active SPH particles.dx is the distance between mesh cells and n is the number of cells needed for the calculation of updated values for a single cell for the FVM solver used.The fluid values in the active particle zone are interpolated to the overlaying FVM mesh at every timestep using linear approximation and serve as boundary cells to the adjacent FVM cells. Similarly, the values of the FVM cells in the ghost particle regions are interpolated to the SPH ghost particles at every timestep. The boundary layers are set to a value greater than the interaction distance for a given cell or particle. The interaction distance Δ is defined as the distance at which h, particles are only injected near existing particles with a regular spacing proportional to h, defined at the initialization of the SPH simulation. SPH particles are also deleted in regions that no longer lie within ghost particle regions as the simulation advances.Once the SPH particle regions have been defined for a given timestep, SPH particles are injected where absent in flagged regions and tagged as ghost particles if they lie within the ghost particle regions. Since particle interaction is weighted by the smoothing length f at the location Extrapolating values between particles and the FVM mesh requires interpolating fluid values in the appropriate regions. When the buffer size, used to calculate the active particle and ghost particle regions in discontinuous areas, is larger than the interaction distance, linear interpolation is sufficient for accurate results. For a given ghost particle or cell, the value of a field h is held constant for ghost particles to avoid having to calculate h at every timestep. As a consequence, the spacing between the ghost particles and active particles must remain regular for the updated active particle values to be calculated with the appropriate boundary values. The ghost particles are repositioned at each timestep such that the spacing of particles adjacent to the active particles is regular before the FVM cell values are interpolated to the ghost particles.Special care must be taken in ghost particle regions to ensure the stability of the SPH simulation. The smoothing length 5The simulations were performed using Oregon State University College of Engineering's HPC platform Rogue in a serial configuration. The code was built using a conda virtual environment with all the respective python dependencies for Pyro2 and PySPH installed, allowing each framework to run independently or as elements of the hybrid code. For each test problem, the simulation is first performed using both Pyro2 and PySPH independently to establish a baseline timing comparison; then, the hybrid implementation is performed and compared.5.1The Sod problem was first developed in 1978 and involves a left/right discontinuity Simulations were performed in Pyro2 and PySPH for a range of resolutions. The results are shown in The results for the hybrid implementation are displayed in The upper plot in 5.2The strong shock test problem emulates the Sod shock tube problem but with a uniform density and a significantly larger pressure difference. The initial conditions are as follows: The results for various Pyro2 and PySPH resolutions are shown in The results of the hybrid shock simulation are shown in 5.3The Woodward-Collela blastwave is a problem designed to test the limits of a computational fluid dynamics code. The problem consists of two shock waves of different strengths originating on either side of a simulated domain and colliding and interacting in the center The results for various Pyro2 and PySPH resolutions are shown in The results of the hybrid shock simulation are shown in 5.4The hybrid algorithm flags discontinuities in the field variables using a sensitivity variable called the discontinuity threshold. The threshold value is a relative term that is used to partition the space with the goal of efficiently dividing the domain between the FVM mesh and SPH particles. For problems with stronger shocks, more of the domain will become dominated by regions with high field gradients, and more of the domain will be flagged for SPH treatment for a given threshold value. However, because the discretization size varies between problems, the threshold value is not directly correlated with the accuracy of the final solution in hybrid simulations.For each hybrid simulation, an appropriate threshold must be selected to balance the accuracy and efficiency. A low threshold value will result in more of the domain being flagged and populated with SPH particles, increasing the computational expense by favoring SPH over the computationally cheaper FVM mesh, particularly when a coarse mesh is used. A high threshold value will result in field gradients at the site of FVM-SPH boundaries, which can negatively impact the accuracy of the coupling scheme used, particularly for boundary SPH particles which are highly sensitive to the value and position of neighboring ghost particles.For a given problem, a threshold is selected by conducting a scan over a range of options and determining the optimal threshold for efficiency without reducing accuracy. A threshold of 3 was found to be optimal for the Sod shock tube problem, while thresholds of 2000 were used for the strong shock and Woodward-Colella problems. A range of thresholds was investigated in each case, and plots showing the partition of FVM and SPH active simulation are shown in The optimal threshold values typically correspond to the strength of the largest shock, and this can be used to estimate the threshold for similar problems. For example, the strength of the largest shock in the Woodward-Colella problem is the same as the strength of the shock in the strong shock problem, and so the same threshold was used and found to be approximately optimal in each case. In further investigations, a table of thresholds for a given shock strength or an empirical relationship can be used to streamline hybrid simulations. However, complex problems that include features such as colliding shocks or vacuums should be thoroughly investigated to determine the relationship between the threshold and the accuracy and efficiency.6The cost of coupling the two approaches together will lead to an increase in runtime unless each approach has advantages in different parts of the domain. The hybrid approach for the Sod problem leads to a longer runtime when compared with the FVM and SPH approaches alone since the FVM approach can easily model the problem. Even the SPH approach, while less efficient, is faster than the hybrid approach due to coupling overhead in the Sod problem. In the strong shock problem and Woodward-Colella blastwave, the advantages of each approach captured by the hybrid method outweigh the overhead of coupling the Pyro2 and PySPH simulation codes. We cannot conclude that coupling a more efficient, compiled FVM solver with SPH will produce better results than the FVM solver alone. Still, it does indicate that coupling the FVM and SPH while preserving accuracy and efficiency is possible.One natural advantage of implementing a hybrid method is that the approach allows for a form of multi-resolution modeling to be included between the two methods. Different orders of resolution can be used in the FVM and SPH methods meaning a coarser resolution can be used in parts of the domain. Multi-resolution modeling is common in hydrodynamics, with AMR being a dynamic form of a multi-resolution approach. While additional effort is needed to include multi-resolution modeling in a standard approach, the multi-resolution functionality is already built into the hybrid SPH method, as the interpolative coupling works for a range of different resolutions. If the resolution becomes too low, however, the size of boundary cells may inhibit the accurate and efficient simulation of the problem.A unique advantage of the hybrid approach is the Lagrangian characteristics of SPH are retained while reducing the total range of SPH particles. As the shockwaves move through the simulation, the SPH particles are swept along and clump up at the location of the shocks, providing a higher resolution at the shock front. In the strong shock problem, the SPH number density varies by a factor of 10 across the extremes in the domain, while in the Woodward-Colella blastwave, the number density varies by over 30. The high density around shocks allows for simulations with a low number of SPH particles globally to have surprisingly good resolution, as is seen in the 500-particle Woodward-Colella simulation, which only required 72 seconds of runtime. Through coupling FVM and SPH, the number of cells and particles to attain a high resolution can be minimized, leading to an increase in computational efficiency.An interesting feature of the SPH approach is that the simulation runtime doesn't scale with the resolution. One aspect of this behavior is likely due to the fixed computational costs of the simulation, but initialization of the problem until the first timestep begins only takes approximately 0.1 seconds in each case. A larger contributor is likely the Lagrangian nature of the method and the resulting clumps of particles around shocks being sizable regardless of the initial resolution. This effect is presumably responsible for some of the efficiency of the hybrid method as increasing the resolution of SPH used, and therefore the accuracy of the final result, only marginally increases computational cost.7We have developed a new shock-capturing method coupling the Finite Volume Method framework Pyro2 with Smoothed Particle Hydrodynamics framework PySPH and investigated its application to 1D shock problems. The method uses a coarse FVM mesh across the simulation domain, while SPH particles are used around the location of discontinuities. Active SPH particles in zones around discontinuities interpolate values to adjacent FVM cells at every timestep, with SPH ghost particles bordering the SPH active particles and drawing values from adjacent FVM cells every timestep. The SPH active zones are adjusted each timestep as the shock travels through the simulation with SPH particles added or deleted in newly activated or deactivated particle regions. The location of ghost particles is set to be spaced at a regular distance from active SPH particles to ensure proper boundary treatment.The hybrid approach shows potential in accurately and efficiently modeling strong shock problems. SPH schemes accurately resolve the shock waves, while the FVM grid limits the number of SPH particles needed across the domain. The hybrid implementation adds computational overhead, but the gains in efficiency outweigh the cost for the strong shock and Woodward-Colella blastwave problems. Furthermore, the coupling of FVM and SPH for shock problems allows for the future inclusion of SPH capabilities, such modeling complex geometries and fluid-structure interaction with large deformations or fracturing.The demonstrated advantage of the hybrid approach for strong shocks in one dimension is expected to increase in two dimensional problems, where the number of particles or cells is increased by the square of the resolution. The number of SPH particle interactions also increases significantly for each additional dimension, but coupling the approach to a coarse FVM for 2D shock problems may result in a significant reduction in baseline computational costs. The extension of the hybrid method to two dimensions will be presented in future work, along with the results for a number of two-dimensional test problems.Conner Myers: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Wrote the paper.Camille Palmer, Todd Palmer: Conceived and designed the experiments; Analyzed and interpreted the data.10.13039/100006234Sandia National Laboratories under contract number 2214652.The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Conner Myers reports financial support, article publishing charges, and travel were provided by


The integration of textile-based flexible sensors and electronic devices has accelerated the development of wearable textiles for posture monitoring. The complexity of the processes required to create a complete monitoring product is currently reflected in three main areas. The first is the sensor production process, which is complex. Second, the integration of the sensor into the garment requires gluing or stitching. Finally, the production of the base garment requires cutting and sewing. These processes deteriorate the user experience and hinder the commercial mass production of wearable textiles. In this paper, we knitted a one-piece seamless knitted vest (OSKV) utilizing the one-piece seamless knitting technique and positioned an embedded needle sensing zone (EHSZ) with good textile properties and electrical performance for monitoring human shoulder activity. The EHSZ was knitted together with the OSKV, eliminating the need for an integration process. The EHSZ exhibited good sensitivity (GF = 2.23), low hysteresis (0.29 s), a large stretch range (200%), and excellent stability (over 300 cycles), satisfying the requirement to capture a wide range of deformation signals caused by human shoulder movements. The OSKV described the common vest process structure without the stitching process. Furthermore, OSKV fulfilled the demand for seamless and trace-free monitoring while effortlessly and aesthetically satisfying the knitting efficiency of commercial garments. Wearable devices based on textile-based flexible sensors are regarded as promising materials for wearable electronics because they are lightweight , have loThere have been several studies on capacitive, resistive, and piezoelectric smart textiles that have demonstrated good performance in monitoring physiological information in the human body ,15,16. TIn recent years, the one-piece seamless knitting technique has demonstrated significant advantages in wearable textile electronics. The knitted fabric is formed by interlocking coils, which have good tensile recovery and can revert to their initial state after a large strain. The knitted flexible sensing fabric deforms in response to human limb movements, and the deformation variables are transformed into electrical or other readable signals that can be used for human posture monitoring ,34,35,36However, there are still certain challenges that prevent the further development of technology. Although the sensor zone can be embedded in commercial garments, it is challenging to achieve unibody formability in commercial garments because of the limited effective strain range of the sensor zone. To prevent the strain range of human activity from exceeding the effective strain range of the sensor zone, it is necessary to avoid pre-stretching of the sensor zone by wearing commercial garments. This further hinders the benefits of universal and seamless manufacturing of commercial garments, which impacts mass production and applications for multiple body types ,43,44,45In this paper, we have employed the process method of floating and loop formation on a weft-knitting circular machine to create a stretchable, comfortable, embedded hanger sensing zone (EHSZ) through yarn addition. This innovative design of EHSZ offers superior sensitivity (GF = 2.23), excellent stability (over 300 cycles), low hysteresis (0.29 s), and good sensitivity to strain measurement at a high stretching capacity of 200%. The combination of the one-piece seamless knitting technology is noteworthy because it allows for the seamless integration of EHSZ in a knitted vest with good aesthetics and comfort, as well as in a one-piece seamless knitted vest (OSKV) with good formability and commodity efficiency. Here, we have built a fully textile wearable health and shoulder movement monitoring system. This system uses the method of establishing a database and then examining the edit distance between two curves to achieve curve pairing. Then, based on the decision tree, the specific posture is identified. The monitor wears the OSKV and detects the limb movements of the human shoulder at different amplitudes by EHSZ, demonstrating good wearable comfort and accuracy.One benefit of the one-piece seamless knitting technique is that the sensor and the monitoring vest can be knitted in one piece, which enables the integration of embedded knitted sensors to be eliminated. This section demonstrates how this technique enables seamless knitting of the monitoring vest, improving comfort while reducing the production process and improving commercial properties.The one-piece seamless knitting technique was used to knit three of the more common weft knit vest styles from the base garment side. While the vest style “a” eliminates the side seams of a normal vest, the shoulder straps still need to be stitched. Furthermore, the disconnection of the shoulder straps makes integration of the sensor at the shoulder challenging and can impair sensor performance. Despite the elimination of the shoulder seam in vest styles b and c, stitching is still required at the shoulder strap attachment or on the side, which will affect the usability of the sensing area .To address the aforementioned technical problems, this paper presents a weft-knitted base vest for monitoring with a modified shoulder structure. As shown in To achieve the structural transformation of the shoulders, it is necessary to match reasonable functional zoning of the vest, design a suitable tissue structure, and choose the right yarn material. We created a structural, functional partitioning of the weft-knitted vests for monitoring purposes and flattened their 3D modeled partitioning into 2D structural template diagrams c, where We conducted experiments using six different yarn materials and shoulder structures and found that the transformation of the shoulder structure was dependent on the choice of shoulder structure and yarn material . We chosThe OSKV can be knitted with a seamlessly embedded knit EHSZ using the inlaid yarn guide technique, which not only eliminates the need for integration but also makes the OSKV comfortable to wear a. The seThe resistance of the highly elastic silver-plated conductive yarn increases with yarn length a. The opThe fabric was knitted on a seamless circular knitting machine, an SM8-TOP2 MP2 single cylinder jacquard knitting circular knitting machine  was used with a cylinder diameter of 15 inches, a needle count of 1344, a gauge of 28 stitches/cm, and 8 tracks a. After 2 soft silicone conductive wire. The other end of the conductive wire was wrapped around the conductive wire of the data collection system to create a closed series circuit. The dynamic resistance data collection system was equipped with PC desktop application software, which was a testing platform built on the tester’s computer. Compared to a multimeter, this software could display real-time resistance change waveforms. As shown in Two sides of the flexible sensing area were left with connectable floating threads. These floating threads were fixed by twisting them together with a 0.08 mThe OSKV is the pinnacle of excellence for the monitoring product and the sensing area since they are knitted in one piece, free of integration and sewing. The vest can be made without stitching due to the transformation of the shoulder structure. This facilitates the integration of EHSZ in the shoulder knit. The OSKV fully satisfies the need for seamless and seamless monitoring owing to the soft raw material and the knitted structure. EHSZ can be seamlessly integrated into any part of the OSKV to detect information about the body’s shoulder movements. Moreover, it permits a reduction in the production process of the monitored product, resulting in efficient production with lower costs.R is the corresponding resistance change of the strain sensor, R0 is the initial resistance in the unstretched state, ε is the strain in the stretching direction of the sensor.)As shown in As shown in R/R0 and the applied strain is evident. The response time to stimuli is crucial for the strain sensors to detect strains in real time. On the application of a small loading strain to the sensor and subsequently unloading at a fast rate, the loading and unloading durations of the sensor are observed to be 0.36 and 0.29 s, respectively  using the one-piece seamless knitting technique and positioned an embedded knitted hanger sensing zone (EHSZ) with good textile and electrical properties for the monitoring of human shoulder movement. The following conclusions were drawn: converting the shoulder straps of weft-knitted shaped vests from longitudinal to transverse knitting eliminates the shoulder seams commonly found in weft-knitted shaped vests and makes it easier to integrate sensors. The sensor in the hanging needle construction matches the performance of the sensor in use and enables effective monitoring compared to plain knit fabrics. Analyzing the Edit Distance on Real sequence of the resistance curve ensures precise posture recognition. It is anticipated that in the future, smart products such as EHSZ will be perfectly incorporated into our technological lives in a more comfortable and sensory-free way.We will conduct research from the following three perspectives. First, we will try to place the monitoring vest on individuals with different body types to observe the changes in strain resistance and examine the impact of body type on the data. Second, we will wash and dry the monitoring vest and immerse it in sweat to simulate wearing conditions on the monitoring data. Third, we will add additional sensing areas to other parts of the body and collect data on the shoulder movement posture in reference to specific shoulder rehabilitation or treatment actions. We will also conduct multiple measurements and establish a confusion matrix to examine the accuracy of the recognition system.


Hot-melt extrusion is increasingly applied in the pharmaceutical area as a continuous processing technology, used to design custom products by co-processing drugs together with functional excipients. In this context, the residence time and processing temperature during extrusion are critical process parameters for ensuring the highest product qualities, particularly of thermosensitive materials. Within this study, a novel strategy is proposed to predict the residence time distribution and melt temperature during pharmaceutical hot-melt extrusion processes based on experimental data. To do this, an autogenic extrusion mode without external heating and cooling was applied to process three polymers  at different specific feed loads, which were set by the screw speed and the throughput. The residence time distributions were modeled based on a two-compartment approach that couples the behavior of a pipe and a stirred tank. The throughput showed a substantial effect on the residence time, whereas the influence of the screw speed was minor. On the other hand, the melt temperatures during extrusion were mainly affected by the screw speed compared to the influence of the throughput. Finally, the compilation of model parameters for the residence time and the melt temperature within design spaces serve as the basis for an optimized prediction of pharmaceutical hot-melt extrusion processes. Hot melt extrusion was established as a common unit operation in pharmaceutical applications in the early 1970s ,3. In thCo-rotating twin screw extrusion is the most common technique in HME because of its favorable mixing capacity. Here, two intermeshing screws transport the material from a feeding port toward a die within an extrusion barrel. This continuous process is affected by numerous critical material attributes  as well as critical process parameters  . The intThere are numerous studies investigating the residence time of various materials in pharmaceutical hot melt extrusion ,11. GeneThe material or melt temperature is one key variable of the hot melt extrusion process since it determines the melt viscosity during processing as well as the solid-state properties of the final product . When prIn a previous investigation  the throThe aim of this study was to extend the theoretical framework from previous investigations, finding a mathematical model to describe the influence of throughput and screw speed on residence time and melt temperature. This novel approach of coupling the prediction of residence time and melt temperature in autogenic extrusion is highly relevant in pharmaceutical hot melt extrusion since these two process parameters are key factors for assessing drug dissolution in the polymer. Thus, it is possible to predict and propose optimized process conditions that enable the preparation of ASDs, while minimizing energy consumption and drug degradation.Three polymers commonly used in pharmaceutical hot melt extrusion were utilized in this study as model materials. Poly-vinylpyrrolidone-vinylacetate (PVPVA) , graft co-polymer Soluplus (SOL)  and basic butylated methacrylate copolymer (bBMA)  were selected  was used for dosing the powder material in the extruder. The extrusion experiments were carried out in a co-rotating twin screw extruder  containing modular screw elements with a 28.3 mm diameter and a length of 32 D . A heateThe screw and barrel design were similar to previous investigations . For allFor the residence time determination, the marker substance quinine-dihydrochloride  was utilized with a fraction of 16–23 mg per polymer mass flow of 1 kg/h. The marker was added as a Dirac-impulse through the hopper of the extruder, and the response signal was measured in the die with an inline UV-Vis-spectrophotometer  at 250 to 650 nm. This was performed in transmission with two probes  at an offset of 180°. The transmission, expressed as the ratio of transmitted light intensity to impinging light intensity, is converted to absorbance using the Lambert-Beer law.The rheological properties of the polymers were taken from the literature . To do tIn accordance with Carreau (Equation (1)), the dynamic viscosity , numerator) in relation to the theoretical transport capacity of the extruder (Equation (3), denominator). Thus, the specific feed load (SFL) is a function of the mass flow (for bBMA ), the scDifferent maximum SFL values were found for the three considered polymers, which was attributed to the differences in bulk density. The lowest value  , where tGenerally, higher SFL values lead to longer residence times, which is attributed to a higher barrel load resulting in a higher hold-up. Considering one specific SFL value, the horizontal alignment of the data points is related to the throughput increasing from left to right. Shorter residence times are found at the right since higher throughput through a confined volume leads to shorter residence times.In terms of the melt temperature, lower values are found at higher SFL, since less shear is applied to the material at lower screw speeds, causing less energy dissipation. For one SFL, the horizontal alignment of the data points also includes a change in screw speed, increasing from the left to the right. The increase in temperature can be attributed to an increased shear rate, resulting in higher energy dissipation.There are remarkable differences between the polymers in the melt temperature, which might be related to differing melt rheology as found previously . In thisPharmaceutical hot melt extrusion is usually a continuous process where multiple sub-processes are performed sequentially in a co-rotating twin screw extruder. Common residence-time models for hot melt extrusion distinguish between material conveying and mixing . In thisThis model comprises three parameters that describe the residence time distribution. The dead time  , are givThe quality of all three regression models is rather low, as indicated by the low coefficient of determination and coefficient of prediction values, which ideally should be close to one. The repeatability is fairly high at the center point. However, it might be different at other points in the design space, which could cause the invalidity of the model. Looking at the raw data, the data points tend to scatter at experiments that were performed at low throughputs within the entire dataset.The dead volume is only affected by the specific feed load, which is a measure for the use of the transport capacity of the extruder. The specific feed load also represents the barrel load. Therefore, higher SFL values lead to higher barrel loads (hold up), which results in a higher dead volume in the residence time model.3 for PVPVA, 597 kg/m3 for SOL and 339 kg/m3 for bBMA [The mixing volume depends on the used polymer: where PVPVA is the standard in this regression model, SOL is lowering and bBMA is increasing the mixing volume. In initial attempts, this behavior was correlated with the rheological properties of the individual polymers. This was not successful. However, a correlation was found for the bulk density of the polymer . There, the extruder shear stress was independent of the specific feed load looking at different polymers. This behavior was explained by differences in the polymer rheology and an inherent adjustment of the melt temperature to a corresponding melt viscosity at the die. In this study, the extruder shear stress is not constant but the same dependency to specific feed load was found for all three polymers. This contradiction between the studies can be solved by the higher SFL values used in the previous investigation. Apparently, there is a change in the extrusion regime at about SFL = 0.035 (1/SFL = 29), which might be indicated by the high scattering of the PVPVA data in this region as well.Lowering the specific feed load below a critical value by lowering the throughput leads to less volume flow as well as less shear in the die and thus to a higher melt viscosity in the die. According to Equation (11), the viscosity at the die is related to the screw speed rather than the shear rate so the shear stress of the extruder has to increase in order to accommodate the increased viscosity. Assuming a fixed processing volume in the extruder, lower feed rates lead to less filling of the barrel, resulting in a hyperbolic influence of the specific feed load to the applied shear stress. When exceeding a certain value of the specific feed load, the processing volume is completely filled resulting in a constant extruder shear stress.Based on these observations, the throughput and the screw speed can be transferred into a melt viscosity at the die using two material-independent parameters  and related to the maximum specific feed load. At these feed rates, the screw speed is too low to transport the material through the extruder. Moreover, there is a material-dependent upper limit for the throughput which was found to be 30 kg/h for PVPVA, 42 kg/h for SOL and 36 kg/h for PVPVA, related to the capacity of the powder feeder and the bulk properties of the polymer.90-t10) in seconds is provided as black numbers to describe the width of the residence time distribution.The grayscale in those diagrams encodes the melt temperature and residence time, which were taken from the models discussed before. The data points of the extrusion experiments are also given in the diagrams and coded in the same grayscale used for the model. The marked symbols (*) were taken from a previous study  and servThe melt temperatures differ between the polymers. The highest temperatures were seen for PVPVA and the lowest for bBMA. This is related to the individual melt rheology of the polymers. However, the temperature distribution within the design space is quite similar. Higher throughput and higher screw speed lead to higher melt temperatures. The screw speed increases the shear rate in the extruder, leading to higher energy dissipation and higher melt temperatures. The throughput, in turn, increases the hold-up (90-t10) and the 10% quantile led to similar values. Therefore, it is impossible to achieve high residence times and narrow size distributions as often desired just by varying throughput and screw speed. Overall, the residence times are rather short for dissolving a crystalline drug substance within the polymer melt [With respect to the residence time, the throughput dominated the process while the effect of screw speed was minor. Note that the grayscale uses a logarithmic transformation to cover the entire range. The width of the residence time distribution is correlated with the residence time itself since the span . These process conditions with respect to melt temperature and residence time deviate highly from the production scale. That is why different product properties can be expected.Pharmaceutical hot melt extrusion is an emerging but challenging manufacturing process due to its high number of process variables. In terms of amorphous solid dispersions, the material temperature and process time are considered to be critical process parameters, since the drug substance has to be dissolved in the polymer melt during manufacturing. In this work, these two critical process parameters are altered systematically by varying throughput and screw speed. Based on this, a predictive model of a previous study  was exte