GLOBAL SOLUTIONS TO A HYDRODYNAMIC MODEL FOR SEMICONDUCTORS WITH VELOCITY RELAXATION

In this paper,we apply the method given in the paper“Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors”(Mathematische Annalen,2022,382:1031–1046)to study the Cauchy problem for a one dimensional inhomogeneous hydrodynamic model of two-carrier types for semiconductors with the velocity relaxation.

Constitutive modeling and springback prediction of stress relaxation age forming of pre-deformed 2219 aluminum alloy

Stress relaxation ageing behavior of pre-deformed AA2219 is studied through stress relaxation age experiments and finite element(FE) simulation. The results show that the stress can promote the process of ageing precipitation, and shorten the time to reach the peak strength. Meanwhile,the residual stress and yield strength increase along with the increase in the initial stress. Based on microstructure evolution and ageing strengthening theory,a unified constitutive model is established and incorporated into the FE simulation model through a user subroutine. It is found that the relative error of the radius is 3.6% compared with the experimental result and the springback is 16.8%. This indicates that the proposed stress relaxation ageing constitutive model provides a good prediction on the springback of such stiffened panel during its ageing process.

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.

EXISTENCE OF GLOBAL SMOOTH SOLUTION TO INITIAL BOUNDARY VALUE PROBLEM FOR A VISCOELASTIC MODEL WITH RELAXATION

This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the C^1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the 'maximum principle' of first-order quasilinear hyperbolic system.

Calorimetric Studies on Enthalpy Relaxation in Maltitol Glass Transition Based on Phenomenological Models

To investigate the enthalpy relaxation behavior of maltitol glass system,differential scanning calorimetry（DSC） was used to obtain the specific heat capacity[C p（T）] near the glass transition temperature（T g） at different cooling rates ranged between 1 and 20 K/min.Three phenomenological models of enthalpy relaxation,ToolNarayanaswamy-Moynihan（TNM） model,Adam-Gibbs-Vogel（AGV） model and Gómez Ribelles（GR） model,were used to simulate the experimental data.The models＇ parameters were obtained via a curve-fitting method.The results indicate that TNM and AGV models gave the almost identical prediction powers and can reproduce the curves of experimental C p（T） very well.However,the prediction power of GR model evolved from configurational entropy approach is not so good as those of TNM and AGV models.In particular,the metastable limit state parameter（δ） introduced by Gómez Ribelles has insignificant effect on the enthalpy relaxation of the small molecular hydrogen-bonding glass system.

Transverse relaxation characteristic and stress relaxation model considering molecular chains of HTPB coating based on pre-strained thermal aging

In order to accurately describe the transverse relaxation characteristic and stress relaxation modulus of HTPB coating during pre-strain thermal aging process,a one month thermal aging test was carried out at70C with pre-strain of 0%,3%,6%and 9%,respectively.The low-field1 H NMR and stress relaxation modulus tests were carried out for HTPB coating at different aging stages.The stress relaxation model considering the molecular chains was proposed according to the changes of crosslinking chain and dangling chain of HTPB coating during pre-strain aging.The results showed that with the increase of aging time,the decay rate of transverse relaxation curve became faster,the transverse relaxation time decreased,the value of combined parameter q Mrl increased,the proportion of crosslinking chain decreased,while the proportion of dangling chain increased.Moreover,the stress relaxation modulus increased,the crosslinking network structure of HTPB coating became denser and the degree of crosslinking increased.At the initial aging stage,the pre-strain will destroy the crosslinking network structure of HTPB coating to a certain extent.With the increase of aging time,the effect of pre-strain will gradually weaken and the influence of aging on materials will gradually increase.The correlations between the stress relaxation model considering the molecular chains and the test results were more than 0.9950,which can accurately describe the stress relaxation modulus of HTPB coating during the pre-strain thermal aging process.

A numerical study of the South China Sea Warm Current during winter monsoon relaxation

Using a Finite-Volume Community Ocean Model, we investigated the dynamic mechanism of the South China Sea Warm Current(SCSWC) in the northern South China Sea(NSCS) during winter monsoon relaxation. The model reproduces the mean surface circulation of the NSCS during winter, while model-simulated subtidal currents generally capture its current pattern. The model shows that the current over the continental shelf is generally southwestward, under a strong winter monsoon condition, but a northeastward counter-wind current usually develops between 50-and 100-m isobaths, when the monsoon relaxes. Model experiments, focusing on the wind relaxation process, show that sea level is elevated in the northwestern South China Sea(SCS), related to the persistent northeasterly monsoon. Following wind relaxation, a high sea level band builds up along the mid-shelf, and a northeastward current develops, having an obvious vertical barotropic structure. Momentum balance analysis indicates that an along-shelf pressure gradient provides the initial driving force for the SCSWC during the first few days following wind relaxation. The SCSWC subsequently reaches a steady quasi-geostrophic balance in the cross-shelf direction, mainly linked to sea level adjustment over the shelf. Lagrangian particle tracking experiments show that both the southwestward coastal current and slope current contribute to the northeastward movement of the SCSWC during winter monsoon relaxation.

Stress relaxation analysis of single chondrocytes using porohyperelastic model based on AFM experiments

Based on atomic force microscopy technique, we found that the chon- drocytes exhibits stress relaxation behavior. We explored the mechanism of this stress relaxation behavior and concluded that the intracellular fluid exuding out from the cells during deformation plays the most important role in the stress relax- ation. We applied the inverse finite element analysis technique to determine nec- essary material parameters for porohyperelastic （PHE） model to simulate stress relaxation behavior as this model is proven capable of capturing the non-linear behavior and the fluid-solid interaction during the stress relaxation of the single chondrocytes. It is observed that PHE model can precisely capture the stress re- laxation behavior of single chondrocytes and would be a suitable model for cell biomechanics.

A new linearly-combined bi-exponential model for kinetic analysis of the isometric relaxation process of Bufo gastrocnemius under electric stimulation in vitro

There was a slow-relaxing tail of skeletal muscles in vitro upon the inhibition of Ca2+-pump by cyclopiazonic acid (CPA). Herein, a new linearly-combined bi-exponential model to resolve this slow-relaxing tail from the fast-relaxing phase was investigated for kinetic analysis of the isometric relaxation process of Bufo gastrocnemius in vitro, in comparison to the single exponential model and the classical bi-exponential model. During repetitive stimulations at a 2-s interval by square pulses of a 2-ms duration at 12 V direct currency (DC), the isometric tension of Bufo gastrocnemius was recorded at 100 Hz. The relaxation curve with tensions falling from 90% of the peak to the 15th datum before next stimulation was analyzed by three exponential models using a program in MATLAB 6.5. Both the goodness of fit and the distribution of the residuals for the best fitting sup- ported the comparable validity of this new bi-exponential model for kinetic analysis of the relaxation process of the control muscles. After CPA treatment, however, this new bi-exponential model showed an obvious statistical superiority for kinetic analysis of the muscle relaxation process, and it gave the estimated rest tension consistent to that by experimentation, whereas both the classical bi-exponential model and the single exponential model gave biased rest tensions. Moreover, after the treatment of muscles by CPA, both the single exponential model and the classical bi-exponential model yielded lowered relaxation rates, nevertheless, this new bi-exponential model had relaxation rates of negligible changes except much higher rest tensions. These results suggest that this novel linearly-combined bi-exponential model is desirable for kinetic analysis of the relaxation process of muscles with altered Ca2+-pumping activity.

On the validity of the Boltzmann–BGK model through relaxation evaluation

The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.

Coupling model for calculating prestress loss caused by relaxation loss,shrinkage,and creep of concrete

The calculation model for the relaxation loss of concrete mentioned in the Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts(JTG D62—2004) was modified according to experimental data. Time-varying relaxation loss was considered in the new model. Moreover, prestressed reinforcement with varying lengths(caused by the shrinkage and creep of concrete) might influence the final values and the time-varying function of the forecast relaxation loss. Hence, the effects of concrete shrinkage and creep were considered when calculating prestress loss, which reflected the coupling relation between these effects and relaxation loss in concrete. Hence, the forecast relaxation loss of prestressed reinforcement under the effects of different initial stress levels at any time point can be calculated using the modified model. To simplify the calculation, the integral expression of the model can be changed into an algebraic equation. The accuracy of the result is related to the division of the periods within the ending time of deriving the final value of the relaxation loss of prestressed reinforcement. When the time division is reasonable, result accuracy is high. The modified model works excellently according to the comparison of the test results. The calculation result of the modified model mainly reflects the prestress loss values of prestressed reinforcement at each time point, which confirms that adopting the finding in practical applications is reasonable.

Continuous Iteratively Reweighted Least Squares Algorithm for Solving Linear Models by Convex Relaxation

In this paper, we present continuous iteratively reweighted least squares algorithm (CIRLS) for solving the linear models problem by convex relaxation, and prove the convergence of this algorithm. Under some conditions, we give an error bound for the algorithm. In addition, the numerical result shows the efficiency of the algorithm.

AN IMPROVED MODEL FOR COMPUTING SOLUTION DYNAMICS OF NATURAL PRODUCTS WITH ^(13)C NUCLEAR MAGNETIC RELAXATION

The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rates of ponicidin are computed with this model from ~C relaxation parameters.

Relaxation-rate formula for the entropic lattice Boltzmann model

A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives full consideration to the consistency with hydrodynamics. The relaxation rate calculated with the formula effectively characterizes the drastic changes of the flow fields. By using this formula, the computational cost of the ELBM is significantly reduced and the model now can be efficiently used for a broad range of applications including high Reynolds number flows.

Stress Relaxation of a Paper Sheet under Cyclic Load: An Experimental and Theoretical Model

Mechanical experiments have been performed to study the dynamic stress relaxation of a paper sheet material mainly used in food packaging industry. The material was cyclically tensile-loaded with a strain range between 2.4% and 4%. The time period for each cycle was 400 seconds. It was found that stress will decrease when the number of cycles increases in the case of upper load and vice versa in the case of lower load. At the same time, the stress to strain curves followed the same pattern as the one from the previous cycle. The stress relaxation behavior of each cycle has been analyzed and the dynamic relaxation modulus was derived. An improved model is proposed to describe the dynamic relaxation behavior of the paper sheet. This model shows a very good fit to the experimental results and trends of prediction are observed. Furthermore, the physical description of this model and the variation by the cycles is discussed.

Kagome Project:Physical and Numerical Modeling Comparison for a Post-formed Elastic Gridshell

An elastic gridshell is an efficient constructive typology for crossing large spans with little material.A flat elastic grid is built before buckling the structure into shape,in active and post-formed bending.The design and structural analysis of such a structure requires a stage of form finding that can mainly be done:(1)With a physical model:either by a suspended net method,or an active bending model;(2)With a numerical model performed by dynamic relaxation.All these solutions have various biases and assumptions that make them reflect more or less the reality.These three methods have been applied by Happold and Liddell[1]during the design of the Frei Otto’s Mannheim Gridshell which has allowed us to compare the results,and to highlight the significant differences between digital and physical models.Based on our own algorithm called ELASTICA[2],our study focuses on:(1)Comparing the results of the ELASTICA’s numerical models to load tests on physical models;(2)The identification of the various factors that can influence the results and explain the observed differences,some of which are then studied;(3)Applying the results to build a full-scale interlaced lattice elastic gridshell based on the Japanese Kagome pattern.

Correlation of Cooperatively Localized Rearrangement on the ＂Fluidized Domain＂ of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes （I）： A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp

Based on the structure of glass （or liquid） polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain” has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free en-ergy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitu- tive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush-Williams-Watts （K-W-W） stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established.

Image Relaxation Matching Based on Feature Points for DSM Generation

In photogrammetry and remote sensing, image matching is a basic and crucial process for automatic DEM generation. In this paper we presented a image relaxation matching method based on feature points. This method can be considered as an extention of regular grid point based matching. It avoids the shortcome of grid point based matching. For example, with this method, we can avoid low or even no texture area where errors frequently appear in cross correlaton matching. In the mean while, it makes full use of some mature techniques such as probability relaxation, image pyramid and the like which have already been successfully used in grid point matching process. Application of the technique to DEM generaton in different regions proved that it is more reasonable and reliable.

Viscoelastic relaxation of the upper mantle and afterslip following the 2014 M_(W)8.1 Iquique earthquake

An improved understanding of postseismic crustal deformation following large subduction earthquakes may help to better understand the rheological properties of upper mantle and the slip behavior of subduction interface.Here we construct a three-dimensional viscoelastic finite element model to study the postseismic deformation of the 2014 M_(W)8.1 Iquique,Chile earthquake.Elastic units in the model include the subducting slab,continental and oceanic lithospheres.Rheological units include the mantle wedge,the oceanic asthenosphere and upper mantle.We use a 2 km thick weak shear zone attached to the subduction fault to simulate the time-dependent stress-driven afterslip.The viscoelastic relaxation in the rheological units is represented by the Burgers rheology.We carry out grid-searches on the shear zone viscosity,thickness and viscosity of the asthenosphere,and they are determined to be 10^(17)Pa s,110 km and 2×10^(18)Pa s,respectively.The stress-driven afterlsip within the first two years is up to~47 cm and becomes negligible after two years(no more than 5 cm/yr).Our results suggest that a thin,low-viscosity oceanic asthenosphere together with a weak shear zone attached to the fault are required to better reproduce the observed postseismic deformation.

Intrinsic transverse relaxation mechanisms of polarized alkali atoms enclosed in radio-frequency magnetometer cell

The intrinsic transverse relaxation mechanisms of polarized alkali atoms enclosed in the radio-frequency magnetometer cell are investigated.The intrinsic transverse relaxation rate of cesium atoms as a function of cell temperature is obtained.The absorption of alkali atoms by the glass wall and the reservoir effect are the main error factors which contribute to the disagreements between theory and experiments.A modified relaxation model is presented, in which both the absorption of alkali atoms by the glass wall and the reservoir effect are included.This study provides a more accurate description of the intrinsic transverse relaxation mechanisms of polarized alkali atoms, and enlightens the optimization of the cell design.