Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Enhanced Metastatic Potential in a 3D Tissue Scaffold toward a Comprehensive in Vitro Model for Breast Cancer Metastasis

Metastasis is clinically the most challenging and lethal aspect of breast cancer. While animal-based xenograft models are expensive and time-consuming, conventional two-dimensional (2D) cell culture systems fail to mimic in vivo signaling. In this study we have developed a three-dimensional (3D) scaffold system that better mimics the topography and mechanical properties of the breast tumor, thus recreating the tumor microenvironment in vitro to study breast cancer metastasis. Porous poly(e-caprolactone) (PCL) scaffolds of modulus 7.0 +/- 0.5 kPa, comparable to that of breast tumor tissue were fabricated, on which MDA-MB-231 cells proliferated forming tumoroids. A comparative gene expression analysis revealed that cells growing in the scaffolds expressed increased levels of genes implicated in the three major events of metastasis, viz., initiation, progression, and the site-specific colonization compared to cells grown in conventional 2D tissue culture polystyrene (TCPS) dishes. The cells cultured in scaffolds showed increased invasiveness and sphere efficiency in vitro and increased lung metastasis in vivo. A global gene expression analysis revealed a significant increase in the expression of genes involved in cell cell and cell matrix interactions and tissue remodeling, cancer inflammation, and the PI3K/Akt, Wnt, NF-kappaB, and HIFI signaling pathways all of which are implicated in metastasis. Thus, culturing breast cancer cells in 3D scaffolds that mimic the in vivo tumor-like microenvironment enhances their metastatic potential. This system could serve as a comprehensive in vitro model to investigate the manifold mechanisms of breast cancer metastasis.

Detection of quantum well induced single degenerate-transition-dipoles in ZnO nanorods

Quantifying and characterising atomic defects in nanocrystals is difficult and low-throughput using the existing methods such as high resolution transmission electron microscopy (HRTEM). In this article, using a defocused wide-field optical imaging technique, we demonstrate that a single ultrahigh-piezoelectric ZnO nanorod contains a single defect site. We model the observed dipole-emission patterns from optical imaging with a multi-dimensional dipole and find that the experimentally observed dipole pattern and model-calculated patterns are in excellent agreement. This agreement suggests the presence of vertically oriented degenerate-transition-dipoles in vertically aligned ZnO nanorods. The HRTEM of the ZnO nanorod shows the presence of a stacking fault, which generates a localised quantum well induced degenerate-transition-dipole. Finally, we elucidate that defocused wide-field imaging can be widely used to characterise defects in nanomaterials to answer many difficult questions concerning the performance of low-dimensional devices, such as in energy harvesting, advanced metal-oxide-semiconductor storage, and nanoelectromechanical and nanophotonic devices.

Investigations on the physical origin of lateral photovoltage in PbS-colloidal quantum dot/Si heterojunctions

Restricted area heterojunctions, an array of lead sulfide colloidal quantum dots (PbS-CQDs) and crystalline silicon, are studied with a non-destructive remote contact light beam induced current (RC-LBIC) technique. As well as getting good quality active area images we observed an anomalous unipolar signal response for the PbS-CQD/n-Si devices and a conventionally expected bipolar signal profile for the PbS-CQD/p-Si devices. Interestingly, our simulation results consistently yielded a unipolar and bipolar nature in the signals related to the PbSCQD/n-Si and PbS-CQD/p-Si heterostructures, respectively. In order to explain the physical mechanism involved in the unipolar signal response of the PbS-CQD/n-Si devices, we propose a model based on the band alignment in the heterojunctions, in addition to the distribution of photo-induced excess majority carriers across the junction. Given that the RC-LBIC technique is well suited to this context, the presence of these two distinct mechanisms (the bipolar and unipolar nature of the signals) needs to be considered in order to have a better interpretation of the data in the characterization of an array of homo/heterojunctions.

An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites

A three-phase piezoelectric cylinder model is proposed and an exact solution is obtained for the model under a farfield antiplane mechanical load and a far-field inplane electrical load. The three-phase model can serve as a fiber/interphase layer/matrix model, in terms of which a lot of interesting mechanical and electrical coupling phenomena induced by the interphase layer are revealed. It is found that much more serious stress and electrical field concentrations occur in the model with the interphase layer than those without any interphase layer. The three-phase model can also serve as a fiber/matrix/composite model, in terms of which a generalized self-consistent approach is developed for predicting the effective electroelastic moduli of piezoelectric composites. Numerical examples are given and discussed in detail.

Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

Mechanical effects of the self-organization of dislocations and related critical characteristics

The effects of the dislocation pattern formed due to the self-organization of the dislocations in crystals on the macroscopic hardening and dynamic internal friction (DIF) during deformation are studied. The classic dislocation models for the hardening and DIF corresponding to the homogeneous dislocation configuration are extended to the case for the non-homogeneous one. In addition, using the result of dislocation patterning deduced from the non-linear dlislocation dynamics model for single slip, the correlation between the dislocation pattern and hardening as well as DIF is obtained. It is shown that in the case of the tension with a constant strain rate, the bifurcation point of dislocation patterning corresponds to the turning point in the stress versus strain and DIF versus strain curves. This result along with the critical characteristics of the macroscopic behavior near the bifurcation point is microscopically and macroscopically in agreement with the experimental findings on mono-crystalline pure aluminum at temperatures around 0.5T(m). The present study suggests that measuring the DIF would be a sensitive and useful mechanical means in order to study the critical phenomenon of materials during deformation.

Electromechanical Model of RF MEMS Switches

With the recent rapid growth of Radio Frequency Micro-Electro-Mechanical Systems (RF MEMS) switches, there has developed an emergent requirement for more accurate theoretical models to predict their electromechanical behaviors. Many parameters exist in the analysis of the behavior of the switch, and it is inconvenient for further study. In this paper, an improved model is introduced, considering simultaneously axial stress, residual stress, and fringing-field effect of the fixed-fixed bridge structure. To avoid any unnecessary repetitive model tests and numerical simulation for RF MEMS switches, some dimensionless numbers are derived by making governing equation dimensionless. The electromechanical behavior of the fixed-fixed bridge structure of RF MEMS switches is totally determined by these dimensionless numbers.

Stochastic Structural Model of Rock and Soil Aggregates by Continuum-Based Discrete Element Method

This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.

A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response. © 2005 Elsevier Ltd. All rights reserved.

A Thermodynamic Constitutive Model for Stress Induced Phase Transformation in Shape Memory Alloys

In this paper a thermodynamic constitutive model is developed for stress induced phase transformation in single crystalline and polycrystalline shape memory alloys (SMAs). Volume fractions of different martensite variants are chosen as internal variables to describe the evolution of microstructure state in the material. This model is then used in prediction the transformation behavior of a SMA (Cu-Al-Zn-Mn) under complex thermomechanical load (including complete and incomplete transformation in mechanical cycling, and proportional/non-proportional loading). (C) 2002 Elsevier Science Ltd. All rights reserved.

Simulations of Mechanical Behavior of Polycrystalline Copper with Nano-Twins

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.

Determination Ofinterfacial Mechanical Parameters For An Al/Epoxy/Al2O3 System Byusing Peel Test Simulations

Peel test measurements and simulations of the interfacial mechanical parameters for the Al/Epoxy/Al2O3 system are performed in the present investigation. A series of Al film thicknesses between 20 and 250 microns and three peel angles of 90, 135 and 180 degrees are considered. Two types of epoxy adhesives are adopted to obtain both strong and weak interface adhesions. A finite element model with cohesive zone elements is used to identify the interfacial parameters and simulate the peel test process. By simulating and recording normal stress near the crack tip, the separation strength is obtained. Furthermore, the cohesive energy is identified by comparing the simulated steady-state peel force and the experimental result. It is found from the research that both the cohesive energy and the separation strength can be taken as the intrinsic interfacial parameters which are dependent on the thickness of the adhesive layer and independent of the film thickness and peel angle.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Basic Mechanical Behaviors And Mechanics Of Shear Banding In Bmgs

In this paper, some basic mechanical behaviors of bulk metallic glasses (BMGs) were discussed. It can be found from the discussions that the mechanical behaviors of BMGs are mainly due to the formation and operation of shear bands in BMGs. Furthermore, the relevant mechanics of shear banding were investigated in the paper. The theoretical analysis of deformation coupling thermal softening and free volume creation softening demonstrates that the free volume creation and thermal softening can jointly promote the formation of shear bands in BMGs, and the observed post mortem. shear band width looks more like that governed by free volume creation. (C) 2007 Elsevier Ltd. All rights reserved.