Elasticity and melting of vortex crystals in anisotropic superconductors: Beyond the continuum regime.

The elastic moduli of vortex crystals in anisotropic superconductors are frequently involved in the investigation of their phase diagram and transport properties. We provide a detailed analysis of the harmonic eigenvalues (normal modes) of the vortex lattice for general values of the magnetic field strength, going beyond the elastic continuum regime. The detailed behavior of these wave-vector-dependent eigenvalues within the Brillouin zone (BZ), is compared with several frequently used approximations that we also recalculate. Throughout the BZ, transverse modes are less costly than their longitudinal counterparts, and there is an angular dependence which becomes more marked close to the zone boundary. Based on these results, we propose an analytic correction to the nonlocal continuum formulas which fits quite well the numerical behavior of the eigenvalues in the London regime. We use this approximate expression to calculate thermal fluctuations and the full melting line (according to Lindeman's criterion) for various values of the anisotropy parameter.

Anisotropic fluid with SU(2) type structure in general relativity: A model of localized matter

A model of anisotropic fluid with three perfect fluid components in interaction is studied. Each fluid component obeys the stiff matter equation of state and is irrotational. The interaction is chosen to reproduce an integrable system of equations similar to the one associated to self-dual SU(2) gauge fields. An extension of the BelinskyZakharov version of the inverse scattering transform is presented and used to find soliton solutions to the coupled Einstein equations. A particular class of solutions that can be interpreted as lumps of matter propagating in empty space-time is examined.

Patient-specific anisotropic model of human trunk based on MR data

There are many ways to generate geometrical models for numerical simulation, and most of them start with a segmentation step to extract the boundaries of the regions of interest. This paper presents an algorithm to generate a patient-specific three-dimensional geometric model, based on a tetrahedral mesh, without an initial extraction of contours from the volumetric data. Using the information directly available in the data, such as gray levels, we built a metric to drive a mesh adaptation process. The metric is used to specify the size and orientation of the tetrahedral elements everywhere in the mesh. Our method, which produces anisotropic meshes, gives good results with synthetic and real MRI data. The resulting model quality has been evaluated qualitatively and quantitatively by comparing it with an analytical solution and with a segmentation made by an expert. Results show that our method gives, in 90% of the cases, as good or better meshes as a similar isotropic method, based on the accuracy of the volume reconstruction for a given mesh size. Moreover, a comparison of the Hausdorff distances between adapted meshes of both methods and ground-truth volumes shows that our method decreases reconstruction errors faster. Copyright © 2015 John Wiley & Sons, Ltd.

Elasticity and melting of vortex crystals in anisotropic superconductors: Beyond the continuum regime.

The elastic moduli of vortex crystals in anisotropic superconductors are frequently involved in the investigation of their phase diagram and transport properties. We provide a detailed analysis of the harmonic eigenvalues (normal modes) of the vortex lattice for general values of the magnetic field strength, going beyond the elastic continuum regime. The detailed behavior of these wave-vector-dependent eigenvalues within the Brillouin zone (BZ), is compared with several frequently used approximations that we also recalculate. Throughout the BZ, transverse modes are less costly than their longitudinal counterparts, and there is an angular dependence which becomes more marked close to the zone boundary. Based on these results, we propose an analytic correction to the nonlocal continuum formulas which fits quite well the numerical behavior of the eigenvalues in the London regime. We use this approximate expression to calculate thermal fluctuations and the full melting line (according to Lindeman's criterion) for various values of the anisotropy parameter.

Properties of Anisotropic Superconductors in SR Model

The present thesis deals with the theoretical investigations on the effect of anisotropy on various properties of magnetically doped superconductors described by fihiba — Rusinov model.Chapter 1 is introductory. It contains a brief account of the current status of theory of superconductivity. In’ chapter 2 we give the formulation of the problem. Chapter 2.1 gives the BCS theory. The effect of magnetic impurities in superconductors as described by A8 theory is given in chapter 2.2A and that described by SR model is discussed in chapter 2.28. Chapter 2.2c deals with Kondo effect. In chapter 2.3 the anisotropy problem is reviewed. Our calculations, results and discussions are given in chapter 3. Chapter 3.1 deals with Josephson tunnel effect. In chapter 3.2 the thermodynamic critical field H62 is described. Chtpter 3.3 deals with the density of states. The ultrasonic attenuation coefficient and ufitlear spin relaxation are given in chapter 3.4 and 3.5 respectively. In chapter 3.6 we give the upper critical field calculations and chapter 3.7 deals with the response function. The Kondo effect is given in chapter 3.8. In chapter 4 we give the sumary of our results

A continuum receptor model of hepatic lipoprotein metabolism

A mathematical model describing the uptake of low density lipoprotein (LDL) and very low density lipoprotein (VLDL) particles by a single hepatocyte cell is formulated and solved. The model includes a description of the dynamic change in receptor density on the surface of the cell due to the binding and dissociation of the lipoprotein particles, the subsequent internalisation of bound particles, receptors and unbound receptors, the recycling of receptors to the cell surface, cholesterol dependent de novo receptor formation by the cell and the effect that particle uptake has on the cell's overall cholesterol content. The effect that blocking access to LDL receptors by VLDL, or internalisation of VLDL particles containing different amounts of apolipoprotein E (we will refer to these particles as VLDL-2 and VLDL-3) has on LDL uptake is explored. By comparison with experimental data we find that measures of cell cholesterol content are important in differentiating between the mechanisms by which VLDL is thought to inhibit LDL uptake. We extend our work to show that in the presence of both types of VLDL particle (VLDL-2 and VLDL-3), measuring relative LDL uptake does not allow differentiation between the results of blocking and internalisation of each VLDL particle to be made. Instead by considering the intracellular cholesterol content it is found that internalisation of VLDL-2 and VLDL-3 leads to the highest intracellular cholesterol concentration. A sensitivity analysis of the model reveals that binding, unbinding and internalisation rates, the fraction of receptors recycled and the rate at which the cholesterol dependent free receptors are created by the cell have important implications for the overall uptake dynamics of either VLDL or LDL particles and subsequent intracellular cholesterol concentration. (C) 2008 Elsevier Ltd. All rights reserved.

Impact of a new anisotropic rheology on simulations of Arctic sea ice

new rheology that explicitly accounts for the subcontinuum anisotropy of the sea ice cover is implemented into the Los Alamos sea ice model. This is in contrast to all models of sea ice included in global circulation models that use an isotropic rheology. The model contains one new prognostic variable, the local structure tensor, which quantifies the degree of anisotropy of the sea ice, and two parameters that set the time scale of the evolution of this tensor. The anisotropic rheology provides a subcontinuum description of the mechanical behavior of sea ice and accounts for a continuum scale stress with large shear to compression ratio and tensile stress component. Results over the Arctic of a stand-alone version of the model are presented and anisotropic model sensitivity runs are compared with a reference elasto-visco-plastic simulation. Under realistic forcing sea ice quickly becomes highly anisotropic over large length scales, as is observed from satellite imagery. The influence of the new rheology on the state and dynamics of the sea ice cover is discussed. Our reference anisotropic run reveals that the new rheology leads to a substantial change of the spatial distribution of ice thickness and ice drift relative to the reference standard visco-plastic isotropic run, with ice thickness regionally increased by more than 1 m, and ice speed reduced by up to 50%.

Solvent effects on the electronic absorption spectrum of camphor using continuum, discrete or explicit approaches

We address the effect of solvation on the lowest electronic excitation energy of camphor. The solvents considered represent a large variation in-solvent polarity. We consider three conceptually different ways of accounting for the solvent using either an implicit, a discrete or an explicit solvation model. The solvatochromic shifts in polar solvents are found to be in good agreement with the experimental data for all three solvent models. However, both the implicit and discrete solvation models are less successful in predicting solvatochromic shifts for solvents of low polarity. The results presented suggest the importance of using explicit solvent molecules in the case of nonpolar solvents. (C) 2009 Elsevier B.V. All rights reserved.

Integrable anisotropic spin-ladder model

We present an integrable spin-ladder model, which possesses a free parameter besides the rung coupling J. Wang's system based on the SU(4) symmetry can be obtained as a special case. The model is exactly solvable by means of the Bethe ansatz method. We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram. Finally, we show that the model is a special case of a more general Hamiltonian with three free parameters.

Layered superconductivity models at the London limit and their continuum properties

We write the London limit of the Lawrence Doniach free energy in terms of the local magnetic field and of the average supercurrent over the interplane distance. Starting from this formulation we study a model where the supercurrent at the buffer layers is obtained from the superconducting sheets by a Taylor expansion. The continuum limit of this model gives corrections to the anisotropic London theory due to the layered structure.

A Monte Carlo study of the anisotropic N=3 Ashkin-Teller model

The phase diagram of an asymmetric N = 3 Ashkin-Teller model is obtained by a numerical analysis which combines Monte Carlo renormalization group and reweighting techniques. Present results reveal several differences with those obtained by mean-field calculations and a Hamiltonian approach. In particular, we found Ising critical exponents along a line where Goldschmidt has located the Kosterlitz-Thouless multicritical point. On the other hand, we did find nonuniversal exponents along another transition line. Symmetry breaking in this case is very similar to the N = 2 case, since the symmetries associated to only two of the Ising variables are broken. However, for large values of the coupling constant ratio XW = W/K, when the only broken symmetry is of a hidden variable, we detected first-order phase transitions giving evidence supporting the existence of a multicritical point, as suggested by Goldschmidt, but in a different region of the phase diagram. © 2002 Elsevier Science B.V. All rights reserved.

Development of a continuum mechanics model of passive skeletal muscle

Skeletal muscle force evaluation is difficult to implement in a clinical setting. Muscle force is typically assessed through either manual muscle testing, isokinetic/isometric dynamometry, or electromyography (EMG). Manual muscle testing is a subjective evaluation of a patient’s ability to move voluntarily against gravity and to resist force applied by an examiner. Muscle testing using dynamometers adds accuracy by quantifying functional mechanical output of a limb. However, like manual muscle testing, dynamometry only provides estimates of the joint moment. EMG quantifies neuromuscular activation signals of individual muscles, and is used to infer muscle function. Despite the abundance of work performed to determine the degree to which EMG signals and muscle forces are related, the basic problem remains that EMG cannot provide a quantitative measurement of muscle force. Intramuscular pressure (IMP), the pressure applied by muscle fibers on interstitial fluid, has been considered as a correlate for muscle force. Numerous studies have shown that an approximately linear relationship exists between IMP and muscle force. A microsensor has recently been developed that is accurate, biocompatible, and appropriately sized for clinical use. While muscle force and pressure have been shown to be correlates, IMP has been shown to be non-uniform within the muscle. As it would not be practicable to experimentally evaluate how IMP is distributed, computational modeling may provide the means to fully evaluate IMP generation in muscles of various shapes and operating conditions. The work presented in this dissertation focuses on the development and validation of computational models of passive skeletal muscle and the evaluation of their performance for prediction of IMP. A transversly isotropic, hyperelastic, and nearly incompressible model will be evaluated along with a poroelastic model.

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.