Physics behind the minimum of relative entropy measures for correlations

The relative entropy of a correlated state and an uncorrelated reference state is a reasonable measure for the degree of correlations. A key question is however which uncorrelated state to compare to. The relative entropy becomes minimal for the uncorrelated reference state that has the same one-particle density matrix as the correlated state. Hence, this particular measure, coined nonfreeness, is unique and reasonable. We demonstrate that for relevant physical situations, such as finite temperatures or a correlation enhanced orbital splitting, other choices of the uncorrelated state, even educated guesses, overestimate correlations.Comment: 4 pages, 1 figure, final version as to appear European Physical Journal

On two-temperature problem for harmonic crystals

We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components,$d,n \ge 1$. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The random function converges to different space-homogeneous processes as $x_d\to\pm\infty$, with the distributions $\mu_\pm$. We study the distribution $\mu_t$ of the solution at time $t\in\R$. The main result is the convergence of $\mu_t$ to a Gaussian translation-invariant measure as $t\to\infty$. The proof is based on the long time asymptotics of the Green function and on Bernstein's `room-corridor' argument. The application to the case of the Gibbs measures $\mu_\pm=g_\pm$ with two different temperatures $T_{\pm}$ is given. Limiting mean energy current density is $- (0,...,0,C(T_+ - T_-))$ with some positive constant $C>0$ what corresponds to Second Law

The nonrelativistic limit of the Magueijo-Smolin model of deformed special relativity

We study the nonrelativistic limit of the motion of a classical particle in a model of deformed special relativity and of the corresponding generalized Klein-Gordon and Dirac equations, and show that they reproduce nonrelativistic classical and quantum mechanics, respectively, although the rest mass of a particle no longer coincides with its inertial mass. This fact clarifies the meaning of the different definitions of velocity of a particle available in DSR literature. Moreover, the rest mass of particles and antiparticles differ, breaking the CPT invariance. This effect is close to observational limits and future experiments may give indications on its effective existence.Comment: 10 pages, plain TeX. Discussion of generalized Dirac equation and CPT violation adde

3D Bioprinting and Near-Field Electrospinning Composite Scaffolds for the Bone-Ligament Interface

3D bioprinting is an additive manufacturing technique that can utilize a range of bioactive materials to construct specific architectures that mimic native tissue. Near-field electrospinning (NFE) offers precise alignment control to create non-woven mats with high tensile strengths. We built a custom E-spin printer that enables layer-by-layer alternating deposition between 3D bioprinting and NFE to create composite scaffolds for the bone-ligament interface. This complex region is difficult to simulate due to its functionally graded mechanical and biochemical properties. We created NFE poly(caprolactone) highly aligned micro-fibers which formed collagen fibril-like bundles. Poly(ethylene glycol) diacrylate with decellularized bone was encased in the PCL fibers to create bony ligament support structures in a composite scaffold. Cytotoxicity of all materials was determined through a Live/Dead assay (Thermo Fisher) with NIH/3T3 cells. The materials and the composite scaffold were seeded with 3T3 cells and cultured for three days before undergoing an immunocytochemistry staining (ICC) to assess cell adhesion and spreading. Increased adhesion and spreading on decellularized bone scaffolds along with cell elongation in the direction of the fibers suggests the ability of the scaffold to encourage osteoblastic differentiation and ligamentous tissue formation, though a longitudinal study is still underway. Mechanical results suggest that the composite scaffolds have increased compressive strength over PEGDA alone as the PCL fibers constrict horizontal elongation, thus yielding a higher compressive modulus. The PCL fibers demonstrated a tensile strength approaching native ligament (3.96 ± 1.10 MPa), which shows promise as the ligament phase of the scaffold. The E-spin printer’s versatility with materials of disparate viscosities enabled the layer-by-layer fabrication of composite (PCL/PEGDA+bone) scaffolds that begin to mimic the complex nature of the bone-ligament interface

Computational micromagnetics with Commics

We present our open-source Python module Commics for the study of the magnetization dynamics in ferromagnetic materials via micromagnetic simulations. It implements state-of-the-art unconditionally convergent finite element methods for the numerical integration of the Landau–Lifshitz–Gilbert equation. The implementation is based on the multiphysics finite element software Netgen/NGSolve. The simulation scripts are written in Python, which leads to very readable code and direct access to extensive post-processing. Together with documentation and example scripts, the code is freely available on GitLab. Program summary: Program title: Commics Program Files doi: http://dx.doi.org/10.17632/29wv9h78h7.1 Licensing provisions: GPLv3 Programming language: Python3 Nature of problem: Numerical integration of the Landau–Lifshitz–Gilbert equation in three space dimensions Solution method: Tangent plane scheme [1]: original first-order version, projection-free version, second-order version, efficient second-order IMEX version; Midpoint scheme [2]: original version, IMEX version; Magnetostatic Maxwell equations are treated by the hybrid FEM–BEM method [3] Additional comments including restrictions and unusual features: An installation of the finite element software Netgen/NGSolve and an installation of the boundary element library BEM++ are required. References [1] F. Alouges. A new finite element scheme for Landau–Lifchitz equations. Discrete Contin. Dyn. Syst. Ser. S, 1(2):187–196, 2008. [2] S. Bartels and A. Prohl. Convergence of an implicit finite element method for the Landau–Lifshitz–Gilbert equation. SIAM J. Numer. Anal., 44(4):1405–1419, 2006. [3] D. R. Fredkin and T. R. Koehler. Hybrid method for computing demagnetization fields. IEEE Trans. Magn., 26(2):415–417, 1990