304 research outputs found
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 dimensions with
components,. 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 , with the
distributions . We study the distribution of the solution at
time . The main result is the convergence of to a Gaussian
translation-invariant measure as . 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
with two different temperatures is given. Limiting mean energy
current density is with some positive constant
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
- …