7 research outputs found
Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model
We derive a finite set of nonlinear integral equations (NLIE) for the
thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model.
Our NLIE can be evaluated numerically for arbitrary finite temperature and
chemical potentials. We recover the NLIE for sl(3) as a limiting case. In
comparison to other recently derived NLIE, the evaluation at low temperature
poses no problem in our formulation. The model shows a rich ground-state phase
diagram. We obtain the critical fields from the T to zero limit of our NLIE. As
an example for the application of the NLIE, we give numerical results for the
SU(4) spin-orbital model. The magnetic susceptibility shows divergences at
critical fields in the low-temperature limit and logarithmic singularities for
zero magnetic field.Comment: 32 pages, 7 figures; references added, minor corrections, final
versio
Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation
Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and (i) characterized regarding their cellular and matrix composition or secondly (ii) treated with interleukin-1β (IL–1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate the distribution of IL–1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics.publishedVersio
Short-distance thermal correlations in the XXZ chain
Recent studies have revealed much of the mathematical structure of the static
correlation functions of the XXZ chain. Here we use the results of those
studies in order to work out explicit examples of short-distance correlation
functions in the infinite chain. We compute two-point functions ranging over 2,
3 and 4 lattice sites as functions of the temperature and the magnetic field
for various anisotropies in the massless regime . It turns
out that the new formulae are numerically efficient and allow us to obtain the
correlations functions over the full parameter range with arbitrary precision.Comment: 25 pages, 5 colored figure
Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation
Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and (i) characterized regarding their cellular and matrix composition or secondly (ii) treated with interleukin-1β (IL–1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate the distribution of IL–1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics