Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity Theory

We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy density given by the Cauchy-Born rule, as the interatomic distances tend to zero. These results hold for small data close to a stable lattice for general finite range interaction potentials. We also discuss the notion of stability in detail.Comment: new version with only minor change

The Effect of Fluctuations on the QCD Critical Point in a Finite Volume

We investigate the effect of a finite volume on the critical behavior of the theory of the strong interaction (QCD) by means of a quark-meson model for two quark flavors. In particular, we analyze the effect of a finite volume on the location of the critical point in the phase diagram existing in our model. In our analysis, we take into account the effect of long-range fluctuations with the aid of renormalization group techniques. We find that these quantum and thermal fluctuations, absent in mean-field studies, play an import role for the dynamics in a finite volume. We show that the critical point is shifted towards smaller temperatures and larger values of the quark chemical potential if the volume size is decreased. This behavior persists for antiperiodic as well as periodic boundary conditions for the quark fields as used in many lattice QCD simulations.Comment: 9 pages, 2 figures, 1 tabl

On the passage from atomistic systems to nonlinear elasticity theory

We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the continuum theory which depends on the underlying atomistic interaction potentials and the lattice geometry. The interaction potentials to which our theory applies are general finite range models on multilattices which in particular can also account for multi-pole interactions and bond-angle dependent contributions. Furthermore, we discuss the applicability of the Cauchy-Born rule. Our class of limiting energy densities consists of general quasiconvex functions and the class of linearized limiting energies consistent with the Cauchy-Born rule consists of general quadratic forms not restricted by the Cauchy relations

Chloride channels ClC-2 and ICln mRNA expression differs in renal epithelial ontogeny

Chloride channels ClC-2 and ICln mRNA expression differs in renal epithelial ontogeny. Development-dependent mRNA expression of the chloride channels ClC-2 and ICln was studied by quantitative reverse transcriptase-polymerase chain reaction in rat ureteric bud and cortical collecting duct primary monolayer cultures. Abundance of ClC-2 mRNA increased in ureteric bud cells between embryonic day 15 (E15) and E17, peaked at postnatal day 3 (P3), and was down-regulated at P7 when morphogenesis is complete, suggesting a specific embryonic function. Expression of ICln mRNA, in contrast, up-regulated continuously with development

On the Phase Structure of QCD in a Finite Volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.Comment: 11 pages, 3 figures, 4 tables; minor text corrections, one figure added, appendix added, references added, matches PLB versio

Elasticity-based determination of isovolumetric phases in the human heart

<p>Abstract</p> <p>Background/Motivation</p> <p>To directly determine isovolumetric cardiac time intervals by magnetic resonance elastography (MRE) using the magnitude of the complex signal for deducing morphological information combined with the phase of the complex signal for tension-relaxation measurements.</p> <p>Methods</p> <p>Thirty-five healthy volunteers and 11 patients with relaxation abnormalities were subjected to transthoracic wave stimulation using vibrations of approximately 25 Hz. A <it>k</it>-space-segmented, ECG-gated gradient-recalled echo steady-state sequence with a 500-Hz bipolar motion-encoding gradient was used for acquiring a series of 360 complex images of a short-axis view of the heart at a frame rate of less than 5.2 ms. Magnitude images were employed for measuring the cross-sectional area of the left ventricle, while phase images were used for analyzing the amplitudes of the externally induced waves. The delay between the decrease in amplitude and onset of ventricular contraction was determined in all subjects and assigned to the time of isovolumetric tension. Conversely, the delay between the increase in wave amplitude and ventricular dilatation was used for measuring the time of isovolumetric elasticity relaxation.</p> <p>Results</p> <p>Wave amplitudes decreased during systole and increased during diastole. The variation in wave amplitude occurred ahead of morphological changes. In healthy volunteers the time of isovolumetric elasticity relaxation was 75 ± 31 ms, which is significantly shorter than the time of isovolumetric tension of 136 ± 36 ms (<it>P </it>< 0.01). In patients with relaxation abnormalities (mild diastolic dysfunction, <it>n </it>= 11) isovolumetric elasticity relaxation was significantly prolonged, with 133 ± 57 ms (<it>P </it>< 0.01), whereas isovolumetric tension time was in the range of healthy controls (161 ± 45 ms; <it>P </it>= 0.053).</p> <p>Conclusion</p> <p>The complex MRE signal conveys complementary information on cardiac morphology and elasticity, which can be combined for directly measuring isovolumetric tension and elasticity relaxation in the human heart.</p