Nonstationary heat conduction in one-dimensional models with substrate potential.

The paper investigates nonstationary heat conduction in one-dimensional models with substrate potential. To establish universal characteristic properties of the process, we explore three different models: Frenkel-Kontorova (FK), phi4+ (φ(4)+), and phi4- (φ(4)-). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with the parabolic Fourier equation of heat conduction and clearly demonstrates the necessity for hyperbolic corrections in the phenomenological description of the heat conduction process. The crossover wavelength decreases with an increase in the average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for the temperature field is justified. In all models investigated, the relaxation of thermal perturbations is exponential, contrary to a linear chain, where it follows a power law. The most popular lowest-order hyperbolic generalization of the Fourier law, known as the Cattaneo-Vernotte or telegraph equation, is also not valid for the description of the observed behavior of the models with the substrate potential, since the characteristic relaxation time in an oscillatory regime strongly depends on the excitation wavelength. For some of the models, this dependence seems to obey a simple scaling law.

Prolylcarboxypeptidase (PRCP) as a new target for obesity treatment.

Recently, we serendipitously discovered that mice with the deficiency of the enzyme prolylcarboxypeptidase (PRCP) have elevated alpha-melanocyte-stimulating hormone (alpha-MSH) levels which lead to decreased food intake and weight loss. This suggests that PRCP is an endogenous inactivator of alpha-MSH and an appetite stimulant. Since a modest weight loss can have the most profound influence on reducing cardiovascular risk factors, the inhibitors of PRCP would be emerging as a possible alternative for pharmacotherapy in high-risk patients with obesity and obesity-related disorders. The discovery of a new biological activity of PRCP in the PRCP-deficient mice and studies of alpha-MSH function indicate the importance and complexity of the hypothalamic pro-opiomelanocortin (POMC) system in altering food intake. Identifying a role for PRCP in regulating alpha-MSH in the brain may be a critical step in enhancing our understanding of how the brain controls food intake and body weight. In light of recent findings, the potential role of PRCP in regulating fuel homeostasis is critically evaluated. Further studies of the role of PRCP in obesity are much needed.