Modeling of the formation of complex molecules in protostellar objects

The results of molecular composition modeling are presented for the well studied low-mass star-forming region TMC-1 and the massive star-forming region DR21(OH), which is poorly studied from a chemical point of view. The column densities of dozens of molecules, ranging from simple diatomic to complex organic molecules, are reproduced to within an order of magnitude using a one-dimensional model for the physical and chemical structure of these regions. The chemical ages of the regions are approximately 105 years in both cases. The main desorption mechanisms that are usually included in chemical models (photodesorption, thermal desorption, and cosmic-ray-induced desorption) do not provide sufficient gasphase abundances of molecules that are synthesized in surface reactions; however, this shortcoming can be removed by introducing small amount of reactive desorption into the model. It is possible to reproduce the properties of the TMC-1 chemical composition in a standard model, without requiring additional assumptions about an anomalous C/O ratio or the recent accretion of matter enriched with atomic carbon, as has been proposed by some researchers. © 2013 Pleiades Publishing, Ltd

Dietary fiber is a reliable and apparent element of treatment for patients with type 2 diabetes mellitus and cardiovascular diseases: an easy solution to a complicated problem

Cardiovascular diseases are a frequent comorbid condition in patients with type 2 diabetes mellitus (t2DM). This problem tends to remain acute because of the progression of t2DM, which increases the chances of cardiovascular events. Medicine today has a range of innovative hypoglycemic drugs, which proved their safety and effectiveness towards diseases of cardiovascular system. However, high cardiovascular mortality demonstrates that the medication is not enough effective. Partly lack of success may be explained by not enough work with unmodified risk factors, such as physical activity, smoking and excessive and wrong nutrition. Studies about dietary fiber (DF) let us discuss their including in the dietary plan of patients with t2DM and cardiovascular diseases. One of the promising DF types is Cyamopsis tetragonoloba extract. It showed its effectiveness concerning carbohydrate metabolism and lipid profile, improving, metabolic features of t2DM patients and lowering the risks of cardiovascular events. What is more, the advantage of Cyamopsis tetragonoloba extract is easy to use and has no side effects

Invariant Sets and Explicit Solutions to a Third-Order Model for the Shearless Stratified Turbulent Flow

We study dynamics of the shearless stratified turbulent flows. Using the method of differential constraints we find a class of explicit solutions to the problem under consideration and establish that the differential constraint obtained coincides with the well-known Zeman--Lumley model for stratified flows.Comment: arxiv version is already officia

A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation

We present a new class of exact solutions for the so-called {\it Laplacian Growth Equation} describing the zero-surface-tension limit of a variety of 2D pattern formation problems. Contrary to common belief, we prove that these solutions are free of finite-time singularities (cusps) for quite general initial conditions and may well describe real fingering instabilities. At long times the interface consists of N separated moving Saffman-Taylor fingers, with ``stagnation points'' in between, in agreement with numerous observations. This evolution resembles the N-soliton solution of classical integrable PDE's.Comment: LaTeX, uuencoded postscript file

Generic critical points of normal matrix ensembles

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry $x^3 \sim y^2$ is described by the first Painlev\'e transcendent. The regularization of the curve resulting from discretization is discussed.Comment: Based on a talk given at the conference on Random Matrices, Random Processes and Integrable Systems, CRM Montreal, June 200

Sudden drawdown and drainage of a horizontal aquifer

Drainage of a saturated horizontal aquifer following a sudden drawdown is reanalyzed using the Boussinesq equation. The effect of the finite length of the aquifer is considered in detail. An analytical approximation based on a superposition principle yields a very good estimate of the outflow when compared to accurate numerical solutions. An illustration of the new analytical approach to analyze basin-scale field data is used to demonstrate possible field applications of the new solution.<br /

Random Matrices in 2D, Laplacian Growth and Operator Theory

Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of theoretical physics, from condensed matter to high energy. The fundamental results obtained so far rely mostly on the theory of random matrices in one dimension (the dimensionality of the spectrum, or equilibrium probability density). In the last few years, this theory has been extended to the case where the spectrum is two-dimensional, or even fractal, with dimensions between 1 and 2. In this article, we review these recent developments and indicate some physical problems where the theory can be applied.Comment: 88 pages, 8 figure