Rotating saddle trap as Foucault's pendulum

One of the many surprising results found in the mechanics of rotating systems is the stabilization of a particle in a rapidly rotating planar saddle potential. Besides the counterintuitive stabilization, an unexpected precessional motion is observed. In this note we show that this precession is due to a Coriolis-like force caused by the rotation of the potential. To our knowledge this is the first example where such force arises in an inertial reference frame. We also propose an idea of a simple mechanical demonstration of this effect.Comment: 13 pages, 9 figure

Analysis of Transient Processes in a Radiophysical Flow System

Transient processes in a third-order radiophysical flow system are studied and a map of the transient process duration versus initial conditions is constructed and analyzed. The results are compared to the arrangement of submanifolds of the stable and unstable cycles in the Poincare section of the system studied.Comment: 3 pages, 2 figure

Chaotic Phenomenon in Nonlinear Gyrotropic Medium

Nonlinear gyrotropic medium is a medium, whose natural optical activity depends on the intensity of the incident light wave. The Kuhn's model is used to study nonlinear gyrotropic medium with great success. The Kuhn's model presents itself a model of nonlinear coupled oscillators. This article is devoted to the study of the Kuhn's nonlinear model. In the first paragraph of the paper we study classical dynamics in case of weak as well as strong nonlinearity. In case of week nonlinearity we have obtained the analytical solutions, which are in good agreement with the numerical solutions. In case of strong nonlinearity we have determined the values of those parameters for which chaos is formed in the system under study. The second paragraph of the paper refers to the question of the Kuhn's model integrability. It is shown, that at the certain values of the interaction potential this model is exactly integrable and under certain conditions it is reduced to so-called universal Hamiltonian. The third paragraph of the paper is devoted to quantum-mechanical consideration. It shows the possibility of stochastic absorption of external field energy by nonlinear gyrotropic medium. The last forth paragraph of the paper is devoted to generalization of the Kuhn's model for infinite chain of interacting oscillators

The Possibility of Reconciling Quantum Mechanics with Classical Probability Theory

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.Comment: Latex, 14 pages, 1 figur

Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

Density functional formalism in the canonical ensemble

Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails, work in nanopore systems could certainly benefit from such extension. We show that, if the asymptotic behaviour of the canonical distribution functions is taken into account, the HKSM theorem can be extended to the canonical ensemble. We generate $N$-modified correlation and distribution functions hierarchies and prove that, if they are employed, either a modified external field or the density profiles can be indistinctly used as independent variables. We also write down the $N$% -modified free energy functional and prove that its minimum is reached when the equilibrium values of the new hierarchy are used. This completes the extension of the HKSM theorem.Comment: revtex, to be submitted to Phys. Rev. Let

Shapes, contact angles, and line tensions of droplets on cylinders

Using an interface displacement model we calculate the shapes of nanometer-size liquid droplets on homogeneous cylindrical surfaces. We determine effective contact angles and line tensions, the latter defined as excess free energies per unit length associated with the two contact lines at the ends of the droplet. The dependences of these quantities on the cylinder radius and on the volume of the droplets are analyzed.Comment: 26 pages, RevTeX, 10 Figure

Modeling adsorption in metal-organic frameworks with open metal sites : propane/propylene separations

We present a new approach for modeling adsorption in metal-organic frameworks (MOFs) with unsaturated metal centers and apply it to the challenging propane/propylene separation in copper(II) benzene-1,3,5-tricarboxylate (CuBTC). We obtain information about the specific interactions between olefins and the open metal sites of the MOP using quantum mechanical density functional theory. A proper consideration of all the relevant contributions to the adsorption energy enables us to extract the component that is due to specific attractive interactions between the pi-orbitals of the alkene and the coordinatively unsaturated metal. This component is fitted using a combination of a Morse potential and a power law function and is then included into classical grand canonical Monte Carlo simulations of adsorption. Using this modified potential model, together with a standard Lennard-Jones model, we are able to predict the adsorption of not only propane (where no specific interactions are present), but also of propylene (where specific interactions are dominant). Binary adsorption isotherms for this mixture are in reasonable agreement with ideal adsorbed solution theory predictions. We compare our approach with previous attempts to predict adsorption in MOFs with open metal sites and suggest possible future routes for improving our model

Evaluation of the effectiveness of weight loss and the return of lost weight after sleeve gastrectomy in the long term follow-up period

Sleeve gastrectomy, originally proposed as part of a two-stage operation, more than 15 years ago, is recognized as an independent, effective intervention for the treatment of obesity. The purpose of this review was to evaluate the effectiveness of sleeve gastrectomy based on data on long-term follow-up of patients. A search was performed in two databases, 33 literary sources were selected based on the results of the selection. In this review, the authors evaluated some parameters characterizing the effectiveness of sleeve gastrectomy in the long term after surgery. The percentage of follow-up of patients in the long-term period (follow up, %) varied from 5,6% to 97%, the expected decrease in % follow up over time did not occur. The authors have suggested similar results due to the heterogeneity of the data of the analyzed sources. By the five-year period, the detected average % of follow-up did not correspond to the optimal recommended level of follow-up for operated patients by this time. The most common criterion for assessing the return of weight is an increase in body weight by more than 10 kg from the lowest achieved. The prevalence of this phenomenon ranged from 26.3% to 44%. Among the reasons predisposing to weight loss are the initial high BMI, old age, dilatation of the formed stomach. In the absence of a universal definition of various terms (follow up, unsatisfactory result of surgery, weight loss, etc.), the results among the same patients when using different definitions will differ, there is a need to adopt standards when describing these phenomena. Despite the likelihood of weight loss after longitudinal resection, this operation is relatively simple from a technical point of view, safer, it can be used to improve the course of concomitant pathology (diabetes mellitus, hypertension), improve the quality and increase the life expectancy of patients