Mechanical systems subjected to generalized nonholonomic constraints

We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit formula to obtain the ``post-impact'' momentum in terms of the ``pre-impact'' momentum.Comment: 24 pages, no figure

Heat Transfer Model of Hyporthermic Intracarotid Infusion of Cold Saline for Stroke Therapy

A 3-dimensional hemispheric computational brain model is developed to simulate infusion of cold saline in the carotid arteries in terms of brain cooling for stroke therapy. The model is based on the Pennes bioheat equation, with four tissue layers: white matter, gray matter, skull, and scalp. The stroke lesion is simulated by reducing blood flow to a selected volume of the brain by a factor of one-third, and brain metabolism by 50%. A stroke penumbra was also generated surrounding the core lesion (blood volume reduction 25%, metabolism reduction 20%). The finite difference method was employed to solve the system of partial differential equations. This model demonstrated a reduction in brain temperature, at the stroke lesion, to 32°C in less than 10 minutes

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

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

Sequential Acquisition and Processing of Perfusion and Diffusion MRI Data for a Porcine Stroke Model

An automated data processing pipeline, designed for handling a large throughput of sequentially acquired MRI brain data, is described. The system takes as input multiple diffusion weighted (DWI) and perfusion weighted imaging (PWI) volumes acquired at different temporal points, automatically segments and registers them, and ultimately outputs a database used to track various perfusion and diffusion parameters through time at individual brain voxels. This pipeline has been utilized to successfully process two pig brains from an induced stroke experiment

Decorated vertices with 3-edged cells in 2D foams: exact solutions and properties

The energy, area and excess energy of a decorated vertex in a 2D foam are calculated. The general shape of the vertex and its decoration are described analytically by a reference pattern mapped by a parametric Moebius transformation. A single parameter of control allows to describe, in a common framework, different types of decorations, by liquid triangles or 3-sided bubbles, and other non-conventional cells. A solution is proposed to explain the stability threshold in the flower problem.Comment: 13 pages, 17 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

A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define an almost aff-Poisson bracket on the constraint AV-bundle, which plays a prominent role in the description of nonholonomic dynamics. Moreover, these developments give a general description of nonholonomic systems and the unified treatment permits to study nonholonomic systems after or before reduction in the same framework. Also, it is not necessary to distinguish between linear or affine constraints and the methods are valid for explicitly time-dependent systems.Comment: 50 page

Geometry dominated fluid adsorption on sculptured substrates

Experimental methods allow the shape and chemical composition of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption characteristics compared to that occuring for planar systems, which may well play an important role in developing technologies such as super-repellent surfaces or micro-fluidics. Recent studies have concentrated on adsorption of liquids at rough and heterogeneous substrates and the characterisation of nanoscopic liquid films. However, the fundamental effect of geometry has hardly been addressed. Here we show that varying the shape of the substrate can exert a profound influence on the adsorption isotherms allowing us to smoothly connect wetting and capillary condensation through a number of novel and distinct examples of fluid interfacial phenomena. This opens the possibility of tailoring the adsorption properties of solid substrates by sculpturing their surface shape.Comment: 6 pages, 4 figure

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