Seminars 2011-2012

 Date Lecturer Topic
16/05/2012Alexander Rasin
Weizmann Institute, Rehovot, Israel
Title: The Gardner method for symmetries

Abstract: The Gardner method, traditionally used to generate conservation laws
of integrable equations, is generalized to generate symmetries. The method is demonstrated for
the KdV, Camassa-Holm and Sine-Gordon equations. The method involves identifying a symmetry which depends
upon a parameter; expansion of this symmetry in a (formal) power series in the
parameter then gives the usual infinite hierarchy of symmetries. We show that the obtained
symmetries commute.

09/05/2012Golberg Anatoly

Holon technology Center, Israel

“Strengthened version of the Bohr-Menshoff-Trokhimchuk theory”.

Abstract.
There are various conditions which provide the analyticity of a
function of complex variable. The well-known conditions are due to Bohr (1918) and Menshoff (1937),
latter somethat generalized by Trokhimchuk.
Our main theorem presented in the talk is an essentual strengthening
of classical results of Bohr, Menshoff and Trokhimchuk concerning the
homeomorphic mappings which preserve the infnitesimal circles, and continuous mappings as well.
We also give an extension of this result to much more general classes of mappings in the multidimensional euclidean space.
This extension involves the modern tools in geometric function theory and potential theory based on conformal moduli of ring domains and
capacities of condensers.
28/03/2012Dr. Boaz Ben Moshe

Ariel University, Israel

Positioning problems

Formulation, analysis and various applications of positioning problems are considered.

08/02/2012Yaniv Almog, Louisiana State University, USA,Stability of the Normal State for Superconductors of Large Normal Conductivity in the Presence of Electric Current

Abstract. We consider the linearization of the time-dependent Ginzburg-Landau near the normal state. We assume that an electric current is applied through the sample, which captures the half plane, inducing thereby, a magnetic field. We obtain the critical current where the normal state looses its stabilities in two limit cases: the small normal conductivity limit, where we obtain it rigorously, and the large normal conductivity limit where we obtain it formally.

Joint work with B. Helffer and X. B. Pan.

21/12/2011Prof. Gilbert Weinshtein (Maths Sciences dpt., Faculty of Science, Monash University, Australia)Riemannian Penrose inequalities with charge

Title: Riemannian Penrose inequalities with charge

Abstract: The Riemannian Penrose inequality states that the total mass of an

asymptotically flat 3-manifold with non-negative scalar curvature is not

less than half the area radius of the outermost horizon with equality only

in the case of the Schwarzschild metric. Several natural generalizations to

the charged case can be proposed. We present counter-examples to some of

these generalizations and discuss a tentative approach to prove the

remaining one.

07/12/2011Dr. Sergey Bondarenko Ariel University, IsraelAsymptotic Solutions of Lotka-Volterra equations in RFT-o

 

Abstract:

We consider the example of Lotka-Volterra equations emerging in Regge Field Theory (RFT) in zero

transverse dimension and discuss asymptotic solutions of the equations as well as their stability.

23/11/20111. Prof. A. Domoshnitsky

Ariel University, Israel

 

2. Dr. Alexey L.Chadov

(Department of Information Systems and Mathematical Methods in Economics, Perm State University, Perm, Russia)

 

3. Dr. Konstantin A. Gavrilov

(Department of Information Systems and Mathematical Methods in Economics, Perm State University, Perm, Russia)

 

4. Dr. Galina V. Kutergina, Dr. Natalia F. Frolova (Department of Information Systems and Mathematical Methods in Economics, Perm State University, Perm, Russia)

1. Opening season of seminars

 

2. Hybrid models in economic dynamics problems

 

3. Numerical Modeling of Atmospheric Boundary Layer Flow over Forest Canopy

 

4. The Support System of Risk Management in Regional Industrial Complexes

 

 

Abstracts to the Workshop in  Ariel University Center of Samaria, Ariel, Israel November 23, 2011

Hybrid models in economic dynamics problems

Alexey L. Chadov, Department of Information Systems and Mathematical Methods in Economics, Perm State University, 614990, Perm, Bukirev Str., 15

Dynamic models under consideration, formally speaking, are concrete realizations of the so-called abstract functional differential equation (AFDE). On the other hand, they are typical ones met with in mathematical modeling economic dynamic processes and cover many kinds of dynamic models with aftereffect (integro-differential, delayed differential, differential difference, difference) and impulsive perturbations resulting in system’s state jumps at prescribed time moments. The equations of the system contain simultaneously terms depending on continuous time and discrete time typical for econometric models, this is why the term “hybrid” seems to be suitable. We are concerned with the representation of general solution to the system, give the setting of the general linear boundary value problem for the hybrid model as a problem of the attainability with respect to given values of main indexes of development. The control problem is set up and considered then. Conditions for the solvability of the problems are obtained. Questions of computer-aided techniques for studying these problems are discussed.

Key words: economic dynamic models, hybrid models, boundary value problems, control problems, computer experiment

Numerical Modeling of Atmospheric Boundary Layer Flow over Forest Canopy

Konstantin A. Gavrilov,  Department of Information Systems and Mathematical Methods in Economics, Perm State University, 614990, Perm, Bukirev Str., 15

The report is dedicated to the investigation of the interaction between an Atmospheric Boundary Layer and a canopy (representing a forest cover). We have focused our attention to the complex problem of the generation and transformation of turbulent vortices over homogeneous, heterogeneous and sparse canopy. This problem corresponds to the Computational Fluid Dynamics research domain. The problem has been studied using Large Eddy Simulation approach and High Performance Computing technique.

The numerical results reproduced correctly all the main characteristics of this flow, as reported in the literature: the formation of a first generation of coherent structures aligned transversally with the wind flow direction, the reorganization and the deformation of these vortex tubes into horse-shoe structures. The results obtained with the introduction of a discontinuity in the canopy (reproducing a clearing or a fuel break in a forest) are compared with the experimental data collected in a wind tunnel. In this case, the results confirmed the existence of a strong turbulence activity inside the canopy at a distance equal to 8 times the height of the canopy, referenced in the literature as the Enhance Gust Zone (EGZ) characterized by a local peak of the skewness factor. Then, the process of passive scalar transport from a forest canopy into a clear atmosphere is studied for two cases, i.e., when the concentration held by the forest canopy is either constant or variable. While this difference has little influence on the concentration patterns, results show that it has an important influence on the concentration magnitude as well as on the dynamics of the total concentration in the atmosphere.

The Support System of Risk Management in Regional Industrial Complexes.

Galina V. Kutergina,  Natalia V. Frolova, Department of Information Systems and Mathematical Methods in Economics, Perm State University, 614990, Perm, Bukirev Str., 15The report deals with the current state of the problem and typical lacks of control systems of risk management. The reasons not allowing to realize effective control systems of risk management in large industrial complexes are also investigated. The approach of creation of information and analytical systems of support risk-focused management is described.