The flow of two falling balls mixes rapidly

In this paper we study the system of two falling balls in continuous time. We modell the system by a suspension flow over a two dimensional, hyperbolic base map. By detailed analysis of the geometry of the system we identify special periodic points and show that the ratio of certain periods in continuous time is Diophantine for almost every value of the mass parameter in an interval. Using results of Melbourne (\cite{M}) and our previous achievements \cite{BBNV} we conclude that for these values of the parameter the flow mixes faster than any polynomial. Even though the calculations are presented for the specific physical system, the method is quite general and can be applied to other suspension flows, too

On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a one-dimensional interval partially intersecting the cell. This model can be considered as the elementary building block of a spatially extended high-dimensional billiard modeling heat transport in a class of hybrid materials exhibiting the kinetics of gases and spatial structure of solids. Using heuristic arguments and numerical analysis, we argue that, in a regime of rare interactions, the billiard process converges to a Markov jump process for the energy exchanges and obtain the expression of its generator.Comment: 23 pages, 6 figure

Biliárdok modern elmélete és annak alkalmazásai = Modern billiard theory and its applications

1. Egyenletesen hiperbolikus biliárdok. Tóth Imre Péterrel közösen elsőként sikerült magas dimenziós puha biliárdok egy osztályának hiberbolicitását belátni. Legfontosabb eredményünk, hogy magas dimenziós szóróbiliárdokra természetes feltételek mellett exponenciális korrelációlecsengést bizonyítottunk. Pavel Bachurinnal közösen a lokális ergodicitási tétel új bizonyítását adtuk ezekre a rendszerekre. 2. Gyengén hiperbolikus biliárdok. Sebastien Gouezellel közösen a Bunimovich stadionra igazoltunk nemstandard határeloszlástételt. Ian Melbourne-nel bizonyítottuk, hogy folytonos időben a cusp dinamikára gyors keverés és majdnem biztos invariancia elv teljesül. Tökbiliárdok kétparaméteres családjában az ergodicitáshoz és a KAM szigetekhez kapcsolódó bifurkációs jelenségeket tártunk fel Halász Miklóssal. 3. Statisztikus fizikai problémák. Tóth Bálinttal és Tóth Imre Péterrel kis tömeg határesetben adtunk a jelölt részecske aszimptotikus szórására új becsléseket a Rayleigh gázban. Kevin Linnel és Lai-Sang Younggal közösen egydimenziós hővezetési jelenségeket vizsgáltunk: bizonyítottuk, hogy egy a gerjesztés hiányában integrálható dinamika a hőtartályok hatására ergodikus invariáns mértékkel rendelkezik, valamint kimutattuk a lokális termikus egyensúly hiányát. | 1. Uniformly hyperbolic billiards. With Imre Péter Tóth we gave the first rigorous proof of hyperbolicity for a class of mutidimensional soft billiard models. Our most important result is, nonetheless, exponential decay of correlations under natural assumptions for multidimensional dispersing billiards. With Pavel Bachurin we also gave a new proof of the local ergodicity theorem for the same class of systems. 2. Weakly hyperbolic billiards. With Sebastien Gouezel we proved a non-standard limit theorem for the Bunimovich stadium. In a joint work with Ian Melbourne, rapid mixing and almost sure invariance principle is proved for billiards with cusps in continuous time. For the two parameter family of squash billiards with Miklós Halász we discuss bifurcation phenomena concerning ergodicity vs. KAM islands. 3. Problems in statistical physics. In the zero mass limit of the Rayleigh gas new estimates on the asymptotic variance of the tagged particle are given in a joint work with Bálint Tóth and Imre Péter Tóth. With Kevin Lin and Lai-Sang Young we study heat conductivity in one dimension: we prove that an integrable chain, when driven at the boundary, has a unique ergodic invariant measure, and the lack of local thermodynamical equilibrium is also shown

Diálogos de juicio e interpretación de sueños en los cuentos populares: Consejeros reales e intérpretes de sueños

Some of the kings in the narrative actually follow Kantian orientation in their judgment and allow the right of necessity to enter into their thinking: they listen to others or (the good sense of) the truthful heart because of their limited or deficient knowledge. Others, delighted with their self-belief and mania for power, throw scorn on the law, on mercy, pardon, and forgiveness, and let themselves be led by anger, stupidity, complacency, stigma and desire for exclusion. In the tale narratives, they are further represented as scholars/wisemen, fortune-tellers, the ‘foresighted’, ancient old men, old women, wizards, taltoses (in the words of folklorist Ilona Nagy “mysterious people of fate”), doubles/doppelgangers, or animals with extraordinary abilities (the ability to speak human languages, or to transfigure themselves), prestigious kings from another country, ministers, advisors, witches who deceive the king (not uncommonly Gypsy women), depending on whether the intention is to link the giver of advice and the meaning of what he says to the sacred (biblical) or the profane (sometimes mythical), as it illuminates his/her existential character.Algunos de los reyes en la narración siguen en realidad la orientación kantiana en su juicio y permiten que el derecho de la necesidad entre en su pensamiento: escuchan a los demás o (el buen sentido del) corazón debido a su conocimiento limitado o deficiente. Otros, encantados con la fe en sí mismo y la manía por el poder, desprecian la ley, la piedad y el perdón, y se dejan llevar por la ira, la estupidez, la complacencia, el estigma y el deseo de exclusión. En los cuentos populares se los representa además como eruditos/sabios, adivinos, los ‘previsores’, ancianos o ancianas, magos, taltoses (en palabras de la folclorista Ilona Nagy “la misteriosa gente del destino”), dobles/doppelgänger, o animales con habilidades extraordinarias (la de hablar lenguas humanas o de transfigurarse), reyes prestigiosos de otros países, ministros, consejeros, brujas que engañan al rey (no es raro que sean mujeres gitanas), dependiendo de si la intención es vincular al consejero y el significado de lo que dice con lo sagrado (bíblico) o lo profano (a veces mítico), ya que ilumina su carácter existencial

Synchronization versus stability of the invariant distribution for a class of globally coupled maps

We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant measure (acim), which is furthermore mixing. Interaction arises in the form of diffusive coupling, which involves a function that is discontinuous on the circle. We show that for sufficiently small coupling strength the coupled map system admits a unique absolutely continuous invariant distribution, which depends on the coupling strength $\varepsilon$. Furthermore, the invariant density exponentially attracts all initial distributions considered in our framework. We also show that the dependence of the invariant density on the coupling strength $\varepsilon$ is Lipschitz continuous in the BV norm. When the coupling is sufficiently strong, the limit behavior of the system is more complex. We prove that a wide class of initial measures approach a point mass with support moving chaotically on the circle. This can be interpreted as synchronization in a chaotic state

Ultrasound imaging in joint and soft tissue inflammation

The use of ultrasound as an extended and more objective investigation performed as an extension of physical examination has a potential role in studying inflammation in different rheumatic diseases such as rheumatoid arthritis (RT) and spondylarthropathy (SpA). Rheumatoid arthritis is a chronic disease causing joint inflammation and destruction. Metacarpophalangeal (MCP) joint involvement is one of the earliest and most permanent signs of RA. US has been used to detect synovitis and erosions in MCP joints with high accuracy when compared to X-ray and magnetic resonance imaging (MRI). In RA joints, power Doppler has been used to detect increased blood flow as a potential sign of inflammation but grey-scale and power Doppler ultrasonography was not compared to another method to detect increased blood flow in MCP joints. After RA the next most common inflammatory group of diseases are the seronegative spondylarthropathies. In SpA joint inflammation and ankylosis occur in addition to periarticular enthesitis, which is one of the major hallmarks of the disease and has been poorly studied by ultrasonography. In order to reduce observer variation in musculoskeletal ultrasound examination to the level of other imaging methods it is necessary to avoid direct contact between the observer and the subject. This problem has been addressed in the aerospace industry and led to the development of air-coupled non-destructive testing. Air-coupled ultrasonography has the potential in medial imaging to exclude observer variation if it is able to depict human anatomy. There are currently no data regarding airborne ultrasound in the musculoskeletal ultrasound literature

Társadalmi és gazdasági tényezők hatása a Kassai kerület munkanélküliségének alakulására 1993-tól napjainkig = The impact of social and economic factors on unemployment in the Košice region from 1993 to the present

Szlovákia különböző térségei más-más helyzetből indulva eltérően reagáltak a piacgazdasági átmenet kihívásaira. Társadalmi-gazdasági egyenlőtlenségek alakultak ki, éles határ húzódik a keleti és a nyugati országrész között. A kilencvenes évek társadalmi-gazdasági folyamatainak egyik meghatározó eleme volt a tömeges és tartós munkanélküliség. A tanulmány célja, hogy bemutassuk a munkanélküliség alakulását a Kassai kerületben a szlovák államalapítástól napjainkig. Tanulmányunk kiemelten foglalkozik azokkal a kormányzati intézkedésekkel, amelyeket a munkaerő-piaci körülmények változtatásának érdekében tettek. A következő megállapítások vonhatók le röviden: a Kassai kerületben kialakult előnytelen munkaerő-piaci helyzet az átgondolatlan rendszerváltás és az egyes szlovákiai kormányok intézkedéseinek negatív „mellékterméke”. Napjainkban a munkanélküliség súlyos problémának számít, elengedhetetlen a különböző gazdasági és társadalmi eszközökkel, aktív munkaerő-piaci politikával történő beavatkozás