Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems

We consider the system of $N$ ($\ge2$) hard disks of masses $m_1,...,m_N$ and radius $r$ in the flat unit torus $\Bbb T^2$. We prove the ergodicity (actually, the B-mixing property) of such systems for almost every selection $(m_1,...,m_N;r)$ of the outer geometric parameters.Comment: 58 page

Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional billiards without using the Ansatz.Comment: 17 pages, 2 figure

Circle Decompositions of Surfaces

We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic zero, and with compact boundary components. As a byproduct, we get that any circle decomposition of a surface is upper semicontinuous.Comment: 9 pages, final version, to appear in Topology and its Applications (2010). A few missprints have been correcte

The characteristic exponents of the falling ball model

We study the characteristic exponents of the Hamiltonian system of $n$ ($\ge 2$) point masses $m_1,\dots,m_n$ freely falling in the vertical half line $\{q|\, q\ge 0\}$ under constant gravitation and colliding with each other and the solid floor $q=0$ elastically. This model was introduced and first studied by M. Wojtkowski. Hereby we prove his conjecture: All relevant characteristic (Lyapunov) exponents of the above dynamical system are nonzero, provided that $m_1\ge\dots\ge m_n$ (i. e. the masses do not increase as we go up) and $m_1\ne m_2$

Heat conduction and diffusion of hard disks in a narrow channel

Using molecular dynamics we study heat conduction and diffusion of hard disks in one dimensional narrow channels. When collisions preserve momentum the heat conduction $\kappa$ diverges with the number of disks $N$ as $\kappa\sim N^\alpha$ $(\alpha \approx 1/3)$. Such a behaviour is seen both when the ordering of disks is fixed ('pen-case' model), and when they can exchange their positions. Momentum conservation results also in sound-wave effects that enhance diffusive behaviour and on an intermediate time scale (that diverges in the thermodynamic limit) normal diffusion takes place even in the 'pen-case' model. When collisions do not preserve momentum, $\kappa$ remains finite and sound-wave effects are absent.Comment: 4 pages, accepted in Phys.Rev.

Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

In this paper we study the ergodic properties of mathematical billiards describing the uniform motion of a point in a flat torus from which finitely many, pairwise disjoint, tubular neighborhoods of translated subtori (the so called cylindric scatterers) have been removed. We prove that every such system is ergodic (actually, a Bernoulli flow), unless a simple geometric obstacle for the ergodicity is present.Comment: 24 pages, AMS-TeX fil

Singularities and nonhyperbolic manifolds do not coincide

We consider the billiard flow of elastically colliding hard balls on the flat $\nu$-torus ($\nu\ge 2$), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai Ergodic Hypothesis.Comment: Final version, to appear in Nonlinearit

A fogyasztóvá válás folyamata Magyarországon = The process of consumerization in Hungary

Kutatásunk célul tűzte ki, hogy (1) feltárja a fogyasztással kapcsolatos személyes értelmezéseket, véleményeket, attitűdöket, koncepciókat, (2) a fogyasztással kapcsolatos mindennapi élményeket (3) a fogyasztáshoz való viszony időbeli változását az egyének élete során (4) azokat a befolyásoló tényezőket, amelyek alapján az értelmezések és élmények eltérnek. Mindezek megismerésének érdekében kvalitatív és kvantitatív kutatást végeztünk. A kvalitatív kutatás során a mintába kerülés kritériuma alapján olyan családok kerültek kiválasztásra, amelyek legalább két, vagy több generációból állnak. Az első generáció 1939 előtt, a második 1969, a harmadik pedig 1990 előtt született. A kvalitatív minta 15 családból állt, összesen 44 fővel készült interjú. Az alkalmazott kvalitatív módszertan epizodikus interjúk voltak, amelyet vásárlási megfigyelésekkel egészítettünk ki. A kvantitatív kutatásban a minta elemszáma 500 fő volt, az országos minta reprezentatív nemre, korra, településtípusra és régióra. | People in a generation or cohort experience the same significant events when they're growing up. Attitudes and values are formed to a great extent when a generation or cohort passes into adulthood. In Hungary the fall of the socialist regime and the transition to market economy represented an axial moment, as the principles and logic ruling life and leading to success have transformed substantially. After the transition, not only the socialist ideology, but also its economic implications have been wiped away by the market economy. In our study we investigate familial relationships in consumption patterns using a sample of grandparents, parents and their children in Hungary. Attention is focused on generational differences in the attitudes and the personal experiences toward consumption. First we conducted in-depth interviews with 15 families (44 respondents) completed with observation of their shopping behavior. In the second phase we did quantitative analysis using national representative sample (N=500). We studied (1) the relationship between consumption and personal values, (2) the accepted degree of consumption and (3) the perception of the consumer society in Hungary

Miért fogyasztanak többet a posztmaterialisták, mint a materialisták?

A cikkben arra a kérdésre keresi a választ a szerző, hogy miért nem érzékelik az ellentmondást a növekvő fogyasztási kiadások és a posztmaterialista értékrend között az iparilag fejlett nyugati országok polgárai. Miként kapcsolódik össze az értékrend és a fogyasztás a ma divatos plurális személyiségképpel