On the speed of approach to equilibrium for a collisionless gas

We investigate the speed of approach to Maxwellian equilibrium for a collisionless gas enclosed in a vessel whose wall are kept at a uniform, constant temperature, assuming diffuse reflection of gas molecules on the vessel wall. We establish lower bounds for potential decay rates assuming uniform $L^p$ bounds on the initial distribution function. We also obtain a decay estimate in the spherically symmetric case. We discuss with particular care the influence of low-speed particles on thermalization by the wall.Comment: 22 pages, 1 figure; submitted to Kinetic and Related Model

Алгоритмы и методы криптографии

В современном мире криптография очень много значит с точки зрения безопасности личных данных людей. В этой статье мы исследуем основной принцип управления, хранения закрытых и открытых ключей в криптографии, методы и алгоритмы, включая автономную аппаратную криптографию и улучшенный алгоритм визуальной криптографии.Nowadays cryptography means a lot in terms of safety of people's personal data. This article addresses to the main principle of management, storage of private and public keys in cryptography, methods and algorithms including autonomous hardware-based cryptography and improved algorithm of visual cryptography

Regularizing effect and local existence for non-cutoff Boltzmann equation

The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially inhomogeneous Boltzmann equation. In this paper, by sharpening the coercivity and upper bound estimates for the collision operator, establishing the hypo-ellipticity of the Boltzmann operator based on a generalized version of the uncertainty principle, and analyzing the commutators between the collision operator and some weighted pseudo differential operators, we prove the regularizing effect in all (time, space and velocity) variables on solutions when some mild regularity is imposed on these solutions. For completeness, we also show that when the initial data has this mild regularity and Maxwellian type decay in velocity variable, there exists a unique local solution with the same regularity, so that this solution enjoys the $C^\infty$ regularity for positive time

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

Inelastically scattering particles and wealth distribution in an open economy

Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trading, closed form of the wealth distribution is calculated analytically.Comment: 8 pages 5 figure

Relationship between the Velocity Ellipsoids of Galactic-Disk Stars and their Ages and Metallicities

The dependences of the velocity ellipsoids of F-G stars of the thin disk of the Galaxy on their ages and metallicities are analyzed based on the new version of the Geneva-Copenhagen Catalog. The age dependences of the major, middle, and minor axes of the ellipsoids, and also of the dispersion of the total residual veltocity, obey power laws with indices 0.25,0.29,0.32, and 0.27 (with uncertainties \pm 0.02). Due to the presence of thick-disk objects, the analogous indices for all nearby stars are about a factor of 1.5 larger. Attempts to explain such values are usually based on modeling relaxation processes in the Galactic disk. With increasing age, the velocity ellipsoid increases in size and becomes appreciably more spherical, turns toward the direction of the Galactic center, and loses angular momentum. The shape of the velocity ellipsoid remains far from equilibrium. With increasing metallicity, the velocity ellipsoid for stars of mixed age increases in size, displays a weak tendency to become more spherical, and turns toward the direction of the Galactic center (with these changes occurring substantially more rapidly in the transition through the metallicity [Fe/H]= -0.25). Thus, the ellipsoid changes similarly to the way it does with age; however, with decreasing metallicity, the rotational velocity about the Galactic center monotonically increases, rather than decreases(!). Moreover, the power-law indices for the age dependences of the axes depend on the metallicity, and display a maximum near [Fe/H]=-0.1. The age dependences of all the velocity-ellipsoid parameters for stars with equal metallicity are roughly the same. It is proposed that the appearance of a metallicity dependence of the velocity ellipsoids for thin-disk stars is most likely due to the radial migration of stars.Comment: 15 pages, 6 figures, accepted 2009, Astronomy Reports, Vol. 53 No. 9, P.785-80

Global existence and full regularity of the Boltzmann equation without angular cutoff

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem

Self-Similarity for Ballistic Aggregation Equation

We consider ballistic aggregation equation for gases in which each particle is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For the constant aggregation rate we prove existence of self-similar solutions as well as convergence to the self-similarity for generic solutions. For some classes of mass and/or impulsion dependent rates we are also able to estimate the large time decay of some moments of generic solutions or to build some new classes of self-similar solutions

Non-alcoholic fatty liver disease in patients with hypertension

To study the relationship of nonalcoholic fatty liver disease (NAFLD) in patients with hypertension (AH) with cardiometabolic risk factors (FR) of cardiovascular disease (CVD) and the effect of NAFLD on their development. 71 patients with stage I-III hypertension were randomly selected for this purpose. Two groups were identified - 37 patients with NAFLD and 34 patients without NAFLD, mainly elderly and senile age. The results of the study can be concluded. The presence of NAFLD in patients with hypertension in the elderly and senile age is not sufficient for patients to be considered as patients with a higher risk of cardiovascular disease. The main reason is the presence of metabolic syndrome and its components, which increase the risk of CVD in the study group, rather than NAFLD itself. Metabolic syndrome, in our opinion, is a common denominator, the Foundation for all risk factors. The level of transaminases in the group of patients with hypertension and NAFLD decreases with age, so it is inappropriate to use ALT as a NAFLD surrogate in elderly and senile patients. The level of transaminases in patients with steatosis and steatohepatitis is not associated with the risk of cardiovascular disease. With the combination of AH and NAFLD there is no connection of NAFLD with ischemic heart disease, AF, LVH and stroke. The presence of hypertension in a patient with NAFLD and without NAFLD, in our opinion, levels the impact of NAFLD on the risk of CVD, as the hypertension itself is a powerful risk factor for cardiovascular disease. There are no differences in the frequency of LVH and in the type of LV remodeling in patients with and without NAFLD.Изучить взаимосвязь неалкогольной жировой болезни печени (НАЖБП) у больных артериальной гипертензией (АГ) с кардиометаболическими факторами риска (ФР) сердечно-сосудистых заболеваний (ССЗ) и влияние НАЖБП на их развитие. для этого методом случайной выборки выбран 71 пациент с артериальной гипертензией I-III стадией (ВОЗ). Выделено две группы - 37 пациентов с НАЖБП и 34 пациента без НАЖБП преимущественно пожилого и старческого возраста. По результатам исследования можно сделать заключение. Наличие НАЖБП у больных с АГ пожилого и старческого возраста недостаточно для того, чтобы пациенты рассматривались как больные с более высоким риском сердечно-сосудистых заболеваний. основная причина - это наличие метаболического синдрома (МС) и его компонентов, которые повышают риск ССЗ в исследуемой группе, а не сама НАЖБП. Метаболический синдром, по нашему мнению, является общим знаменателем, фундаментом для всех факторов риска. Уровень трансаминаз в группе больных с АГ и НАЖБП с возрастом снижается, поэтому использовать АЛТ в качестве суррогата НАЖБП у больных пожилого и старческого возраста неуместно. Уровень трансаминаз у больных со стеатозом и стеатогепатитом не связан с риском сердечно-сосудистых заболеваний. При сочетании АГ и НАЖБП отсутствует связь НАЖБП с ИБС, ФП, ГЛЖ и перенесенным инсультом. Наличие АГ у пациента с НАЖБП и без НАЖБП, по нашему мнению, нивелирует влияние НАЖБП на риск ССЗ, так как сама АГ является мощным фактором риска сердечно-сосудистых заболеваний. По частоте ГЛЖ и по типу ремоделирования ЛЖ различия у больных с НАЖБП и без НАЖБП отсутствуют

Bayesian analysis to identify new star candidates in nearby young stellar kinematic groups

We present a new method based on a Bayesian analysis to identify new members of nearby young kinematic groups. The analysis minimally takes into account the position, proper motion, magnitude and color of a star, but other observables can be readily added (e.g. radial velocity, distance). We use this method to find new young low-mass stars in the \beta Pictoris (\beta PMG) and AB Doradus (ABDMG) moving groups and in the TW Hydrae (TWA), Tucana-Horologium (THA), Columba, Carina and Argus associations. Starting from a sample of 758 mid-KM (K5V-M5V) stars showing youth indicators such as H\alpha\ and X-ray emission, our analysis yields 215 new highly probable low-mass members of the kinematic groups analyzed. One is in TWA, 37 in \beta PMG, 17 in THA, 20 in Columba, 6 in Carina, 50 in Argus, 33 in ABDMG, and the remaining 51 candidates are likely young but have an ambiguous membership to more than one association. The false alarm rate for new candidates is estimated to be 5% for \beta PMG and TWA, 10% for THA, Columba, Carina and Argus, and 14% for ABDMG. Our analysis confirms the membership of 58 stars proposed in the literature. Firm membership confirmation of our new candidates will require measurement of their radial velocity (predicted by our analysis), parallax and lithium 6708 {\AA} equivalent width. We have initiated these follow-up observations for a number of candidates and we have identified two stars (2MASSJ0111+1526, 2MASSJ0524-1601) as very strong candidate members of the \beta PMG and one strong candidate member (2MASSJ0533-5117) of the THA; these three stars have radial velocity measurements confirming their membership and lithium detections consistent with young age. Finally, we proposed that six stars should be considered as new bona fide members of \beta PMG and ABDMG, one of which being first identified in this work, the others being known candidates from the literature.Comment: Accepted for publication in Ap