Self-interaction model of classical point particle in one-dimension

We consider a hamiltonian system on the real line, consisting of real scalar field $\phi(x,t)$ and point particle with trajectory $y(t)$. The dynamics of this system is defined by the system of two equations: wave equation for the field, > by the point particle, and Newton's equation for the particle in its own field. We find the solution where the particle is strongly damped, but the kinetic and interaction energies of the field increase linearly in time, in despite of the full energy conservation.Comment: 6 page

Reversibility and Non-reversibility in Stochastic Chemical Kinetics

Mathematical problems with mean field and local type interaction related to stochastic chemical kinetics,are considered. Our main concern various definitions of reversibility, their corollaries (Boltzmann type equations, fluctuations, Onsager relations, etc.) and emergence of irreversibility

On products of skew rotations

Let $H_1(p,q)$, $H_2(p,q)$ be two time-independent Hamiltonians with one degree of freedom and $\{S_1^t\}$, $\{S_2^t\}$ be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by $H_1$, $H_2$. In some problems of population genetics there appear the transformations of the plane having the form $T^{(h_1,h_2)}=S^{h_2}_2\cdot S_1^{h_1}$ under some conditions on $H_1$, $H_2$. We study in this paper asymptotical properties of trajectories of $T^{(h_1,h_2)}$.Comment: 13 pages, 10 figure

Markov Process of Muscle Motors

We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.Comment: 10 page

A Search for Small-Scale Clumpiness in Dense Cores of Molecular Clouds

We have analyzed HCN(1-0) and CS(2-1) line profiles obtained with high signal-to-noise ratios toward distinct positions in three selected objects in order to search for small-scale structure in molecular cloud cores associated with regions of high-mass star formation. In some cases, ripples were detected in the line profiles, which could be due to the presence of a large number of unresolved small clumps in the telescope beam. The number of clumps for regions with linear scales of ~0.2-0.5 pc is determined using an analytical model and detailed calculations for a clumpy cloud model; this number varies in the range: ~2 10^4-3 10^5, depending on the source. The clump densities range from ~3 10^5-10^6 cm^{-3}, and the sizes and volume filling factors of the clumps are ~(1-3) 10^{-3} pc and ~0.03-0.12. The clumps are surrounded by inter-clump gas with densities not lower than ~(2-7) 10^4 cm^{-3}. The internal thermal energy of the gas in the model clumps is much higher than their gravitational energy. Their mean lifetimes can depend on the inter-clump collisional rates, and vary in the range ~10^4-10^5 yr. These structures are probably connected with density fluctuations due to turbulence in high-mass star-forming regions.Comment: 23 pages including 4 figures and 4 table

Rigorous Analysis of Singularities and Absence of Analytic Continuation at First Order Phase Transition Points in Lattice Spin Models

We report about two new rigorous results on the non-analytic properties of thermodynamic potentials at first order phase transition. The first one is valid for lattice models ($d\geq 2$) with arbitrary finite state space, and finite-range interactions which have two ground states. Under the only assumption that the Peierls Condition is satisfied for the ground states and that the temperature is sufficiently low, we prove that the pressure has no analytic continuation at the first order phase transition point. The second result concerns Ising spins with Kac potentials $J_\gamma(x)=\gamma^d\phi(\gamma x)$, where $0<\gamma<1$ is a small scaling parameter, and $\phi$ a fixed finite range potential. In this framework, we relate the non-analytic behaviour of the pressure at the transition point to the range of interaction, which equals $\gamma^{-1}$. Our analysis exhibits a crossover between the non-analytic behaviour of finite range models ($\gamma>0$) and analyticity in the mean field limit ($\gamma\searrow 0$). In general, the basic mechanism responsible for the appearance of a singularity blocking the analytic continuation is that arbitrarily large droplets of the other phase become stable at the transition point.Comment: 4 pages, 2 figure

NGC 7538 : Multiwavelength Study of Stellar Cluster Regions associated with IRS 1-3 and IRS 9 sources

We present deep and high-resolution (FWHM ~ 0.4 arcsec) near-infrared (NIR) imaging observations of the NGC 7538 IRS 1-3 region (in JHK bands), and IRS 9 region (in HK bands) using the 8.2m Subaru telescope. The NIR analysis is complemented with GMRT low-frequency observations at 325, 610, and 1280 MHz, molecular line observations of H13CO+ (J=1-0), and archival Chandra X-ray observations. Using the 'J-H/H-K' diagram, 144 Class II and 24 Class I young stellar object (YSO) candidates are identified in the IRS 1-3 region. Further analysis using 'K/H-K' diagram yields 145 and 96 red sources in the IRS 1-3 and IRS 9 regions, respectively. A total of 27 sources are found to have X-ray counterparts. The YSO mass function (MF), constructed using a theoretical mass-luminosity relation, shows peaks at substellar (~0.08-0.18 Msolar) and intermediate (~1-1.78 Msolar) mass ranges for the IRS 1-3 region. The MF can be fitted by a power law in the low mass regime with a slope of Gamma ~ 0.54-0.75, which is much shallower than the Salpeter value of 1.35. An upper limit of 10.2 is obtained for the star to brown dwarf ratio in the IRS 1-3 region. GMRT maps show a compact HII region associated with the IRS 1-3 sources, whose spectral index of 0.87+-0.11 suggests optical thickness. This compact region is resolved into three separate peaks in higher resolution 1280 MHz map, and the 'East' sub-peak coincides with the IRS 2 source. H13CO+ (J=1-0) emission reveals peaks in both IRS 1-3 and IRS 9 regions, none of which are coincident with visible nebular emission, suggesting the presence of dense cloud nearby. The virial masses are approximately of the order of 1000 Msolar and 500 Msolar for the clumps in IRS 1-3 and IRS 9 regions, respectively.Comment: 27 pages, 18 figures, 5 tables. Accepted for publication in MNRA

One Step Non SUSY Unification

We show that it is possible to achieve one step gauge coupling unification in a general class of non supersymmetric models which at low energies have only the standard particle content and extra Higgs fields doublets. The constraints are the experimental values of $\alpha_{em}$, $\alpha_s$ and $\sin^2\theta_W$ at $10^2 GeVs$, and the lower bounds for FCNC and proton decay rates. Specific example are pointed out.Comment: 10 pages, Latex file,, uses epsf style, Two Postscript figures included. To appear in Europhysics Letter

A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page

Mean-field driven first-order phase transitions in systems with long-range interactions

We consider a class of spin systems on $\Z^d$ with vector valued spins (\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions $d\ge3$, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions $d=1,2$ for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique ``state,'' then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.Comment: 57 pages; uses a (modified) jstatphys class fil