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

Multi-frequency Studies of Massive Cores with Complex Spatial and Kinematic Structures

Five regions of massive star formation have been observed in various molecular lines in the frequency range $\sim 85-89$ GHz. The studied regions possess dense cores, which host young stellar objects. The physical parameters of the cores are estimated, including kinetic temperatures ($\sim 20-40$ K), sizes of the emitting regions ($\sim 0.1-0.6$ pc), and virial masses ($\sim 40-500 M_{\odot}$). Column densities and abundances of various molecules are calculated in the local thermodynamical equilibrium approximation. The core in 99.982+4.17, associated with the weakest IRAS source, is characterized by reduced molecular abundances. Molecular line widths decrease with increasing distance from the core centers ($b$). For b\ga 0.1~pc, the dependences $\Delta V(b)$ are close to power laws ($\propto b^{-p}$), where $p$ varies from $\sim 0.2$ to $\sim 0.5$, depending on the object. In four cores, the asymmetries of the optically thick HCN(1--0) and HCO$^+$(1--0) lines indicate systematic motions along the line of sight: collapse in two cores and expansion in two others. Approximate estimates of the accretion rates in the collapsing cores indicate that the forming stars have masses exceeding the solar mass.Comment: 18 pages, 7 figures, 6 table

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

Chemical differentiation in regions of high-mass star formation I. CS, dust and N2H^+ in southern sources

Aims. Our goals are to compare the CS, N2H+ and dust distributions in a representative sample of high-mass star forming dense cores and to determine the physical and chemical properties of these cores. Methods. We compare the results of CS(5-4) and 1.2 mm continuum mapping of twelve dense cores from the southern hemisphere presented in this work, in combination with our previous N2H+(1-0) and CS(2-1) data. We use numerical modeling of molecular excitation to estimate physical parameters of the cores. Results. Most of the maps have several emission peaks (clumps). We derive basic physical parameters of the clumps and estimate CS and N2H+ abundances. Masses calculated from LVG densities are higher than CS virial masses and masses derived from continuum data, implying small-scale clumpiness of the cores. For most of the objects, the CS and continuum peaks are close to the IRAS point source positions. The CS(5-4) intensities correlate with continuum fluxes per beam in all cases, but only in five cases with the N2H+(1-0) intensities. The study of spatial variations of molecular integrated intensity ratios to continuum fluxes reveals that I(N2H+)/F{1.2} ratios drop towards the CS peaks for most of the sources, which can be due to a N2H+ abundance decrease. For CS(5-4), the I(CS)/F{1.2} ratios show no clear trends with distance from the CS peaks, while for CS(2-1) such ratios drop towards these peaks. Possible explanations of these results are considered. The analysis of normalized velocity differences between CS and N2H+ lines has not revealed indications of systematic motions towards CS peaks.Comment: 13 pages, 5 figures, accepted by Astronomy and Astrophysic

N2H+(1-0) survey of massive molecular cloud cores

We present the results of N2H+(1-0) observations of 35 dense molecular cloud cores from the northern and southern hemispheres where massive stars and star clusters are formed. Line emission has been detected in 33 sources, for 28 sources detailed maps have been obtained. The optical depth of (23-12) component toward peak intensity positions of 10 sources is ~ 0.2-1. In total, 47 clumps have been revealed in 26 sources. Integrated intensity maps with aspect ratios < 2 have been fitted with a power-law radial distribution $r^{-p}$ convolved with the telescope beam. Mean power-law index is close to unity corresponding to the $\sim r^{-2}$ density profile provided N2H+ excitation conditions do not vary inside these regions. Line widths of the cores either decrease or stay constant with distance from the center. The ratio of rotational to gravitational energy is too low for rotation to play a significant role in the dynamics of the cores. A correlation between mean line widths and sizes of clumps has been found.Comment: 17 pages, Late

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

Rigorous Proof of a Liquid-Vapor Phase Transition in a Continuum Particle System

We consider particles in ${\Bbb R}^d, d \geq 2$, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid-gas phase transition when the interaction range is finite but long compared to the interparticle spacing.Comment: 11 pages, in ReVTeX, e-mail addresses: [email protected], [email protected], [email protected]

Critical droplets in Metastable States of Probabilistic Cellular Automata

We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule which is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters $\beta$ and $h$ which resemble, but are not identical to, the inverse temperature and external magnetic field in a ferromagnetic Ising model; in particular, the phase diagram of the system has two stable phases when $\beta$ is large enough and $h$ is zero, and a unique phase when $h$ is nonzero. When the system evolves, at small positive values of $h$, from an initial state with all spins down, the PCA dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored $+$ phase inside the metastable $-$ phase reaches a critical size. We give heuristic arguments to estimate the critical size in the limit of zero ``temperature'' ($\beta\to\infty$), as well as estimates of the time required for the formation of such a droplet in a finite system. Monte Carlo simulations give results in good agreement with the theoretical predictions.Comment: 5 LaTeX picture