Search results for "statistical"
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Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations
1998
This is the first of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the projection method is used in the primitive variables, to which the Cauchy-Kowalewski theorem is directly applicable. For the Prandtl equations, Cauchy-Kowalewski is applicable once the diffusion operator in the vertical direction is inverted.
Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution
1998
This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of firs…
Analysis of the XENON100 dark matter search data
2014
The XENON100 experiment, situated in the Laboratori Nazionali del Gran Sasso, aims at the direct detection of dark matter in the form of weakly interacting massive particles (WIMPs), based on their interactions with xenon nuclei in an ultra low background dual-phase time projection chamber. This paper describes the general methods developed for the analysis of the XENON100 data. These methods have been used in the 100.9 and 224.6 live days science runs from which results on spin-independent elastic, spin-dependent elastic and inelastic WIMP-nucleon cross-sections have already been reported.
Weak convergence to the coalescent in neutral population models
1999
For a large class of neutral population models the asymptotics of the ancestral structure of a sample of n individuals (or genes) is studied, if the total population size becomes large. Under certain conditions and under a well-known time-scaling, which can be expressed in terms of the coalescence probabilities, weak convergence in D E ([0,∞)) to the coalescent holds. Further the convergence behaviour of the jump chain of the ancestral process is studied. The results are used to approximate probabilities which are of certain interest in applications, for example hitting probabilities.
A comparative evaluation: Oral leukoplakia surgical management using diode laser, CO2 laser, and cryosurgery
2017
Background The comparatively evaluate the three surgical treatment modalities namely cryosurgery, diode and CO2 laser surgery in terms of healing outcomes on the day of surgery, first and second week post operatively and recurrence at the end of 18 months was assessed. Material and methods Thirty selected patients were divided randomly into three groups. Each group comprising of ten patients were subjected to one of the three modalities of treatment namely cryosurgery, diode laser or CO2 laser surgery for ablation of OL. Obtained data was analyzed using mainly using Chi-square and Anova tests. Results Study showed statistical significant differences (p > 0.05) for evaluation parameters like…
Observability of the Risken–Nummedal–Graham–Haken instability in Nd:YAG lasers
2003
Multilongitudinal mode instability in ring Nd:YAG lasers is theoretically analyzed. After we review the way in which the standard two-level laser theory applies to this laser we extend the theoretical treatment to include transverse effects. We do this by taking into account the finite transverse section of the active medium and by assuming a Gaussian transverse distribution for the intracavity field. Finally we demonstrate that multimode emission develops whenever the intracavity field waist diameter is almost equal to the active rod diameter. We conclude that continuous-wave diode-pumped Nd:YAG lasers with low cavity losses are good candidates for the observation of the Risken–Nummedal–Gr…
The Heisenberg dynamics of spin systems: A quasi*‐algebras approach
1996
The problem of the existence of the thermodynamical limit of the algebraic dynamics for a class of spin systems is considered in the framework of a generalized algebraic approach in terms of a special class of quasi*-algebras, called CQ*-algebras. Physical applications to (almost) mean-field models and to bubble models are discussed. © 1996 American Institute of Physics.
Unusual finite size effects in the Monte Carlo simulation of microphase formation of block copolymer melts
1995
Extensive Monte Carlo simulations are presented for the Fried-Binder model of block copolymer melts, where polymer chains are represented as self and mutually avoiding walks on a simple cubic lattice, and monomer units of different kind (A, B) repel each other if they are nearest neighbors (e AB > O). Choosing a chain length N = 20, vacancy concentration Φ v = 0,2, composition f = 3/4, and a L × L × L geometry with periodic boundary conditions and 8 ≤ L ≤ 32, finite size effects on the collective structure factor S(q) and the gyration radii are investigated. It is shown that already above the microphase separation transition, namely when the correlation length ζ(T) of concentration fluctuat…
Discrete KP Equation and Momentum Mapping of Toda System
2003
Abstract A new approach to discrete KP equation is considered, starting from the Gelfand-Zakhharevich theory for the research of Casimir function for Toda Poisson pencil. The link between the usual approach through the use of discrete Lax operators, is emphasized. We show that these two different formulations of the discrete KP equation are equivalent and they are different representations of the same equations. The relation between the two approaches to the KP equation is obtained by a change of frame in the space of upper truncated Laurent series and translated into the space of shift operators.
Mixed Phases, Phase Transitions, Stability of Matter
2016
Phase mixtures and phase transitions are two major themes of thermodynamics. A third one, related to the former, is the stability of macroscopic matter around us. Mixed phases can be analyzed and illustrated in a nice geometric way. Phase transitions are dealt with from the point of view of classical thermodynamics as well as in the framework of models of statistical mechanics.