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Articles 1 - 27 of 27
Full-Text Articles in Physical Sciences and Mathematics
Phase Transition And Surface Sublimation Of A Mobile Potts Model, A. Bailly Reyre, H. T. Diep, M. Kaufman
Phase Transition And Surface Sublimation Of A Mobile Potts Model, A. Bailly Reyre, H. T. Diep, M. Kaufman
Miron Kaufman
We study in this paper the phase transition in a mobile Potts model by the use of Monte Carlo simulation. The mobile Potts model is related to a diluted Potts model, which is also studied here by a mean-field approximation. We consider a lattice where each site is either vacant or occupied by a q-state Potts spin. The Potts spin can move from one site to a nearby vacant site. In order to study the surface sublimation, we consider a system of Potts spins contained in a recipient with a concentration c defined as the ratio of the number of …
Moffatt Eddies In The Single Screw Extruder: Numerical And Analytical Study, Petru S. Fodor, Miron Kaufman
Moffatt Eddies In The Single Screw Extruder: Numerical And Analytical Study, Petru S. Fodor, Miron Kaufman
Miron Kaufman
A detailed analysis of the fluid flow in the single screw extruder is performed by combining numerical and analytical methods. While finite element analysis numerical models are used to extract the transversal velocity field, an analytical model in the limit of zero Reynolds numbers is used to determine the longitudinal component of the fluid velocities. The high resolution 3D model developed for the fluid flow in single screw extruders with aspect ratios (i.e. depth/width) ranging from 1 to 0.1, allows the identification of the position and extent of Moffatt eddies that impede the fluid mixing through the entire extruder’s volume. …
Garma Toolbox For Matlab, Mehdi Jalalpour
Potts–Percolation–Gauss Model Of A Solid, Miron Kaufman, H T. Diep
Potts–Percolation–Gauss Model Of A Solid, Miron Kaufman, H T. Diep
Miron Kaufman
We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookean springs. If the energy is larger than a threshold the spring is more likely to fail, while if the energy is lower than the threshold the spring is more likely to survive. The phase diagram and thermodynamic quantities, such as free energy, numbers of bonds and clusters, and their fluctuations, are determined using renormalization group and Monte Carlo techniques.
The Appearance, Apparent Speed, And Removal Of Optical Effects For Relativistically Moving Objects, Robert J. Deissler
The Appearance, Apparent Speed, And Removal Of Optical Effects For Relativistically Moving Objects, Robert J. Deissler
Robert J. Deissler
Because various parts of an object are different distances from an observer, and light takes a finite time to reach the observer, the appearance of a relativistically moving object will be very different from that given by the Lorentz contraction. We derive equations that can be applied to a photographic image so that the Lorentz contraction can still be observed. We also give equations that quantify the apparent deformation of the object and plots that show the apparent speed of the object as a function of time. In particular, as an object approaches, its apparent speed can be much greater …
A Simple Demonstration Of Mie Scattering Using An Overhead Projector, Charles L. Adler, James A. Lock
A Simple Demonstration Of Mie Scattering Using An Overhead Projector, Charles L. Adler, James A. Lock
James A. Lock
No abstract provided.
A Thermodynamic Model For Pressurized Solids, Miron Kaufman, Herbert Schlosser
A Thermodynamic Model For Pressurized Solids, Miron Kaufman, Herbert Schlosser
Miron Kaufman
A thermodynamic model for solids under pressure is developed by assuming the universal equation of state and that under zero pressure the free energy is equal to the harmonic crystal (Debye) free energy. The model is applied to gold. In the case of nanocrystals this model reproduces the observed enhancement of the isobaric heat capacity and of the thermal expansion. Our model calculations are free of the ambiguities and inconsistencies connected with the Gruneisen equation, which was used in previous theoretical work.
Renormalization-Group Analysis Of Heat Capacity Amplitude, Scott I. Chase, Miron Kaufman
Renormalization-Group Analysis Of Heat Capacity Amplitude, Scott I. Chase, Miron Kaufman
Miron Kaufman
Critical amplitudes A+ associated with the temperature variation of the heat capacity are analyzed by means of renormalization-group techniques in both position and momentum spaces. We describe a mechanism according to which the amplitudes A diverge as the critical exponent a approaches a nonpositive integer. In between two consecutive divergences at least one amplitude vanishes at least once. The coefficient P in the expansion A+ /A- =1—Pa+0 (a~) is computed by means of e expansion and Migdal-Kadanoff renormalization-group technique. Systems for which the critical exponent alpha is negative but larger than —1 exhibit either a cusped heat capacity if A+/A- …
N-Color Spin Models In The Large N Limit, Mehran Kardar, Miron Kaufman
N-Color Spin Models In The Large N Limit, Mehran Kardar, Miron Kaufman
Miron Kaufman
N color spin models are introduced and examined in the large N limit. The free energy and critical properties at the phase transition are studied. With relevant couplings between colors the transition becomes either first order or Fisher renormalized. With irrelevant couplings there is a crossover to first-order transitions through a nonclassical tricritical point. Connections are established between the N-color model, compressible systems, and systems with random impurities.
Random-Field Critical Behavior And The Ginzburg Criterion, Miron Kaufman, Mehran Kardar
Random-Field Critical Behavior And The Ginzburg Criterion, Miron Kaufman, Mehran Kardar
Miron Kaufman
The Ginzburg criterion for crossover from classical to nonclassical critical behavior is derived in the presence of random fields. Experiments on dilute antiferromagnets in a field are examined, and the possibility of such a crossover is investigated. We also point out that the (necessarily) symmetric logarithmic divergence observed in birefringence measurements can be accompanied by a discontinuity, and a fitting form which allows for this and other corrections to scaling is proposed.
Comment On Aproaches To The Tricritical Point In Quasibinary Liquid Mixtures, Miron Kaufman, Robert B. Griffiths
Comment On Aproaches To The Tricritical Point In Quasibinary Liquid Mixtures, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
No abstract provided.
Pseudodimensional Variation And Tricriticality Of Potts Models By Hierarchical Breaking Of Translational Invariance, Miron Kaufman, Mehran Kardar
Pseudodimensional Variation And Tricriticality Of Potts Models By Hierarchical Breaking Of Translational Invariance, Miron Kaufman, Mehran Kardar
Miron Kaufman
Potts models with equivalent- and nearest-neighbor interactions are solved exactly on Cayley trees. A parameter D is identified that plays a role similar to the spatial dimension on Bravais lattices. Breaking translational symmetry by the Cayley-tree hierarchy reduces D, leading to a changeover in the order of the phase transition via a novel tricritical point.
Spin Systems On Hierarchical Lattices. Ii. Some Examples Of Soluble Models, Miron Kaufman, Robert B. Griffiths
Spin Systems On Hierarchical Lattices. Ii. Some Examples Of Soluble Models, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
Several examples are given of soluble models of phase-transition phenomena utilizing classical discrete spin systems with nearest-neighbor interaction on hierarchical lattices. These include critical exponents which depend continuously on a parameter, the Potts model on a lattice with two different coupling constants, surface tension, and excess free energy of a line of defects. In each case we point out similarities and differences with a corresponding Bravais-lattice model.
Duality And Potts Critical Amplitudes On A Class Of Hierarchical Lattices, Miron Kaufman
Duality And Potts Critical Amplitudes On A Class Of Hierarchical Lattices, Miron Kaufman
Miron Kaufman
By using the duality transformation on a class of hierarchical lattices, I show that the Potts critical amplitudes above and below the critical temperature are equal. Logarithmic modifications of the power-law singularity occur when the exponent 2—alpha is an even integer, but do not occur when 2—alpha equals an odd integer.
Short-Range And Infinite-Range Bond Percolation, Miron Kaufman, Mehran Kardar
Short-Range And Infinite-Range Bond Percolation, Miron Kaufman, Mehran Kardar
Miron Kaufman
A method for generalizing bond-percolation problems to include the possibility of infinite-range (equivalent-neighbor) bonds is presented. On Bravais lattices the crossover from nonclassical to classical (mean-field) percolation criticality in the presence of such bonds is described. The Cayley tree with nearest-neighbor and equivalent-neighbor bonds is solved exactly, and a nonuniversal line of percolation transitions with exponents dependent on nearest-neighbor bond occupation probability is observed. Points of logarithmic and exponential singularity are also encountered, and the behavior is interpreted as dimensional reduction due to the breaking of translational invariance by bonds of Cayley-tree connectivity.
Critical Amplitude Of The Potts Model: Zeroes And Divergences, Miron Kaufman, David Andelman
Critical Amplitude Of The Potts Model: Zeroes And Divergences, Miron Kaufman, David Andelman
Miron Kaufman
The critical amplitude of the q-state Potts-model free energy is studied as a function of q in two dimensions and on the diamond hierarchical lattice. The amplitude diverges at an infinite number of q values, qn,introducing logarithmic terms in the free energy. We expect that in each interval (qn,qn+1) there is a q value where the amplitude vanishes, affecting the singularity of the free energy as a function of temperature. Possible consequences for gelation and vulcanization of polymers are discussed.
Comment On Criticality Of The Anisotropic Quantum Heisenberg Model On A Self-Dual Hierarchical Lattice, Miron Kaufman, Mehran Kardar
Comment On Criticality Of The Anisotropic Quantum Heisenberg Model On A Self-Dual Hierarchical Lattice, Miron Kaufman, Mehran Kardar
Miron Kaufman
No abstract provided.
Realizable Renormalization Group And Finite-Size Scaling, Miron Kaufman, K. K. Mon
Realizable Renormalization Group And Finite-Size Scaling, Miron Kaufman, K. K. Mon
Miron Kaufman
We propose a sequence of renormalization-group transformations which are exact on hierarchical lattices and we argue, by employing finite-size scaling, that the corresponding sequence of critical exponents converges towards the exact values associated with a Bravais lattice. A test of this method is also presented.
Convexity Of The Free Energy In Some Real-Space Renormalization-Group Approximations, Miron Kaufman, Robert B. Griffiths
Convexity Of The Free Energy In Some Real-Space Renormalization-Group Approximations, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
Whereas the free energy for a spin system in a hierarchical lattice will be convex as a function of appropriate parameters (and thus the heat capacity positive, etc.), the same need not be true of a corresponding approximate real-space renormalization-group method applied to a Bravais lattice. Some examples are given which illustrate this point.
Competing Criticality Of Short- And Infinite-Range Interactions On The Cayley Tree, Mehran Kardar, Miron Kaufman
Competing Criticality Of Short- And Infinite-Range Interactions On The Cayley Tree, Mehran Kardar, Miron Kaufman
Miron Kaufman
The Ising model, with equivalent-neighbor and nearest-neighbor interactions of Cayley tree connectivity, is solved exactly. Breaking translational symmetry by turning on the Cayley interactions is analogous to lowering spatial dimensionality in Bravais lattices. A range of classical criticality, a point of logarithmic corrections, a range of continuously varying power-law singularities, and a point of exponential singularity are successively encountered.
Spin Systems On Hierarchical Lattices. Introduction And Thermodynamic Limit, Robert B. Griffiths, Miron Kaufman
Spin Systems On Hierarchical Lattices. Introduction And Thermodynamic Limit, Robert B. Griffiths, Miron Kaufman
Miron Kaufman
A number of exactly soluble models in statistical mechanics can be produced with the use of spins interacting with nearest neighbors on a hierarchical lattice. A general definition and several examples of such lattices are given, and the topological properties of one of these, the "diamond" lattice, are discussed in detail. It is shown that the free energy has a well-defined thermodynamic limit for a large class of discrete spin models on hierarchical lattices.
First-Order Transitions In Defect Structures At A Second-Order Critical Point, Miron Kaufman, Robert B. Griffiths
First-Order Transitions In Defect Structures At A Second-Order Critical Point, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
On certain hierarchical lattices the order parameter on a defect line increases discontinuously at the bulk critical temperature for q-state Potts models when q is sufficiently large, even though the bulk order parameter increases continuously. It is suggested that the same behavior may occur for two-dimensional lattices with 2 < q <= 4.
Thermodynamic Model For Tricritical Mixtures With Application To Ammonium, Miron Kaufman, Robert B. Griffiths
Thermodynamic Model For Tricritical Mixtures With Application To Ammonium, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
Procedures are developed for using composition data in the three-phase region and variations of meniscus heights to determine the parameters needed to relate a classical thermodynamic model for fluid mixtures near tricritical points to actual experiments. In the case of the mixture ammonium sulfate + water + ethanol + benzene the result is a reasonably good fit to a variety of data, including light scattering measurements of intensity and correlation length. There is some evidence for deviations from the classical theory, but it is not unambiguous.
Infinite Susceptibility At High Temperatures In The Migdal-Kadanoff Scheme, Miron Kaufman, Robert B. Griffiths
Infinite Susceptibility At High Temperatures In The Migdal-Kadanoff Scheme, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
The Migdal-Kadanoff real-space renormalisation group scheme applied to the Ising and classical XY (and probably other) ferromagnetic models yields an infinite susceptibility at all temperatures above the critical temperature for a hypercubic lattice of dimension d > 2.
Exactly Soluble Ising Models On Hierarchical Lattices, Miron Kaufman, Robert B. Griffiths
Exactly Soluble Ising Models On Hierarchical Lattices, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
Certain approximate renormalization-group recursion relations are exact for Ising models on special hierarchical lattices, as noted by Berker and Ostlund. These lattice models provide numerous examples of phase coexistence and critical points at finite temperatures, including cases of continuously varying critical exponents and phase transitions without phase coexistence. The lattices are, typically, quite inhomogeneous and may possess several inequivalent limits as infinite lattices.
Three-Component Model And Tricritical Points: A Renormalization-Group Study., Miron Kaufman, Robert B. Griffiths, Julia M. Yeomans, Michael E. Fisher
Three-Component Model And Tricritical Points: A Renormalization-Group Study., Miron Kaufman, Robert B. Griffiths, Julia M. Yeomans, Michael E. Fisher
Miron Kaufman
The global phase diagram for a three-component lattice gas or spin-one Ising model with general single-site and nearest-neighbor "ferromagnetic" interactions is worked out for twodimensional lattices using a Migdal-Kadanoff recursion relation. It differs in important qualitative respects from the corresponding mean-field phase diagram. The set of fixed points and flows provides the characteristic'phase diagrams of the three-state Potts multicritical point and the ordinary (n =1) tricritical point in a complete set of symmetry-breaking fields. The latter is associated, in this renormalization-group scheme, with seven distinct critical fixed points, a number which is surprisingly large.
Thermodynamic Model And Sum Rules For Three-Phase Coexistence Near Thetricritical Point In A Liquid Mixture, Miron Kaufman, K. K. Bardhan, Robert B. Griffiths
Thermodynamic Model And Sum Rules For Three-Phase Coexistence Near Thetricritical Point In A Liquid Mixture, Miron Kaufman, K. K. Bardhan, Robert B. Griffiths
Miron Kaufman
Two sum rules for order-parameter susceptibilities are derived for the classical theory of the three-phase region near a tricritical point in ordinary liquid mixtures. The classical theory can also be fitted in a quantitative way to the composition data of Lang and Widom near the tricritical point in the mixture ethanol+ benzene+ water + ammonium sulfate.