From trees to galaxies: The Potts model on a random surface

The matrix model of random surfaces with c = ∞ has recently been solved and found to be identical to a random surface coupled to a q-states Potts model with q = ∞. The mean field-like solution exhibits a novel type of tree structure. The natural question is, down to which—if any—finite values of c and q does this behavior persist? In this work we develop, for the Potts model, an expansion in the fluctuations about the q = ∞ mean field solution. In the lowest—cubic—non-trivial order in this expansion the corrections to mean field theory can be given a nice interpretation in terms of structures (trees and “galaxies”) of spin clusters. When q drops below a finite q_c, the galaxies overwhelm the trees at all temperatures, thus suppressing mean field behavior. Thereafter the phase diagram resembles that of the Ising model, q = 2.     

Noise generation by instabilities in low Reynolds number supersonic jets

An experimental investigation of noise generation by instabilities in low Reynolds number supersonic air jets has been performed. Sound pressure levels, spectra and acoustic phase fronts were measured with a traversing condenser microphone in the acoustic field of axisymmetric, perfectly expanded, cold jets of Mach numbers 1·4, 2·1 and 2·5. Low Reynolds numbers in the range from Re = 3700 to Re = 8700 were obtained by exhausting the jets into an anechoic vacuum chamber test facility. This contrasts with Reynolds numbers of over 10⁶ for similar jets exhausting into atmospheric pressure. The flow fluctuations of the instability in all three jets have been measured with a hot-wire and the results are documented in a previous paper by Morrison and McLaughlin. Acoustic measurements show that the major portion of the sound radiated by all three jets is produced by the instability's rapid growth and decay that occurs near the end of the potential core. This takes place over a relatively short distance (less than two wavelengths of the instability) in the jet. In the lower two Mach number jets the instability has a phase velocity less than the ambient acoustic velocity. In the Mach number 2·5 jet the instability phase speed is 1·11 times the ambient acoustic velocity. In this case the acoustic phase fronts indicate the possibility of a Mach wave component. It was also determined that low level excitation at the dominant frequency of the instability actually decreased the radiated noise by suppressing the broad band component.     

Scale for the Production of Jets in High Energy e+e－ Collisions

The scale for visible jets produced in e⁺e^－ Collisions is studied in some details using Monte Carlo method. It is demonstrated, based on the historical fact that the 3-jet events were firstly observed in e+ e- experiments at √S=17—30GeV,and the relative transverse momentum for visible jets is in the region k_t,～5—10GeV/c. It is further shown, using a concrete example, that the number of jets in an event could be correctly evaluated only when k_t is in this region. The dynamical fluctuations inside jets determined through different values of k_t are compared carefully. It turns out that only when k_t,～5—10GeV/c the dynamical fluctuations inside jets will possess the best anomalous scaling property. The relation between the scale 5-10GeV/c of visible jets and the scale 1-2GeV of perturbative QCD is discussed.     

Settling statistics of hard sphere particles

Direct imaging of settling, non-Brownian, hard sphere, particles allows measurement of particle occupancy statistics as a function of time and sampling volume dimension. Initially random relative particle number fluctuations, (2)>/ = 1, become suppressed, anisotropic, and dependent. Fitting to a simple Gaussian pair correlation model suggests a minute long ranged correlation leads to strong if not complete suppression of number fluctuations. Calflisch and Luke predict a divergence in velocity fluctuations with increasing sample volume size based on random (Poisson) statistics. Our results suggest this is not a valid assumption for settling particles.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Etude numérique des jets turbulents à température élevée

Numerical prediction of the structure of high temperature axisymmetric turbulent jets. Turbulent axisymmetric jets at high temperature are studied numerically by using first and second order turbulence models. Regarding the temperature fields, on which we concentrate in this work, predictions with both types of models do not show large differences. In general, predictions agree well with the measurements; the existing differences are usually favorable for the second order model. The effect of solving a transport equation for the scalar dissipation rate on the prediction of the mechanical to scalar time scale ratio and on the prediction of the scalar fluctuations is studied. The influence of varying the density ratio on parameters such as the axial decay rates of the temperature and velocity and the turbulence intensity are studied. Two definitions of the mixing efficiency are introduced. According to both definitions, the mixing efficiency decreases with increasing effects of buoyancy.     

旋流燃烧室内颗粒运动的数值模拟

本文应用流体相湍流脉动速度大小和方向均具有随机性的颗粒相随机轨道模型,对有直流一次风和旋流二次风的旋流燃烧室内的颗粒运动进行了数值模拟。得到的颗粒相轴向总质量流通量、轴向与切向速度分布与实验测量数据相符合,并比 Gosman 颗粒随机轨道模型的模拟结果有一定的改进。     

Effect of internal waves on intrusions in a thermocline and on upwelling

Results of the investigation into the interaction of internal waves and flows and the elaboration of a relevant mathematical model are reported. It is found in the field experiments that internal waves develop against the background of upwelling, which results in formation of jets causing intrusion velocity fluctuations. The mechanism and mathematical model of this process are proposed. A mathematical model of the suspended matter transport by jets with a wave-modulated trajectory is developed and verified.     

The PMD of sinusoidally spun fibers in the presence of random birefringence perturbations

Although fiber spinning is known to reduce polarization mode dispersion (PMD) effects in optical fibers, relatively few studies have been performed of the dependence of the reduction factor on the strength of random birefringence fluctuations. In this paper, we apply a general mathematical model of random fiber birefringence to sinusoidally spun fibers. We find that while even in the presence of random birefringence perturbations the maximum reduction of PMD is still obtained when the phase matching condition is satisfied, the degree of PMD reduction and the probability distribution function of the DGD both vary with the random birefringence profiles.     

Intermittency and small scale resummation

A method of sampling fluctuations in sub-dimensional phase space of (possibly fractal) dimensionD is proposed. Applied to random cascading models of multi-particle production, it gives aD-dependent nonlinear equation for the generating function of particle multiplicities in the sub-domain, whose solutions lead to new properties, e.g. the correction effects of very small scale ressumations on the generic intermittent fluctuations of the model, the unexpected possibility of non vanishing intermittency after dimensional projection and the connection of KNO scaling violations with a structural phase transition. A phenomenological discussion of \(\bar p\) p SPS data allows one to exhibit a simple fragmentation model describing both local and global multiplicity fluctuations observed in these reactions, and compare it with theoretical gluon cascading.     

A stochastic model of the influence of buffer gas collisions on Mollow spectra

In this paper, using the idea introduced in (K. Wódkiewicz, Noise in strong laser-atom interaction, Proceedings of the VI International School of Coherent Optics, Ustron, Poland, September (1985) 19–26) and developed in (Cao Long Van, Stochastic Models of Isolated Collisions: Applications to Optical Phenomena, paper presented in LAMP Conference’89, Trieste, Italy (1989) II) we consider the influence of collisional fluctuations on the Mollow spectra of resonance fluorescence (RF). The fluctuations are taken into account by a simple shift of the constant detuning, involved in a set of optical Bloch equations by collision frequency noise which is modelled by a two-step random telegraph signal (RTS). We consider in detail the Mollow spectra for RF in the case of an arbitrary detuning of the laser frequency, where the emitter is a member of a statistical ensemble in thermodynamic equilibrium with the buffer gas at temperature T which is treated as a colored environment, and velocity v is distributed with the Maxwell-Boltzmann density.     

Corrected Mean-Field Model for Random Sequential Adsorption on Random Geometric Graphs

A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the d-dimensional Euclidean space with \(d\ge 2\). Spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres. Due to spatial correlations, characterizing the fraction of accepted spheres remains largely intractable. We study this fraction by taking a novel approach that compares random sequential adsorption in Euclidean space to the nearest-neighbor blocking on a sequence of clustered random graphs. This random network model can be thought of as a corrected mean-field model for the interaction graph between the attempted spheres. Using functional limit theorems, we characterize the fraction of accepted spheres and its fluctuations.     

A new model of quantum chaotic billiards: application to granular metals

We discuss the properties of a recently proposed model of quantum chaotic billiards in two and three dimensions. The model is based on a tight-binding Hamiltonian in which the energies of the atomic levels at the boundary sites are chosen at random between -W/2 and W/2. The energy spectra show a complex behavior with regions that obey Wigner-Dyson statistics, and regions with localized and quasi-ideal states distributed according to Poisson statistics. Whereas at low energies long-range energy fluctuations follow Random Matrix Theory (RMT) for all W, at high energies fluctuations are below (above) RMT for small (large) W. For small W, the mean free path l is proportional to L/W ², L being the system size, and reaches a minimum for W of the order of the band width, at which l ≈ L/2. In 3D we found that the energy fluctuations of the highest occupied level are much larger than the average interlevel spacing. This provides an explanation for autoionization effects of the grains in granular metals.     

Radiative noise in circuits with inductance

Using the general idea of the fluctuation–dissipation theorem we study a new contribution to the voltage fluctuations which is associated with the presence of radiation resistance. We consider the particular case of a solenoid immersed in a cavity with equilibrium radiation at temperature T. We prove that these new fluctuations are generated by the random magnetic field present in the cavity. These magnetic voltage fluctuations are shown to be experimentally distinguishable from the voltage fluctuations associated with the well known Nyquist noise. Accordingly we suggest feasible experiments to measure this magnetic noise. All the calculations are made within the context of Stochastic Electrodynamics, a theory in which the vacuum zero-point field is taken as a real electromagnetic field. We also study the average energy of an RLC circuit in thermodynamic equilibrium with the radiation.     

Ericson fluctuations and the distribution of randomS-matrix elements

Starting from a random matrix model for nuclear reactions, we show that the fluctuatingS-matrix elements in general have a non-gaussian distribution. The consequences of this for Ericson fluctuations are pointed out. In the absence of direct reactions symmetry properties of the distribution function lead to simple expressions for the cross section correlation functions. In particular a formula for calculating the cross section auto-correlation function is presented.     

Trapping in the Random Conductance Model

We consider random walks on ? ^d among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time 2n. We show that in the situations when the heat kernel exhibits subdiffusive decay—which is known to occur in dimensions d≥4—the walk gets trapped for a time of order n in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.     

The High Temperature Region of the Viana–Bray Diluted Spin Glass Model

In this paper, we study the high temperature or low connectivity phase of the Viana–Bray model in the absence of magnetic field. This is a diluted version of the well known Sherrington–Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a complete control of the system, proving annealing for the infinite volume free energy and a central limit theorem for the suitably rescaled fluctuations of the multi-overlaps. Moreover, we show that free energy fluctuations, on the scale 1/N, converge in the infinite volume limit to a non-Gaussian random variable, whose variance diverges at the boundary of the replica-symmetric region. The connection with the fully connected Sherrington– Kirkpatrick model is discussed.     

Phase diagram of randomly polymerized membrane

Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. Received: 3 December 1997 / Revised: 31 March 1998 / Accepted: 3 August 1998