Statistical mechanics of probabilistic cellular automata

We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on ^d and translation-invariant Gibbs states for a related Hamiltonian on ( ^d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs.     

Statistical mechanics of the nonlinear Schrödinger equation

We investigate the statistical mechanics of a complex fieldø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian $$H(\phi ) = \int_\Omega {[\frac{1}{2}|\nabla \phi |^2 - (1/p) |\phi |^p ] dx}$$ is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, whenΩ is the circle and theL ² norm of the field (which is conserved by the dynamics) is bounded byN, the Gibbs measureυ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only ifp andN are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, asN and the temperature are varied.     

Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S¹. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H¹(S¹), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then lim_tT* w(t,·) exists in C¹(S¹) but vanishes at some point. We show further that if T* > (1 + √3)/16π² √3 then T* = ∞ and lim_t∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.     

Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

Evaluation of matrix effects in different multipesticide residue analysis methods using liquid chromatography–tandem mass spectrometry,including an automated two‐dimensional cleanup approach

Pesticide residue analysis is an important part of food quality control. Three of the most widely used methods are the DFG S19 (extraction with acetone), the ChemElut method (extraction with methanol), and QuEChERS (quick, easy, cheap, effective, rugged, safe; acetonitrile‐based). Despite many developments in the field of sample preparation, matrix effects are still one of the most disturbing problems in routine analysis. In this study, we compare the matrix effects in LC–MS analysis after using these three methods in pesticide analysis. Using postcolumn infusion, we were able to visualize all suppressions over the whole chromatogram in matrix‐effect profiles. Recently, we also presented a system for the determination of up to 300 pesticides from various kinds of fruit and vegetables. For the measurement, we injected an aliquot of a raw acetonitrile extract. The subsequent cleanup was carried out fully automated by a multidimensional LC. Matrix compounds and analytes are separated in the first dimension on a hydrophilic interaction LC column. In this study, we also compared this new approach with the classical methods. The matrix‐effect profiles showed less suppression with the hydrophilic interaction LC‐based cleanup. A final evaluation of the partitioning steps of all methods confirmed the benefits of the chromatographic cleanup approach.     

On the structure of analytic renormalization

A direct proof is given that analytic renormalization has an additive structure and hence may be implemented by counterterms in the Lagrangian.     

Exact free energy functional for a driven diffusive open stationary nonequilibrium system

We obtain the exact probability exp[-LF([rho(x)])] of finding a macroscopic density profile rho(x) in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system L-->infinity. F, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, F is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in nonconvexity of F, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.     

Electron density decay measurements using the 447.1 nm line of neutral helium

The 447.1 nm line of neutral helium has been used to measure the time-dependent decay of the electron density in the afterglow of a pulsed, atmospheric pressure helium discharge. The technique involves using a shutter which consists of a Pockels cell combined with crossed polarizers to gate the light pulse, allowing observation of the spectrum during various time windows in the discharge.     

Operating characteristics and modeling of the LLNL 100-kV electricgun

In the electric gun, the explosion of an electrically heated metal foil and the accompanying magnetic forces drive a thin flyer plate up a short barrel. Flyer velocities of up to 18 km/s make the gun useful for hypervelocity impact studies. The authors review the technological evolution of the exploding-metal circuit elements that power the gun, describe the 100-kV electric gun designed at Lawrence Livermore National Laboratory (LLNL) in some detail, and present the general principles of electric gun operation. They compare the experimental performance of the LLNL gun with a simple model and with predictions of a magnetohydrodynamics code     

Simultaneous analysis of 70 pesticides using HPlc/MS/MS: a comparison of the multiresidue method of Klein and Alder and the QuEChERS method

Since 2003, two new multipesticide residue methods for screening crops for a large number of pesticides, developed by Klein and Alder and Anastassiades et al. (Quick, Easy, Cheap, Effective, Rugged, and Safe; QuEChERS), have been published. Our intention was to compare these two important methods on the basis of their extraction efficiency, reproducibility, ruggedness, ease of use, and speed. In total, 70 pesticides belonging to numerous different substance classes were analyzed at two concentration levels by applying both methods, using five different representative matrixes. In the case of the QuEChERS method, the results of the three sample preparation steps (crude extract, extract after SPE, and extract after SPE and acidification) were compared with each other and with the results obtained with the Klein and Alder method. The extraction efficiencies of the QuEChERS method were far higher, and the sample preparation was much quicker when the last two steps were omitted. In most cases, the extraction efficiencies after the first step were approximately 100%. With extraction efficiencies of mostly less than 70%, the Klein and Alder method did not compare favorably. Some analytes caused problems during evaluation, mostly due to matrix influences.