Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.     

Space use by foragers consuming renewable resources

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: (i) the high-order moments, ?x(t) ^q ? for q > 2 and the probability density of the process exhibit multiscaling; (ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; (iii) positive order moments satisfying standard scaling does not imply an exact scaling property of the probability density.     

Numerical analysis of the twisted Eguchi-Kawai model in four dimensions

We perform a high statistics Monte Carlo calculation of the string tension in the twisted SU(N) Eguchi-Kawai model for N=36 and N=64. The string tension, calculated from Wilson loops not larger than 3 × 3, clearly shows the renormalization group scaling behaviour.     

Implications of nanoparticle concentration and size distribution in the superparamagnetic behaviour of aging-improved maghemite xerogels

Evolution of static magnetic properties of a set of enhanced γ-Fe₂O₃/SiO₂ nanocomposites with different iron concentration has been studied on the basis of their corresponding hysteresis loops, zero-field/field-cooled (ZFC/FC) magnetization curves and transmission electron microscopy images. The lack of coercivity in all compositions, as well as the fulfillment of the H/T scaling law by the magnetization above the blocking temperature of each system under study, evidence a superparamagnetic behaviour in the iron oxide nanoparticles. In order to study the influence of iron content in the unblocking processes of nanoparticles, ZFC curves under different applied magnetic fields have been fitted to a model considering the systems under study as a distribution of energy barriers. Depart from the superparamagnetic model is discussed considering interparticle interactions.     

缺陷对滞后标度性的影响

对二维Ising铁磁系统中的非磁杂质，利用Monte Carlo方法，获得不同杂质浓度、不同磁场变化速率下的磁滞(?)线，从而得到滞后(?)线面积与磁场变化速率的关系．结果表明，在温度和缺陷浓度组成的相图上，存在一条相变线．低温和低浓度时，(?)线面积与磁场速率的标度指数约为1/3，只微弱地依赖于温度及杂质浓度；而对高温和高浓度的杂质，指数强烈地依赖于温度和浓度 关键词：     

Scaling laws of nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities in two and three dimensions

The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers ( A ) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h∼α·A·gt² with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h∼t^θ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin–Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.     

Advection of a passive vector field by the Gaussian velocity field with finite correlations in time

Using the field theoretic renormalization group technique the model of a passive vector field advected by an incompressible turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation). The turbulent environment is given by statistical fluctuations of the velocity field that has a Gaussian distribution with zero mean and defined noise with finite correlations in time. Two-loop analysis of all possible scaling regimes in general d-dimensional space is done in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∝ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that the scaling regimes of the present model of vector advection have essentially different properties than the scaling regimes of the corresponding model of passively advected scalar quantity. The results demonstrate the fact that within the present model of passively advected vector field the internal tensor structure of the advected field can have nontrivial impact on the diffusion processes deep inside in the inertial interval of given turbulent flow.     

Nuclear incompressibility: From finite nuclei to nuclear matter

The recent increase of experimental data concerning the giant monopole resonance energy E_M gives information on the incompressibility modulus of nuclear matter, provided one can extrapolate the incompressibility of a nucleus K_A, defined by $\text{E}{}_{\mathrm{<mtext>M</mtext>}}\text{=[}\text{h}\text{?}{}^2\text{K}{}_{\mathrm{<mtext>A</mtext>}}\text{/m〈r}{}^2\text{〉]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, to the infinite medium. We discuss the theoretical interpretation of the coefficients of an $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ expansion of K_A by studying the asymptotic behaviour of two RPA sum rules (corresponding to the scaling and the constrained model), evaluated using self-consistent Thomas-Fermi calculations. We show that the scaling model is the most suitable one as it leads to a rapidly converging $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ expansion of the corresponding incompressibility K_A^s, whereas this is not the case with the constrained model. Some semi-empirical relations between the coefficients of the expansion of K_A^s are established, which reduce to one the number of free parameters in a best-fit analysis of the experimental data. This reduction is essential due to the still limited number and accuracy of experimental data. We then show the compatibility of the data given by the various experimental groups with this parametrization and obtain a value of K_n.m. = 220 ± 20 MeV, in good agreement with more microscopic analyses.     

The Feynman Propagator on Perturbations of Minkowski Space

The singular values squared of the random matrix product \({Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}\), where each \({G_{j}}\) is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of \({0 < b < 1}\) is independent of b, and is in fact the same as that known for the case b =  0 due to Kuijlaars and Zhang. The critical regime of b =  1 allows for a double scaling limit by choosing \({{b = (1 - \tau/\sqrt{N})^{-1}}}\), and for this the critical kernel and outlier phenomenon are established. In the simplest case r =  0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of \({b > 1}\) with two distinct scaling rates. Similar results also hold true for the random matrix product \({T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}\), with each \({T_{j}}\) being a truncated unitary matrix.     

Population dynamics of the ions SVI, ClVII and ArVIII interacting with solid surfaces

We used the recently developed time-symmetrized, two-state vector model to investigate the intermediate stages of the electron capture into the Rydberg states (n_A?1,l_A=0−3, m_A=0) of multiply charged ions SVI, ClVII and ArVIII, with polarized core charges Z=6, 7 and 8, respectively, escaping solid surfaces at low velocities. Within the framework of the model, the two wave functions are used to describe the system at intermediate stages; the corresponding probabilities and rates are based on the calculation of the mixed flux. The simple analytical formulae derived for the neutralization rates enable us to analyze the localization of the process and to calculate the neutralization distances. In the pointlike core approximation, the rates are comparable with the available coupled-angular-mode results. The neutralization distances follow the classical predictions for all considered Rydberg states with exception of the states with critical quantum numbers n_A=n_c, mainly populated via tunneling mechanism; the corresponding values are larger than it is predicted by the classical overbarrier model. Inclusion of core polarization significantly reduces the neutralization distances.