Probability distribution of magnetization in the one-dimensional Ising model: Effects of boundary conditions

Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T -> 0), the size of the system going to infinity (N -> oo) while N[1-tanh(J/k_BT)] is kept finite (J being the nearest neighbor coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.Comment: 8 pages, 5 figure

Asymptotic expansion for reversible A + B <-> C reaction-diffusion process

We study long-time properties of reversible reaction-diffusion systems of type A + B C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the asymptotic forms of reactant concentrations and a complete, recursive expression for an arbitrary term of the expansions. Taking an appropriate limit we show that by studying reversible reactions one can obtain "singular" solutions typical of irreversible reactions.Comment: 6 pages, no figures, to appear in PR

Formation of Liesegang patterns: A spinodal decomposition scenario

Spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of Liesegang bands. This mechanism yields a sequence of band positions x_n that obeys the spacing law x_n~Q(1+p)^n. The dependence of the parameters p and Q on the initial concentration of the reagents is determined and we find that the functional form of p is in agreement with the experimentally observed Matalon-Packter law.Comment: RevTex, 4 pages, 4 eps figure

1/f Noise and Extreme Value Statistics

We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary conditions are periodic. We provide a realistic example of periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.Comment: 4 pages, 4 postscript figures, RevTe

Galaxy distribution and extreme value statistics

We consider the conditional galaxy density around each galaxy, and study its fluctuations in the newest samples of the Sloan Digital Sky Survey Data Release 7. Over a large range of scales, both the average conditional density and its variance show a nontrivial scaling behavior, which resembles to criticality. The density depends, for 10 < r < 80 Mpc/h, only weakly (logarithmically) on the system size. Correspondingly, we find that the density fluctuations follow the Gumbel distribution of extreme value statistics. This distribution is clearly distinguishable from a Gaussian distribution, which would arise for a homogeneous spatial galaxy configuration. We also point out similarities between the galaxy distribution and critical systems of statistical physics

Prevalence, significance and predictive value of antiphospholipid antibodies in Crohn’s disease

AIM: To assess the prevalence and stability of different antiphospholipid antibodies (APLAs) and their association with disease phenotype and progression in inflammatory bowel diseases (IBD) patients. METHODS: About 458 consecutive patients [Crohn's disease (CD): 271 and ulcerative colitis (UC): 187] were enrolled into a follow-up cohort study in a tertiary IBD referral center in Hungary. Detailed clinical phenotypes were determined at enrollment by reviewing the patients' medical charts. Disease activity, medical treatment and data about evolvement of complications or surgical interventions were determined prospectively during the follow-up. Disease course (development f complicated disease phenotype and need for surgery), occurrence of thrombotic events, actual state of disease activity according to clinical, laboratory and endoscopic scores and accurate treatment regime were recorded during the follow-up, (median, 57.4 and 61.6 mo for CD and UC). Sera of IBD patients and 103 healthy controls (HC) were tested on individual anti-β2-Glycoprotein-I (anti-β2-GPI IgA/M/G), anti-cardiolipin (ACA IgA/M/G) and anti-phosphatidylserine/prothrombin (anti-PS/PT IgA/M/G) antibodies and also anti-Saccharomyces cerevisiae antibodies (ASCA IgA/G) by enzyme-linked immunosorbent assay (ELISA). In a subgroup of CD (n = 198) and UC patients (n = 103), obtaining consecutive samples over various arbitrary time-points during the disease course, we evaluated the intraindividual stability of the APLA status. Additionally, we provide an overview of studies, performed so far, in which significance of APLAs in IBD were assessed. RESULTS: Patients with CD had significantly higher prevalence of both ACA (23.4%) and anti-PS/PT (20.4%) antibodies than UC (4.8%, P < 0.0001 and 10.2%, P = 0.004) and HC (2.9%, P < 0.0001 and 15.5%, P = NS). No difference was found for the prevalence of anti-β2-GPI between different groups (7.2%-9.7%). In CD, no association was found between APLA and ASCA status of the patients. Occurrence of anti-β2-GPI, ACA and anti-PS/PT was not different between the group of patients with active vs inactive disease state according to appropriate clinical, laboratory and endoscopic scores in CD as well as in UC patients. All subtypes of anti-β2-GPI and ACA IgM status were found to be very stable over time, in contrast ACA IgG and even more ACA IgA status showed significant intraindividual changes. Changes in antibody status were more remarkable in CD than UC (ACA IgA: 49.9% vs 23.3% and ACA IgG: 21.2% vs 5.8%). Interestingly, 59.1% and 30.1% of CD patients who received anti-TNF therapy showed significant negative to positive changes in ACA IgA and IgG antibody status respectively. APLA status was not associated with the clinical phenotype at diagnosis or during follow-up, medical therapy, or thrombotic events and it was not associated with the probability of developing complicated disease phenotype or surgery in a Kaplan-Meier analysis. CONCLUSION: The present study demonstrated enhanced formation of APLAs in CD patients. However, presence of different APLAs were not associated with the clinical phenotype or disease course

Zero-range process with open boundaries

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density \rho_c. In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters

Width Distributions and the Upper Critical Dimension of KPZ Interfaces

Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes smoothly as d is increased, thus strongly suggesting that d=4 is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.Comment: 4 pages, 4 postscript figures, RevTe

Inelastically scattering particles and wealth distribution in an open economy

Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trading, closed form of the wealth distribution is calculated analytically.Comment: 8 pages 5 figure