117,858 research outputs found
Percolation analysis of the two-dimensional Widom-Rowlinson lattice model
No full textWe consider the two-dimensional Widom-Rowlinson lattice model. This discrete spin model describes a surface on Which a one to one mixture of two gases is sprayed.
These gases shall be strongly repelling on short distances.
We indicate the amount of gas by a positive parameter, the so called activity.
The main result of this thesis states that given an activity larger than 2, there are at most two ergodic Widom-Rowlinson measures if the underlying graph is the star lattice.
This falls naturally into two parts:
The first part is quite general and establishes a new sufficient condition for the existence of at most two ergodic Widom-Rowlinson measures.
This condition demands the existence of 1*lassos, i.e., 1*circuits 1*connected to the boundary, with probability bounded away from zero.
Our approach is based upon the infinite cluster method.
More precisely, we prevent the (co)existence of infinite clusters of certain types.
To this end, we first have to improve the existing results in this direction, which will be done in a general setting for two-dimensional dependent percolation.
The second part is devoted to verify the sufficient condition of the first part for activities larger than 2.
To this end, we have to compare the probabilities of configurations exhibiting 1*lassos to the ones exhibiting 0lassos.
This will be done by constructing an injection that fills certain parts of 0circuits with 1spins and, hereby, forms a 1*lasso
Tracy–Widom asymptotics for -TASEP
No full textWe consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q ∈ [0, 1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of q-TASEP at time τ is of order τ 1/3 and asymptotically distributed as the GUE Tracy–Widom distribution, which confirms the KPZ scaling theory conjecture
Operators associated with soft and hard spectral edges from unitary ensembles.
No full textUsing Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as controllability operators for linear systems, and are reporducing kernels for weighted Hardy spaces, known as Sonine spaces. Periodic solutions of Hill's equation give a new family of Tracy--Widom type operators. This paper identifies a pair of unitary groups that satisfy the von Neumann--Weyl anti-commutation relations and leave invariant the subspaces of L^2 that are the ranges of projections given by Tracy--Widom operators for the soft edge of the unitary ensemble and hard edge of the Jacobi ensemble
Relation between the Widom line and dynamic crossover in systems with a liquid-liquid phase transitions
No full textWe investigate, for two water models displaying a liquid–liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid–liquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima Formula (“Widom line”) emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid–liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between Formula and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid–liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions
Widom factors for generalized Jacobi measures
No full textWe study optimal lower and upper bounds for Widom factors W-infinity,W-n(K, w) associated with Chebyshev polynomials for the weights w(x) = N/1 + x and w(x) = N/1 - x on compact subsets of [-1,1]. We show which sets saturate these bounds. We consider Widom factors W-2,W-n(mu) for L-2(mu) extremal polynomials for measures of the form d mu(x) = (1 - x)(alpha)(1 + x)(beta)d mu(K)(x) where alpha + beta >= 1, alpha, beta is an element of N boolean OR {0} and mu K is the equilibrium measure of a compact regular set K in [-1, 1] with +/- 1 is an element of K. We show that for such measures the improved lower bound (which was first studied in [4]) [W2,n(mu)](2) >= 2S(mu) holds. For the special cases d mu(x) = (1 - x(2))d mu K(x), d mu(x) = (1 - x)d mu K(x), d mu(x) = (1 + x)d mu K(x) we determine which sets saturate this lower bound and discuss how saturated lower bounds for [W2,n(mu)](2) and W-infinity,W-n(K,w) are related
Dynamical crossover and its connection to the Widom line in supercooled TIP4P/Ice water
No full textWe perform molecular dynamics simulations with the TIP4P/Ice water model to characterize the relationship between dynamics and thermodynamics of liquid water in the supercooled region. We calculate the relevant properties of the phase diagram, and we find that TIP4P/Ice presents a retracing line of density maxima, similar to what was previously found for atomistic water models and models of other tetrahedral liquids. For this model, a liquid-liquid critical point between a high-density liquid and a low-density liquid was recently found. We compute the lines of the maxima of isothermal compressibility and the minima of the coefficient of thermal expansion in the one phase region, and we show that these lines point to the liquid-liquid critical point while collapsing on the Widom line. This line is the line of the maxima of correlation length that emanates from a second order critical point in the one phase region. Supercooled water was found to follow mode coupling theory and to undergo a transition from a fragile to a strong behavior right at the crossing of the Widom line. We find here that this phenomenology also happens for TIP4P/Ice. Our results appear, therefore, to be a general characteristic of supercooled water, which does not depend on the interaction potential used, and they reinforce the idea that the dynamical crossover from a region where the relaxation mechanism is dominated by cage relaxation to a region where cages are frozen and hopping dominates is correlated in water to a phase transition between a high-density liquid and a low-density liquid
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Structure and phase equilibria of the Widom-Rowlinson model
No full textThe Widom-Rowlinson model plays an important role in the statistical mechanics of second-order phase transitions, and yet there currently exists no theoretical approach capable of accurately predicting both the microscopic structure and phase equilibria. We address this issue using computer simulation, density functional theory and integral equation theory. A detailed study of the pair correlation functions obtained from computer simulation motivates a closure of the Ornstein-Zernike equations which gives a good description of the pair structure, and locates the critical point to an accuracy of 2%.publishe
Square Dancing with the Stars to Enhance Dynamic Hirschman Linkages?
No full textIn this Presidential Address, the author takes the reader on a reconnaissance of his life and time as a regional scientist. He points out scenery he found scintillating along the way, hoping that some may pick up the banner and chew on a few of the ideas for a while. He suggests a revisit to Albert O. Hirschman’s notion of key sectors and more empirical analysis related to Marcus Berliant’s and Masahisa Fujita’s notion of knowledge creation and transfer.Presidential Address, San Antonio, Texas, March 29, 2014 (53rd Meetings of the Southern Regional Science Association
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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