Statistical Properties of Laser Speckles Generated from Far Rough Surfaces

The statistical properties of speckle patterns generated from far rough surfaces, under illumination of a Gaussian beam, are investigated. The surface roughness dependence of the first- and second-order moments of intensity is theoretically investigated, and their analytical expressions have been derived and presented. The analysis indicates that the mean intensity distribution on the receiver plane is closely related to the ratio of the lateral correlation length to the surface root mean square (rms) height. On the other hand, the speckle size and the correlation degree of the speckle intensities are found to be independent of the parameter characterizing the roughness of a surface, and are only determined by the laser beam waist.     

Quantum criticality and Yang–Mills gauge theory

We present a family of nonrelativistic Yang–Mills gauge theories in D+1$D+1$ dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2$z=2$. The ground state wavefunction is intimately related to the partition function of relativistic Yang–Mills in D   dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4+1$4+1$. The theories can be deformed in the infrared by a relevant operator that restores Poincaré invariance as an accidental symmetry. In the large-N limit, our nonrelativistic gauge theories can be expected to have weakly curved gravity duals.     

Book Review: Statistical Physics of Fracture and Breakdown in Disordered Systems

Journal of Statistical Physics -     

Thermodynamic Free Energy Behavior of Diblock Copolymer Chains Confined Between Planar Surfaces Having End-Tethered Flexible Polymer Molecules

A molecular model for the free energy of a confined system of diblock copolymer chains within a 2D slit with the interior surfaces having end-tethered chains is presented, based on a combined lattice and scaling theory approach. The thermodynamics of a model system, based on a constrained minimization of free energy, is explored as a function of the intermolecular energy parameters for interaction between the segments of block copolymer chains, end-tethered chains, and the surfaces. The effects of chain length and the block length ratio are investigated over a wide range of values. The results obtained are qualitative in nature; however, the model can be implemented to real systems provided appropriate parameterization of the model parameters to real systems can be performed. The phase diagrams obtained here provide ways for designing thermodynamically stable systems within the physical parametric variable space.     

Statistical Physics of Evolving Systems

Evolution is customarily perceived as a biological process. However, when formulated in terms of physics, evolution is understood to entail everything. Based on the axiom of everything comprising quanta of actions (e.g., quanta of light), statistical physics describes any system evolving toward thermodynamic balance with its surroundings systems. Fluxes of quanta naturally select those processes leveling out differences in energy as soon as possible. This least-time maxim results in ubiquitous patterns (i.e., power laws, approximating sigmoidal cumulative curves of skewed distributions, oscillations, and even the regularity of chaos). While the equation of evolution can be written exactly, it cannot be solved exactly. Variables are inseparable since motions consume driving forces that affect motions (and so on). Thus, evolution is inherently a non-deterministic process. Yet, the future is not all arbitrary but teleological, the final cause being the least-time free energy consumption itself. Eventually, trajectories are computable when the system has evolved into a state of balance where free energy is used up altogether.     

Surface and bulk properties of ballistic deposition models with bond breaking

We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is controlled through a probability p$p$. These systems present a crossover, for small values of p$p$, from random to correlated (KPZ) growth of surface roughness, which is studied through scaling arguments and Monte Carlo simulations on one- and two-dimensional substrates. We show that the crossover characteristic time _t×$t_{\times }$ scales with p$p$ according to _t×∼p^−y$t_{\times }\sim p^{-y}$ with y=(n+1)$y=(n+1)$ and that the interface width at saturation _Wsat$W_{sat}$ scales as _Wsat∼p^−δ$W_{sat}\sim p^{-\delta }$ with δ=(n+1)/2$\delta =(n+1)/2$, where n$n$ is either the maximal number of broken bonds or of dislodged suspended particles. This result shows that the sets of exponents y=1$y=1$ and δ=1/2$\delta =1/2$ or y=2$y=2$ and δ=1$\delta =1$ found in all previous works focusing on systems with this same type of crossover are not universal. Using scaling arguments, we show that the bulk porosity P$P$ of the deposits scales as P∼p^y−δ$P\sim p^{y-\delta }$ for small values of p$p$. This general scaling relation is confirmed by our numerical simulations and explains previous results present in literature.     

Complexity of Fracturing in Terms of Non-Extensive Statistical Physics: From Earthquake Faults to Arctic Sea Ice Fracturing

Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this article we present a statistical physics approach to fracturing based on the framework of non-extensive statistical physics (NESP). Fracturing phenomena typically present intermittency, multifractality, long-range correlations and extreme fluctuations, properties that motivate the NESP approach. Initially we provide a brief review of the NESP approach to fracturing and earthquakes and then we analyze stress and stress direction time series within Arctic sea ice. We show that such time series present large fluctuations and probability distributions with “fat” tails, which can exactly be described with the q-Gaussian distribution derived in the framework of NESP. Overall, NESP provide a consistent theoretical framework, based on the principle of entropy, for deriving the collective properties of fracturing phenomena and earthquakes.     

Application of Statistical Physics to Understand Static and Dynamic Anomalies in Liquid Water

We present an overview of recent research applying ideas of statistical mechanics to try to better understand the statics and especially the dynamic puzzles regarding liquid water. We discuss recent molecular dynamics simulations using the Mahoney–Jorgensen transferable intermolecular potential with five points (TIP5P), which is closer to real water than previously-proposed classical pairwise additive potentials. Simulations of the TIP5P model for a wide range of deeply supercooled states, including both positive and negative pressures, reveal (i) the existence of a non-monotonic temperature of maximum density line and a non-reentrant spinodal, (ii) the presence of a low-temperature phase transition. The take-home message for the static aspects is that what seems to matter more than previously appreciated is local tetrahedral order, so that liquid water has features in common with SiO₂ and P, as well as perhaps Si and C. To better understand dynamic aspects of water, we focus on the role of the number of diffusive directions in the potential energy landscape. What seems to matter most is not values of thermodynamic parameters such as temperature T and pressure P, but only the value of a parameter characterizing the potential energy landscape—just as near a critical point what matters is not the values of T and P but rather the values of the correlation length.     

Some aspects of conformal field theories on the plane and higher genus Riemann surfaces

We review some aspects of conformal field theories on the plane as well as on higher genus Riemann surfaces.     

Classification of Multiscaling in Fracture and Fragmentation

We propose a method to classify multifractal properties, which have been found in many systems. We then study the multifractal properties previously found in various models of fracture and fragmentation, and show explicitly that they indeed fall into the two classes proposed in our method. Several interesting features are also revealed.     

The three-dimensional origin of the classifying algebra

It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying algebra, a semisimple commutative associative complex algebra.     

Exactly solvable models of conformal-invariant quantum field theory in D-dimensional space

The method for exact solution of a certain class of models of conformal quantum field theory in D-dimensional Euclidean space is proposed. The method allows one to derive closed differential equations for all the Green functions and also algebraic equations to scale dimensions of all field. A scalar field P of a scale dimension d_p = D − 2 is needed for nontrivial solutions to exist. At D ≠ 2 this field is converted to a constant that coincides with the central charge of two-dimensional theories. A new class of D = 2 models has been obtained, where the infinite-parametric symmetry is not manifest. The two-dimensional Wess-Zumino model is used to illustrate the method of solution.     

Dynamic Scaling of Ramified Clusters Formed on Liquid Surfaces

A comprehensive simulation model -- deposition, diffusion, rotation, reaction and aggregation model is presented to simulate the formation processes of ramified clusters on liquid surfaces, where clusters can disuse and rotate easily. The mobility （including diffusion and rotation） of clusters is related to its mass, which is given by Dm = Dos^-γD and θm = θos^-γθ, respectively. The influence of the reaction probability on the kinetics and structure formation is included in the simulation model. We concentrate on revealing dynamic scaling during ramified cluster formation. For this purpose, the time evolution of the cluster density and the weight-average cluster size as well as the cluster-size distribution scaling function at different time are determined for various conditions. The dependence of the cluster density on the deposition flux and time-dependence of fractal dimension are also investigated. The obtained results are helpful in understanding the formation of clusters or thin film growth on liquid surfaces.     

Dynamic Scaling of Ramified Clusters Formed on Liquid Surfaces

A comprehensive simulation model -deposition,diffusion, rotation, reaction and aggregation model is presented to simulate the formation processes of ramified clusters on liquid surfaces, where clusters can diffuse and rotate easily. The mobility (including diffusion and rotation) of clusters is related to its mass, which is given by Dm = Dos-γD and θm =′θos-γθ, respectively. The influence of the reaction probability on the kinetics and structure formation is included in the simulation model. We concentrate on revealing dynamic scaling during ramified cluster formation. For this purpose, the time evolution of the cluster density and the weight-average cluster size as well as the cluster-size distribution scaling function at different time are determined for various conditions. The dependence of the cluster density on the deposition flux and time-dependence of fractal dimension are also investigated. The obtained results are helpful in understanding the formation of clusters or thin film growth on liquid surfaces.     

Gauge natural formulation of conformal gravity

We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to conformal and diffeomorphism symmetries.     

Caratheodory and the Foundations of Thermodynamics and Statistical Physics

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the Foundations of Statistical Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way.     

Statistical Aspects of Tensile Fracture of Isotactic Polypropylene

The fracture behavior of isotactic polypropylene (iPP) specimen with double-notched shape under a fixed elongation speed at room temperature is described. Over 100 tensile tests were performed, and the statistic fracture data were obtained for the tensile condition. The statistical data of fracture were obtained by examining the time to fracture, the ultimate stress, and the tensile toughness (determined from the area under the nominal stress–strain curve from the origin to the fracture point). The probability density distributions for time to fracture, the ultimate stress, and the tensile toughness approximately followed the normal Gaussian statistics. Using a linear relationship between stress and elongation time near the fracture point, we can apply a static Kalman filter system to the present fracture data to determine a conditional probability density function. As a consequence, this application makes it possible to predict the probability of fracture of iPP under any static condition.     

Expectation values of descendent fields in the sine-Gordon model

We obtain exactly the vacuum expectation values in the sine-Gordon model and in Φ_1,3 perturbed minimal CFT. We discuss applications of these results to short-distance expansions of two-point correlation functions.