Short Talk Schedule Session

We take initial steps in extending our study of stealthy disordered point-particle systems to stealthy spin systems or digitized two-phase random media. A point-particle configuration or spin system is called "stealthy" if the structure factor, S(k), remains zero for vector k in some region (usually a spherical region around the origin). For point-particle systems, stealthy configurations can be successfully generated by minimizing S(k) using local optimization algorithms. However, for spin systems fixed on a lattice, even simulated annealing has difficulty finding stealthy configurations. We mitigate this problem by a logarithmic transformation of the objective function. We can also generate stealthy spin systems by superposing multiple configurations. A2: Duyu Chen, Princeton University Coauthors: Salvatore Torquato Characterization of heterogeneous materials via stochastic reconstruction/construction technique Abstract: The Yeong-Torquato stochastic reconstruction/construction algorithm enables one to generate microstructures of heterogeneous materials from limited morphological information, i.e., a finite set of lower-order correlation functions. In this work we employ this technique to characterize various real and hypothetical microstructures in two and three dimensions. In particular we consider two-point probability function $S_2(r)$, two-point cluster function $C_2(r)$, and their generalized versions. In two dimensions we find that the salient structural features of random ellipse packings are captured by their angular $S_2(r)$, while the combination of generalized $S_2(r)$ and $C_2(r)$ is sufficient to characterize epithelial patterns in skin. In three dimensions we find that anisotropic snow microstructures could be accurately reconstructed by utilizing their angular $S_2(r)$ and $C_2(r)$, while the generalized angular $S_2(r)$ and $C_2(r)$ could character ize anisotropic bone microstructures well. In addition, we also construct hypothetical microstructures that correspond to specified correlation functions by employing the Yeong-Torquato algorithm. Specifically we tune the parameters in our basis functions for $S_2(r)$ consisting of an exponentially decreasing one and a damped-oscillating one in order to generate a wide range of microstructures. These microstructures include “particle” systems, labyrinth patterns, and spinodal decomposition patterns, to name a few. Our work will serve a first step to systematically classify various microstructures of interest based on the characteristics of their lower-order correlation functions. The Yeong-Torquato stochastic reconstruction/construction algorithm enables one to generate microstructures of heterogeneous materials from limited morphological information, i.e., a finite set of lower-order correlation functions. In this work we employ this technique to characterize various real and hypothetical microstructures in two and three dimensions. In particular we consider two-point probability function $S_2(r)$, two-point cluster function $C_2(r)$, and their generalized versions. In two dimensions we find that the salient structural features of random ellipse packings are captured by their angular $S_2(r)$, while the combination of generalized $S_2(r)$ and $C_2(r)$ is sufficient to characterize epithelial patterns in skin. In three dimensions we find that anisotropic snow microstructures could be accurately reconstructed by utilizing their angular $S_2(r)$ and $C_2(r)$, while the generalized angular $S_2(r)$ and $C_2(r)$ could character ize anisotropic bone microstructures well. In addition, we also construct hypothetical microstructures that correspond to specified correlation functions by employing the Yeong-Torquato algorithm. Specifically we tune the parameters in our basis functions for $S_2(r)$ consisting of an exponentially decreasing one and a damped-oscillating one in order to generate a wide range of microstructures. These microstructures include “particle” systems, labyrinth patterns, and spinodal decomposition patterns, to name a few. Our work will serve a first step to systematically classify various microstructures of interest based on the characteristics of their lower-order correlation functions. A3: Uttam Bhat, Boston University Coauthors: Sidney Redner, Caterina DeBacco Stochastic search with reset Abstract: Stochastic/Brownian search problems have been studied extensively. We present intriguing results from a model where the Brownian searcher resets to the origin if it does not find the target, either at deterministic times, or with a Poisson rate. (e.g. search party coming back to the base camp at the end of the day corresponds to `reset'). We show optimal reset rates and show regions of reset rate where deterministic reset performs better than Poisson reset in different dimensions. Stochastic/Brownian search problems have been studied extensively. We present intriguing results from a model where the Brownian searcher resets to the origin if it does not find the target, either at deterministic times, or with a Poisson rate. (e.g. search party coming back to the base camp at the end of the day corresponds to `reset'). We show optimal reset rates and show regions of reset rate where deterministic reset performs better than Poisson reset in different dimensions. A4: Fei Lu, UC Berkeley Coauthors: Alexandre J. Chorin, Kevin Lin Data-driven stochastic model reduction in nonlinear dynamical systems Abstract: There are many high-dimensional dynamical systems in science and engineering that are too complex or computationally expensive to solve in full, and where only a relatively small subset of the degrees of freedom are observable and of direct interest. Therefore it is useful to derive low-dimensional models that can predict the evolution of the observable variables of interest, and reproduce their statistics at an acceptable cost. The challenges come from the nonlinear interactions between the observed There are many high-dimensional dynamical systems in science and engineering that are too complex or computationally expensive to solve in full, and where only a relatively small subset of the degrees of freedom are observable and of direct interest. Therefore it is useful to derive low-dimensional models that can predict the evolution of the observable variables of interest, and reproduce their statistics at an acceptable cost. The challenges come from the nonlinear interactions between the observed variables and the unobserved variables, and the difficulties in quantifying uncertainties from discrete data. We address these challenges by developing discrete-time stochastic reduced systems for the observed variables, by using data and statistical methods to account for the impact of the unobserved variables. A key ingredient in the construction of the stochastic reduced systems is a discrete-time stochastic parametrization based on inference of nonlinear time series. We demonstrate our approach on the twolayer Lorenz 96 system and the Kuramoto-Sivashinsky equation. We also discuss the relation between our construction and the Mori-Zwanzig formalism of statistical physics. Joint work with Alexandre Chorin and Kevin Lin. A5: Thomas Foley, Penn State University Coauthors: W.G. Noid, M. Scott Shell The impact of resolution upon entropy and information in coarse-grained models Abstract: Coarse-graining, wherein one reduces the dimensionality of a system by grouping together (or 'integrating out') degrees of freedom, is a well-known method in statistical mechanics. In the subfield of soft matter simulations, it has emerged in a specific context as a means to reach physically relevant length and time scales. Here we discuss some of the underlying formalism and focus on the so-called potential of mean force. In particular we show this potential is, intuitively, a free energy, and that its entropic component has important theoretical and potentially practical consequences. Coarse-graining, wherein one reduces the dimensionality of a system by grouping together (or 'integrating out') degrees of freedom, is a well-known method in statistical mechanics. In the subfield of soft matter simulations, it has emerged in a specific context as a means to reach physically relevant length and time scales. Here we discuss some of the underlying formalism and focus on the so-called potential of mean force. In particular we show this potential is, intuitively, a free energy, and that its entropic component has important theoretical and potentially practical consequences. A6: Grant Rotskoff, UC Berkeley Coauthors: Gavin Crooks, Eric vanden Eijnden Optimal nonequilibrium protocols in high dimensional control spaces Abstract: Nonequilibrium control of small, fluctuating systems has emerged as an urgent goal in a diverse Nonequilibrium control of small, fluctuating systems has emerged as an urgent goal in a diverse set of problems, from magnetic spintronics for efficient computing to estimating free energy differences with the Jarzynski equality. In the limit of slow driving, optimal control protocols benefit from a geometric interpretation. I will describe the nature of this protocol geometry and describe a numerical technique that can be used to determine optimal protocols, even in high dimensional control spaces. In addition, I will show results for magnetization reversal protocols on a 2d Ising model using a large number of local magnetic fields. A7: David Wolpert, Santa Fe Institute Extending Landauer’s Bound to Arbitrary Computation Abstract: Recently there has been great progress in bounding the thermodynamic work required to perform any computation whose output is independent of its input, e.g., bit erasure. Here I extend these results to bound the work required for any computation, even one whose output depends on its input. I use this extension to show that if the computer implementing the computation will be re-used, then the work bound depends only on the dynamics of the logical variable under the computation, with no dependence on the physical details of that computer (e.g., its internal entropy). This establishes a formal identity between the thermodynamics of (re-usable) computers and theoretical computer science. As an illustration Recently there has been great progress in bounding the thermodynamic work required to perform any computation whose output is independent of its input, e.g., bit erasure. Here I extend these results to bound the work required for any computation, even one whose output depends on its input. I use this extension to show that if the computer implementing the computation will be re-used, then the work bound depends only on the dynamics of the logical variable under the computation, with no dependence on the physical details of that computer (e.g., its internal entropy). This establishes a formal identity between the thermodynamics of (re-usable) computers and theoretical computer science. As an illustration of this identity, I use it to prove that the work needed to compute a bit string σ on a Turing machine M is kBT ln(2) × [Kolmogorov complexity of σ + log of the (Bernoulli) measure of the set of strings that compute σ + log of the halting probab ility of M]. A8: Joel Bader, Johns Hopkins University Coauthors: Benjamin Strober, Jianan Zhan, Dan E. Arking Bayesian inference of genotype-phenotype networks Abstract: Identifying genetic variants that increase disease risk is a major goal of the post-genome era; discoveries provide basic biological understanding and could lead to new diagnostics and therapies. The main challenge of current genome-wide association studies (GWAS) is gathering cohorts of 50,000 to 100,000 individuals or more required for adequate power to discover the genetic variants responsible for complex diseases, including cardiovascular diseases, psychiatric disorders, and cancer predisposition. Many diseases have far smaller cohorts to date, but share biological mechanisms; the contribution of a single gene to multiple phenotypes is termed pleiotropy. We present a Bayesian probability model that exploits pleiotropy to permit us to merge smaller cohorts covering 10's to 100's of phenotypes into a larger effective cohort with far greater power. This model explicitly includes phenotype-phenotype and genotypegenotype correlations to distinguish causation from correlation. It also infers patterns of phenotypes that are likely to share underlying genetic factors. We show that our method has greater power than competing methods, and we present results of applications to large population studies from the NIH Database of Genotypes and Phenotypes (dbGaP) to identify genotype-phenotype networks underlying complex disease. Identifying genetic variants that increase disease risk is a major goal of the post-genome era; discoveries provide basic biological understanding and could lead to new diagnostics and therapies. The main challenge of current genome-wide association studies (GWAS) is gathering cohorts of 50,000 to 100,000 individuals or more required for adequate power to discover the genetic variants responsible for complex diseases, including cardiovascular diseases, psychiatric disorders, and cancer predisposition. Many diseases have far smaller cohorts to date, but share biological mechanisms; the contribution of a single gene to multiple phenotypes is termed pleiotropy. We present a Bayesian probability model that exploits pleiotropy to permit us to merge smaller cohorts covering 10's to 100's of phenotypes into a larger effective cohort with far greater power. This model explicitly includes phenotype-phenotype and genotypegenotype correlations to distinguish causation from correlation. It also infers patterns of phenotypes that are likely to share underlying genetic factors. We show that our method has greater power than competing methods, and we present results of applications to large population studies from the NIH Database of Genotypes and Phenotypes (dbGaP) to identify genotype-phenotype networks underlying complex disease. A9: Alberto Imparato, University of Aarhus Stochastic thermodynamics in many-particle systems Abstract: We study the thermodynamic properties of a microscopic model of coupled oscillators that exhibits a dynamical phase transition from a desynchronized to a synchronized phase. We consider two different configurations for the thermodynamic forces applied on the oscillators, one resembling the macroscopic power grids, and one resembling autonomous molecular motors. We characterize the input and the output power as well as the efficiency at maximum power, providing analytic expressions for such quantities near the critical coupling strength. We discuss the role of the quenched disorder in the thermodynamic force distributions and show that such a disorder may lead to an enhancement of the efficiency at maximum power. A.I New J. Phys. 17 (2015) 125004 We study the thermodynamic properties of a microscopic model of coupled oscillators that exhibits a dynamical phase transition from a desynchronized to a synchronized phase. We consider two different configurations for the thermodynamic forces applied on the oscillators, one resembling the macroscopic power grids, and one resembling autonomous molecular motors. We characterize the input and the output power as well as the efficiency at maximum power, providing analytic expressions for such quantities near the critical coupling strength. We discuss the role of the quenched disorder in the thermodynamic force distributions and show that such a disorder may lead to an enhancement of the efficiency at maximum power. A.I New J. Phys. 17 (2015) 125004 A10: Panos Argyrakis, University of Thessaloniki Variation of the critical percolation threshold Abstract: We show that the critical percolation threshold strongly depends on the method that the binary percolation system is prepared. This is inspired by the recent Achlioptas model (2009) that showed that when one does not use a completely random lattice, but uses a biased model to fill the lattice, favoring the formation of smaller clusters, then there is a delay in criticality. We present several different variations of this model which actually give someone the possibility to construct a binary system with any critical point that he/she wishes. All results are derived by detailed Monte-Carlo simulations. We show that the critical percolation threshold strongly depends on the method that the binary percolation system is prepared. This is inspired by the recent Achlioptas model (2009) that showed that when one does not use a completely random lattice, but uses a biased model to fill the lattice, favoring the formation of smaller clusters, then there is a delay in criticality. We present several different variations of this model which actually give someone the possibility to construct a binary system with any critical point that he/she wishes. All results are derived by detailed Monte-Carlo simulations. A11: Robert Ziff, University of Michigan Coauthors: Hao Hu and Yougin Deng, University of Science and Technology of China Holes In Percolation Clusters Abstract: For different percolation models, we did simulations to observe holes in the largest cluster, and holes in the largest backbone cluster. We find that the distribution of the size of the holes follows a power For different percolation models, we did simulations to observe holes in the largest cluster, and holes in the largest backbone cluster. We find that the distribution of the size of the holes follows a power law distribution, the dimension of the holes is 2, and a general hyperscaling relation is satisfied. For site percolation on both the triangular and the square lattice, and bond percolation on the square lattice, it is found that the largest hole occupies exactly half of the lattice sites, which follows by a symmetry argument. We also define a percolation model on sites in the holes -a kind of recursive percolation. We find a critical line, on which the dimension of clusters formed in the holes is also 2. A12: Eugene Kolomeisky, University of Virgina Coauthors: J. P. Straley and D. L. Abrams Anomalous screening in two-dimensional materials with extremum loop in dispersion law Abstract: A variety of two-dimensional materials, for instance, surfaces and interfaces with Rashba spinorbit interaction or biased bilayer graphene, possess band structure with energy extrema reaches along a loop in momentum space. When topology of occupied states in these systems is annular they exhibit an effect of anomalous screening: reducing the doping enhances linear screening response. We argue that due to anomalous screening the Rashba materials may undergo a transition into Mott insulating state upon increase of doping. Non-linear manifestation and three-dimensional realizations of the effect are also predicted A variety of two-dimensional materials, for instance, surfaces and interfaces with Rashba spinorbit interaction or biased bilayer graphene, possess band structure with energy extrema reaches along a loop in momentum space. When topology of occupied states in these systems is annular they exhibit an effect of anomalous screening: reducing the doping enhances linear screening response. We argue that due to anomalous screening the Rashba materials may undergo a transition into Mott insulating state upon increase of doping. Non-linear manifestation and three-dimensional realizations of the effect are also predicted