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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,801 records · Page 100
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DOE OSTI2018

Evolution of a Modified Binomial Random Graph by Agglomeration

In the classical Erdős–Rényi random graph G(n, p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n, p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the Erdős-Rényi random graph G(n, p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G(n, p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G(n, p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real-world applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Review of Recent Developments in the Random-Field Ising Model

A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Fiber Bundle Model Under Heterogeneous Loading

The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model

We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed v̄ of the walk. Namely, there exists some critical value λ{sub c}>0 such that v̄>0 if λ∈(0,λ{sub c}) and v̄=0 if λ≥λ{sub c}. We show that the speed v̄ is continuous in λ on (0,∞) and differentiable on (0,λ{sub c}/2). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of v̄ on (0,λ{sub c}/2), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for λ≥λ{sub c}/2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Two Populations Mean-Field Monomer–Dimer Model

A two populations mean-field monomer–dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a variational principle. A detailed analysis is made in the limit of one population is much smaller than the other and a ferromagnetic mean-field phase transition is found.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Phase Transitions in Edge-Weighted Exponential Random Graphs: Near-Degeneracy and Universality

Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is especially problematic. We extend the existing exponential framework by proposing a generic common distribution for the edge weights. Minimal assumptions are placed on the distribution, that is, it is non-degenerate and supported on the unit interval. By doing so, we recognize the essential properties associated with near-degeneracy and universality in edge-weighted exponential random graphs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The ϵ Expansion and Universality in Three Dimensions

It has been observed that the classification into universality classes of critical behavior, as established by perturbative renormalization group in the vicinity of four or six dimensions of space by the epsilon expansion, remains valid down to three dimensions in all known cases, even when perturbative renormalization group fails in lower dimensions. In this paper we argue that this classification into universality classes remains true in lower dimensions of space, even when perturbative renormalization group fails, because of the well known phenomenon of eigenvalue repulsion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Subexponentially Growing Hilbert Space and Nonconcentrating Distributions in a Constrained Spin Model

Motivated by recent experiments with two-component Bose–Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly with the system size. We discuss the unconventional statistical physical and thermodynamic properties of such a system, in particular the absence of concentration of the underlying probability distributions. As a consequence, expectation values are less suitable to characterize such systems, and full distribution functions are required instead. Sharp signatures of phase transitions do not occur in such a setting, but transitions from singly peaked to doubly peaked distribution functions of an “order parameter” may be present.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Potts Model in One-Dimension on Directed Small-World Networks

The critical properties of the Potts model with q=3 and 8 states in one-dimension on directed small-world networks are investigated. This disordered system is simulated by updating it with the Monte Carlo heat bath algorithm. The Potts model on these directed small-world networks presents in fact a second-order phase transition with a new set of critical exponents for q=3 considering a rewiring probability p=0.1. For q=8 the system exhibits only a first-order phase transition independent of p.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Periodic p-adic Gibbs Measures of q-State Potts Model on Cayley Trees I: The Chaos Implies the Vastness of the Set of p-Adic Gibbs Measures

We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts–Bethe mapping over ℚ{sub p} for the prime numbers p≡1 (mod 3). In fact, for 0<|θ−1|{sub p}<|q|{sub p}{sup 2}<1 where θ=exp{sub p} (J) and J is a coupling constant, there exists a subsystem that is isometrically conjugate to the full shift on three symbols. Meanwhile, for 0<|q|{sub p}{sup 2}≤|θ−1|{sub p}<|q|{sub p}<1, there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r≥4. However, these subshifts on r symbols are all topologically conjugate to the full shift on three symbols. The p-adic Gibbs measures of the same model for the prime numbers p=2,3 and the corresponding Potts–Bethe mapping are also discussed. On the other hand, for 0<|θ−1|{sub p}<|q|{sub p}<1, we remark that the Potts–Bethe mapping is not chaotic when p=3 and p≡2 (mod 3) and we could not conclude the vastness of the set of the periodic p-adic Gibbs measures. In a forthcoming paper with the same title, we will treat the case 0<|q|{sub p}≤|θ−1|{sub p}<1 for all prime numbers p.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Near Critical Preferential Attachment Networks have Small Giant Components

Preferential attachment networks with power law exponent τ>3 are known to exhibit a phase transition. There is a value ρ{sub c}>0 such that, for small edge densities ρ≤ρ{sub c} every component of the graph comprises an asymptotically vanishing proportion of vertices, while for large edge densities ρ>ρ{sub c} there is a unique giant component comprising an asymptotically positive proportion of vertices. In this paper we study the decay in the size of the giant component as the critical edge density is approached from above. We show that the size decays very rapidly, like exp (−c/√(ρ−ρ{sub c})) for an explicit constant c>0 depending on the model implementation. This result is in contrast to the behaviour of the class of rank-one models of scale-free networks, including the configuration model, where the decay is polynomial. Our proofs rely on the local neighbourhood approximations of Dereich and Mörters (Ann Probab 41(1):329–384, 2013) and recent progress in the theory of branching random walks (Gantert et al. in Ann Inst Henri Poincaré Probab Stat 47(1):111–129, 2011).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A Simple Kinetic Model for the Phase Transition of the van der Waals Fluid

A simple kinetic model, which is presumably minimum, for the phase transition of the van der Waals fluid is presented. In the model, intermolecular collisions for a dense gas has not been treated faithfully. Instead, the expected interactions as the non-ideal gas effect are confined in a self-consistent force term. Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy, even globally. It is demonstrated that (i) by a natural separation of the mean-field self-consistent potential, the potential for the non-ideal gas effect is determined from the equation of state for the van der Waals fluid, with the aid of the balance equation of momentum, (ii) a functional which monotonically decreases in time is identified by the H theorem and is found to have a close relation to the Helmholtz free energy in thermodynamics, and (iii) the Cahn–Hilliard type equation is obtained in the continuum limit of the present kinetic model. Numerical simulations based on the Cahn–Hilliard type equation are also performed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Strict Convexity of the Free Energy of the Canonical Ensemble Under Decay of Correlations

We consider a one-dimensional lattice system of unbounded, real-valued spins. We allow arbitrary strong, attractive, nearest-neighbor interaction. We show that the free energy of the canonical ensemble (ce) converges uniformly in C{sup 2} to the free energy of the grand ce (gce). The error estimates are quantitative. A direct consequence is that the free energy of the ce is uniformly strictly convex for large systems. Another consequence is a quantitative local Cramér theorem which yields the strict convexity of the coarse-grained Hamiltonian. With small adaptations, the argument could be generalized to systems with finite-range interaction on a graph, as long as the degree of the graph is uniformly bounded and the associated gce has uniform decay of correlations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Phase Transition for Infinite Systems of Spiking Neurons

We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate 1 whenever its membrane potential is larger than a threshold value. This membrane potential evolves in time and integrates the spikes of all presynaptic neurons since the last spiking time of the neuron. When a neuron spikes, its membrane potential is reset to 0 and simultaneously, a constant value is added to the membrane potentials of its postsynaptic neurons. Moreover, each neuron is exposed to a leakage effect leading to an abrupt loss of potential occurring at random times driven by an independent Poisson point process of rate γ>0. For this process we prove the existence of a value γ{sub c} such that the system has one or two extremal invariant measures according to whether γ>γ{sub c} or not.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Coexistence of Stable Limit Cycles in a Generalized Curie–Weiss Model with Dissipation

In this paper, we modify the Langevin dynamics associated to the generalized Curie–Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site distribution, the dynamics in the thermodynamic limit can be described by a finite set of ODEs. Depending on the form of the interaction function, the system can have several phase transitions at different critical temperatures. Because of the dissipation effect, not only the magnetization of the systems displays a self-sustained periodic behavior at sufficiently low temperature, but, in certain regimes, any (finite) number of stable limit cycles can exist. We explore some of these peculiarities with explicit examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Opinion Dynamics on Networks under Correlated Disordered External Perturbations

We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The fluctuations (variance and correlations) in the external perturbations are shown to reduce the impact of the external influence by increasing the critical threshold needed for the bimodal distribution of opinions to appear. The external fluctuations also have the surprising effect of driving voters towards biased opinions. Furthermore, the first and second moments of the external perturbations are shown to affect the first and second moments of the vote-share distribution. This is shown analytically in the mean field limit, and confirmed numerically for fully connected networks and other network topologies. Studying the dynamic response of complex systems to disordered external perturbations could help us understand the dynamics of a wide variety of networked systems, from social networks and financial markets to amorphous magnetic spins and population genetics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Topological plasmonic modes in graphene-coated nanowire arrays

We investigate the topological edge modes of surface plasmonic polaritons (SPPs) in a two-dimensional waveguide array composed of graphene-coated nanowires. The system experiences topological phase transition by tuning the inter-layer spacing between adjacent unit cells. The topological modes emerge at the edge of topological non-trivial nanowire arrays when the intra-layer spacing is larger than the inter-layer spacing. Thanks to the strong confinement of graphene SPPs, the modal wavelength of topological edge modes can be squeezed as small as 1/20 of incident wavelength. The study provides a promising approach to realizing robust light transport beyond diffraction limit.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

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