Class Of Potential Functions Research Articles

Structural Balance Preserving and Bipartite Static Consensus of Heterogeneous Agents in Cooperation-Competition Networks

The structural balance preserving problem is studied in this article for heterogeneous agents in the state-dependent cooperation-competition network. The heterogeneous agents considered are described by second-order integrator systems with different intrinsic nonlinear dynamics, and velocity damping terms, and the initial network is structurally balanced, and connected, which can be divided into two cooperation subnetworks. To solve this problem, a novel classification strategy is applied, where two kinds of evolution rules among agents, and the distributed protocol based on a class of potential functions are proposed, respectively. Under this strategy, the heterogeneous multi-agent system can not only maintain the structural balance of cooperation-competition networks but also achieve bipartite static consensus. Finally, a numerical example is delivered to demonstrate the effectiveness of the theoretical analysis.

Positive Lyapunov Exponent for Some Schr\xf6dinger Cocycles Over Strongly Expanding Circle Endomorphisms

We show that for a large class of potential functions and big coupling constant lambda the Schrödinger cocycle over the expanding map xmapsto bx ~( text{ mod } 1) on mathbb {T} has a Lyapunov exponent >(log lambda )/4 for all energies, provided that the integer bge lambda ^3.

Thermodynamics via Inducing

We consider continuous maps $f:X\to X$ on compact metric spaces admitting inducing schemes of hyperbolic type introduced in [15] as well as the induced maps $\tilde{f}:\tilde{X}\to\tilde{X}$ and the associated tower maps $\hat{f}:\hat{X} \to \hat {X}$. For a certain class of potential functions $\varphi$ on $X$, which includes all H\"older continuous functions, we establish thermodynamic formalism for each of the above three systems and we describe some relations between the corresponding equilibrium measures. Furthermore we study ergodic properties of these equilibrium measures including the Bernoulli property, decay of correlations, and the Central Limit Theorem (CLT). Finally, we prove analyticity of the pressure function for the three systems.

Equilibrium states beyond specification and the Bowen property

It is well known that for expansive maps and continuous potential functions, the specification property (for the map) and the Bowen property (for the potential) together imply the existence of a unique equilibrium state. We consider symbolic spaces that may not have specification and potentials that may not have the Bowen property, and give conditions under which uniqueness of the equilibrium state can still be deduced. Our approach is to ask that the collection of cylinders which are obstructions to the specification property or the Bowen property is small in an appropriate quantitative sense. This allows us to construct an ergodic equilibrium state with a weak Gibbs property, which we then use to prove uniqueness. We do not use inducing schemes or the Perron–Frobenius operator, and we strengthen some previous results obtained using these approaches. In particular, we consider β-shifts and show that the class of potential functions with unique equilibrium states strictly contains the set of potentials with the Bowen property. We give applications to piecewise monotonic interval maps, including the family of geometric potentials, for example, which have both indifferent fixed points and a non-Markov structure.

Differentiability of spectral functions for nonsymmetric diffusion processes

Let L=(1/2)∇⋅a∇+b⋅∇+W be a critical elliptic operator on Rd. For a certain class of potential functions, we consider the generalized principal eigenvalues λ(t) of Lt=L+tV. We show that it is differentiable if and only if L0 is null critical.

Graphical Models for Structured Classification, with an Application to Interpreting Images of Protein Subcellular Location Patterns

In structured classification problems, there is a direct conflict between expressive models and efficient inference: while graphical models such as Markov random fields or factor graphs can represent arbitrary dependences among instance labels, the cost of inference via belief propagation in these models grows rapidly as the graph structure becomes more complicated. One important source of complexity in belief propagation is the need to marginalize large factors to compute messages. This operation takes time exponential in the number of variables in the factor, and can limit the expressiveness of the models we can use. In this paper, we study a new class of potential functions, which we call decomposable k-way potentials, and provide efficient algorithms for computing messages from these potentials during belief propagation. We believe these new potentials provide a good balance between expressive power and efficient inference in practical structured classification problems. We discuss three instances of decomposable potentials: the associative Markov network potential, the nested junction tree, and a new type of potential which we call the voting potential. We use these potentials to classify images of protein subcellular location patterns in groups of cells. Classifying subcellular location patterns can help us answer many important questions in computational biology, including questions about how various treatments affect the synthesis and behavior of proteins and networks of proteins within a cell. Our new representation and algorithm lead to substantial improvements in both inference speed and classification accuracy.

Convex fourth and sixth-order plastic potentials derived from crystallographic texture

The anisotropic plastic behaviour of metals (without prestrain) can be described rather accurately by means of polycrystalline deformation models based on the Taylor theory. This crystallographic anisotropy can be incorporated into finite-element simulations by means of a semi-analytical approach, using plastic potentials of which the coefficients are derived from the Taylor model and the texture. The convexity of the adopted expressions has since long been a problematic issue. In this paper a new class of potential functions in strain-rate space is introduced. These have the advantage that convexity can be strictly imposed. The new formulation is critically assessed for a bcc material with a sharp model texture consisting of a Gaussian distribution centered around the (100)[011] orientation and with a spread of 11 degrees.

Article

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential function V(x,y,z;Z2, λ,β)= –Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calculations using this expansion and the Hill-determinant approach are reported for a large class of potential functions and for various values of the perturbation parameters Z2, λ, and β. PACS No.:03.65

Calculations for double-well potentials of perturbed oscillator type in three-dimensional systems using the Hill-determinant approach

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential function T %c+c5(~ cbcq '3~ % n+ n5 n b % n+ n5 n2 q % + n % 5 n + 5 , around its minimum. In this paper the results of extensive numerical calculations using this expansion and the Hill-determinant approach are reported for a large class of potential functions and for various values of the perturbation parameters ~ , b, and q.

Statistical mechanics via the method of complementary variational principles

A new, versatile, theoretically self-consistent procedure is proposed for determining the thermodynamic properties of a classical system in the condensed fluid phase. The method of complementary variational principles, developed by A. M. Arthurs and his colleagues, is used to generate reference state (hard core) correlation function data via analysis of a well known (non-linear) integral equation for the pair distribution function (namely, the Yvon-Born-Green equation). These data are then used within the context of the perturbation theory of classical fluids developed by Zwanzig, as implemented by Barker and Henderson, to investigate the role of attractive and repulsive perturbations in influencing the thermodynamics of the reference system. As a specific application of this procedure, one that leads to many new results, we focus on a classical system of particles whose effective interactions are confined to a space of two dimensions. We consider two classes of potential functions (the square well/square shoulder and linear well/linear shoulder potentials) and consider separately the effects of attractive and repulsive perturbations. Where possible, the predictions of the theory are compared against known results (specifically, the results obtained via molecular dynamics simulation); we find that the variational method accurately represents the thermodynamics of the reference state (the hard disc fluid) up to densities of σρ2 ≈0·8, and the variational method in tandem with perturbation theory adequately represents the thermodynamics of the square shoulder system over the same density range. The effects of increasing the strength and range parameters of the potential are explored in detail and quantified. Both for the case of attractive and repulsive perturbations, isotherms of the van der Waals type are found to develop below a certain critical temperature in the dense fluid regime. The possible significance of these mean field results is discussed.

Rotational inelastic scattering of Li-N2and Li-CO systems

A non-perturbative approach to rotationally inelastic scattering is discussed. The method is applicable regardless of the magnitude of the coupling strength for a certain class of potential functions if the energy transfer is either small or equal to zero. Various cross sections for rotational transition (0 → 2) are calculated for Li-N2 and Li-CO systems with an assumption that the diatomic molecules are rigid. With reasonable choice of potential parameters, the calculated elastic differential cross sections agree well with the available experimental results. The inelastic differential cross sections are found peaked in the backward hemisphere for both systems.

Nonaxisymmetric punch and crack problems for initially stressed bodies

Using the theory developed by England and Green [1] for thermoelastic problems for initially stressed bodies and a certain class of potential functions, a group of punch and crack problems are solved. The requirement for solution is that the boundary data be expressible as a trignometric series with the coefficient of each term of the series a function of radial distance from the center of the punch or crack. The solutions are obtained by inversion of Abel’s integral equation.

Steady-State Temperature Solution for a Heat-Generating Circular Cylinder Cooled by a Ring of Holes

A series solution is presented to the heat-conduction equation for a heat-generating circular cylinder pierced axially by a ring of equal holes spaced uniformly on a concentric circle. The solution is based upon a class of potential functions previously defined by Howland. Typical nondimensional curves for peak and average temperatures and optimum location of the ring of holes for uniform convective cooling are presented. In addition, some shape factors or conductances for the geometry are given.

New Class of Potential Functions

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