The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecu...
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A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is...
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A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is a white-in-time random noise acting in a narrow band of high wavenumbers. The inverse-cascade process and the presence of the boundary lead ultimately to a pile-up of energy in the lowest wavenumber (Bose condensation). In the asymptotic limit where the enstrophy cascade range is negligible, Bose condensation is solely responsible for the generation of coherent vortices and intermittency in the system. We present the evolution of the velocity and vorticity fields through the later stages of the condensate state, and explore the possible implications for atmospheric turbulence constrained by the periodic domain about the earth.
We describe here a new technique and a package for rapid reconstruction of smooth surfaces from scattered data points. This method is based on a fast recurrent algorithm for the Delauney triangulation followed by rati...
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We describe here a new technique and a package for rapid reconstruction of smooth surfaces from scattered data points. This method is based on a fast recurrent algorithm for the Delauney triangulation followed by rational interpolation inside triangles. Preprocessing of data includes sorting and takes N log(N) time. Afterwards the computational cost is a linear function of the amount of data. This technique enables a user to construct a surface of any class of smoothness and degree of convergence. Our package reconstructs surfaces that can be uniquely projected either on a plane or on a sphere. The graphical section of this package includes three dimensional transformations, shading, hidden surface removal, interactive adding points into triangulation by mouse, etc. The graphics has been implemented on Iris-4D, SUN-4 and IBM-5080.
In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or ''eruption,'' is described. A fundamental ...
In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or ''eruption,'' is described. A fundamental role is played by the interactions of fixed paints and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The dynamics along the invariant line, in two of the examples, reduces to the one-dimensional Newton's method which is conjugate to a degree two ratoional map. We also determine, computationally, the characteristic exponents for all of the systems. An unexpected coincidence is that the parameter range where the invariant line becomes neutrally stable, as measured by a zero Lyapunov exponent, coincides with the merging of a periodic point with a point on a singular curve. (C) 1996 American Institute of Physics.
This work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form u(t) = Lu + Nf(u), where L and N are linear differential operators and f(u) is a nonlinear f...
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This work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form u(t) = Lu + Nf(u), where L and N are linear differential operators and f(u) is a nonlinear function. These equations are adaptively solved by projecting the solution u and the operators L and N into a wavelet basis. Vanishing moments of the basis functions permit a sparse representation of the solution and operators. Using these sparse representations fast and adaptive algorithms that apply operators to functions and evaluate nonlinear functions, are developed for solving evolution equations. For a wavelet representation of the solution u that contains N-s significant coefficients, the algorithms update the solution using O(N-s) operations. The approach is applied to a number of examples and numerical results are given. (C) 1997 Academic Press.
The dynamical system arising from the problem of billiards is a classical example where the theory of twist maps can be applied. In the case of an elliptic billiard table, the corresponding twist map is integrable and...
The dynamical system arising from the problem of billiards is a classical example where the theory of twist maps can be applied. In the case of an elliptic billiard table, the corresponding twist map is integrable and has a saddle connection between two hyperbolic period two points. Using a discrete analog to the Melnikov method, we are able to show that this saddle connection can be deformed into a transversal heteroclinic connection under certain analytic perturbations of the table. From the formulas that we get, we can show that the splitting of the separatrices is exponentially small as a function of the eccentricity of the original unperturbed elliptic table. In addition, we also include a characterization of the period two periodic points for any billiard table.
An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is prove...
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An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.
We work with symplectic diffeomorphisms of the n-annulus A(n) = T*(R-n/Z(n)). Using the variational approach of Aubry and Mather, we are able to give a local description of the stable (and unstable) manifold for a hyp...
We work with symplectic diffeomorphisms of the n-annulus A(n) = T*(R-n/Z(n)). Using the variational approach of Aubry and Mather, we are able to give a local description of the stable (and unstable) manifold for a hyperbolic fixed point. We use this in order to get a Melnikov-like formula for exact symplectic twist maps. This formula involves an infinite series that could be computed in some specific cases. We apply our formula to prove the existence of heteroclinic orbits for a family of twist maps in R-4.
We present a simple algorithm for the factored polynomial (Finite Impulse Response, FIR) approximation of rational (Infinite Impulse Response, IIR) filters which may be used to construct inverse filters. When applied ...
We present a simple algorithm for the factored polynomial (Finite Impulse Response, FIR) approximation of rational (Infinite Impulse Response, IIR) filters which may be used to construct inverse filters. When applied to quadrature mirror filters, our approach yields a simple way of generating an efficient FIR filter bank which inherits the properties of IIR filter bank with any desired accuracy. (C) 1995 Academic Press, Inc.
We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understa...
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We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understanding of transition pathways between metastable *** method relies on the original formulation of the string method[***.B,66,052301(2002)],*** evolve a smooth curve along a direction normal to the *** algorithm works by performing minimization steps on hyperplanes normal to the *** the problem of finding MEP on the PES is remodeled as a set of constrained minimization *** provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method[***.,126(16),164103(2007)].At the same time,it provides a more direct analog of the finite temperature string *** applicability of the algorithm is demonstrated using various examples.
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