Stealthy interactions are an emerging class of nontrivial, bounded long-ranged oscillatory pair potentials with classical ground states that can be disordered, hyperuniform, and infinitely degenerate. Their hybrid cry...
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In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle...
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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 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 consider a family of three-dimensional, volume preserving maps depending on a small parameter epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for sma...
We consider a family of three-dimensional, volume preserving maps depending on a small parameter epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for small epsilon the heteroclinic connection breaks up and that the splitting between its components scales with epsilon like epsilon(gamma) exp(-beta/epsilon). We estimate beta using the singularities of the epsilon --> 0+ heteroclinic orbit in the complex plane. We then estimate gamma using linearization about orbits in the complex plane. While these estimates are not proven, they are well supported by our numerical calculations. The work described here is a special case of the theory derived by Amick et al. which applies to q-dimensional volume preserving mappings.
The COVID-19 outbreak has highlighted the importance of mathematical epidemic models like the Susceptible-Infected-Recovered (SIR) model, for understanding disease spread dynamics. However, enhancing their predictive ...
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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.
A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The me...
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A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The method is based on the adjoint method of optimal control. It is shown that accurate values of the parameters can be estimated, and the estimates are stable with respect to random perturbations of the data provided that data from a sufficient number of locations are available for assimilation.
We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equ...
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We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.
A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form...
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A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form depends on the assumptions made concerning the intermittency.
The fuzzy optimization problem is one of the prominent topics in the broad area of artificial intelligence. It is applicable in the field of non-linear fuzzy programming. Its application as well as practical realizati...
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The fuzzy optimization problem is one of the prominent topics in the broad area of artificial intelligence. It is applicable in the field of non-linear fuzzy programming. Its application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem was solved by hybrid optimization techniques like Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). An industrial production planning problem with a cubic objective function, eight decision variables and 29 constraints was solved successfully using the LS-SA-PS hybrid optimization techniques. The computational results for the objective function with respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem. (C) 2011 Elsevier Ltd. All rights reserved.
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