The Experts below are selected from a list of 129093 Experts worldwide ranked by ideXlab platform
Jin Zhang - One of the best experts on this subject based on the ideXlab platform.
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asymptotic behavior of solutions of a reaction diffusion equation with inHomogeneous robin boundary condition and free boundary condition
Nonlinear Analysis-real World Applications, 2016Co-Authors: Jin ZhangAbstract:Abstract This paper studies the long time behavior of solutions of a reaction–diffusion model with inHomogeneous Robin boundary condition at x = 0 and free boundary condition at x = h ( t ) . We prove that, for the initial data u 0 = σ ϕ , there exists σ ∗ ⩾ 0 such that u ( ⋅ , t ) converges to a positive stationary solution which tends to 1 as x → ∞ locally uniformly in [ 0 , ∞ ) when σ > σ ∗ . In the Case of σ ⩽ σ ∗ the solution u ( ⋅ , t ) converges to the ground state V ( ⋅ − z ) where V is the unique even positive solution of V ″ + f ( V ) = 0 subject to V ( ∞ ) = 0 and z is the root of a V ′ ( − z ) − ( 1 − a ) V ( − z ) = b . The asymptotic behavior of the solutions is quite different from the Homogeneous Case b = 0 .
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energy efficient cooperative relaying over fading channels with simple relay selection
IEEE Transactions on Wireless Communications, 2008Co-Authors: R Madan, Neelesh B Mehta, Andreas F Molisch, Jin ZhangAbstract:We consider a cooperative wireless network where a set of nodes cooperate to relay in parallel the information from a source to a destination using a decode-and-forward approach. The source broadcasts the data to the relays, some or all of which cooperatively beamform to forward the data to the destination. We generalize the standard approaches for cooperative communications in two key respects: (i) we explicitly model and factor in the cost of acquiring channel state information (CSI), and (ii) we consider more general selection rules for the relays and compute the optimal one among them. In particular, we consider simple relay selection and outage criteria that exploit the inherent diversity of relay networks and satisfy a mandated outage constraint. These criteria include as special Cases several relay selection criteria proposed in the literature. We obtain expressions for the total energy consumption for general relay selection and outage criteria for the non-Homogeneous Case, in which different relay links have different mean channel power gains, and the Homogeneous Case, in which the relay links statistics are identical. We characterize the structure of the optimal transmission scheme. Numerical results show that the cost of training and feedback of CSI is significant. The optimal strategy is to use a varying subset (and number) of relay nodes to cooperatively beamform at any given time. Depending on the relative location of the relays, the source, and the destination, numerical computations show energy savings of about 16% when an optimal relay selection rule is used. We also study the impact of shadowing correlation on the energy consumption for a cooperative relay network.
Shi Jin - One of the best experts on this subject based on the ideXlab platform.
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a stochastic galerkin method for the boltzmann equation with uncertainty
Journal of Computational Physics, 2016Co-Authors: Shi JinAbstract:We develop a stochastic Galerkin method for the Boltzmann equation with uncertainty. The method is based on the generalized polynomial chaos (gPC) approximation in the stochastic Galerkin framework, and can handle random inputs from collision kernel, initial data or boundary data. We show that a simple singular value decomposition of gPC related coefficients combined with the fast Fourier-spectral method (in velocity space) allows one to compute the high-dimensional collision operator very efficiently. In the spatially Homogeneous Case, we first prove that the analytical solution preserves the regularity of the initial data in the random space, and then use it to establish the spectral accuracy of the proposed stochastic Galerkin method. Several numerical examples are presented to illustrate the validity of the proposed scheme.
Iacopo Carusotto - One of the best experts on this subject based on the ideXlab platform.
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excitations in a nonequilibrium bose einstein condensate of exciton polaritons
Physical Review Letters, 2007Co-Authors: Michiel Wouters, Iacopo CarusottoAbstract:We develop a mean-field theory of the dynamics of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied by means of a generalized Gross-Pitaevskii equation. A diffusive behavior of the Goldstone mode is found in the spatially Homogeneous Case and new features are predicted for the Josephson effect in a two-well geometry.
Kalle Parvinen - One of the best experts on this subject based on the ideXlab platform.
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evolution of dispersal in a spatially heterogeneous population with finite patch sizes
Proceedings of the National Academy of Sciences of the United States of America, 2020Co-Authors: Kalle Parvinen, Hisashi Ohtsuki, Joe Yuichiro WakanoAbstract:Dispersal is one of the fundamental life-history strategies of organisms, so understanding the selective forces shaping the dispersal traits is important. In the Wright’s island model, dispersal evolves due to kin competition even when dispersal is costly, and it has traditionally been assumed that the living conditions are the same everywhere. To study the effect of spatial heterogeneity, we extend the model so that patches may receive different amounts of immigrants, foster different numbers of individuals, and give different reproduction efficiency to individuals therein. We obtain an analytical expression for the fitness gradient, which shows that directional selection consists of three components: As in the Homogeneous Case, the direct cost of dispersal selects against dispersal and kin competition promotes dispersal. The additional component, spatial heterogeneity, more precisely the variance of so-called relative reproductive potential, tends to select against dispersal. We also obtain an expression for the second derivative of fitness, which can be used to determine whether there is disruptive selection: Unlike the Homogeneous Case, we found that divergence of traits through evolutionary branching is possible in the heterogeneous Case. Our numerical explorations suggest that evolutionary branching is promoted more by differences in patch size than by reproduction efficiency. Our results show the importance of the existing spatial heterogeneity in the real world as a key determinant in dispersal evolution.
Rodwell Kufakunesu - One of the best experts on this subject based on the ideXlab platform.
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the density process of the minimal entropy martingale measure in a stochastic volatility market a pde approach
Quaestiones Mathematicae, 2011Co-Authors: Rodwell KufakunesuAbstract:In a stochastic volatility market the Radon-Nikodym density of the minimal entropy martingale measure can be expressed in terms of the solution of a semilinear partial differential equation (PDE). This fact has been explored and illustrated for the time-Homogeneous Case in a recent paper by Benth and Karlsen [3]. However, there are some Cases which time-dependent parameters are required such as when it comes to calibration. This paper generalizes their model to the time-inHomogeneous Case.
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the density process of the minimal entropy martingale measure in a stochastic volatility market a pde approach
Quaestiones Mathematicae, 2011Co-Authors: Rodwell KufakunesuAbstract:In a stochastic volatility market the Radon-Nikodym density of the minimal entropy martingale measure can be expressed in terms of the solution of a semilinear partial differential equation (PDE). This fact has been explored and illustrated for the time-Homogeneous Case in a recent paper by Benth and Karlsen [3]. However, there are some Cases which time-dependent parameters are required such as when it comes to calibration. This paper generalizes their model to the time-inHomogeneous Case.
