1,193 research outputs found
On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients
We prove the solvability in Sobolev spaces for both divergence and
non-divergence form higher order parabolic and elliptic systems in the whole
space, on a half space, and on a bounded domain. The leading coefficients are
assumed to be merely measurable in the time variable and have small mean
oscillations with respect to the spatial variables in small balls or cylinders.
For the proof, we develop a set of new techniques to produce mean oscillation
estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in
Arch. Rational Mech. Ana
Partial Schauder estimates for second-order elliptic and parabolic equations
We establish Schauder estimates for both divergence and non-divergence form
second-order elliptic and parabolic equations involving H\"older semi-norms not
with respect to all, but only with respect to some of the independent
variables.Comment: CVPDE, accepted (2010)
Chaos edges of -logistic maps: Connection between the relaxation and sensitivity entropic indices
Chaos thresholds of the -logistic maps are numerically analysed at accumulation points of cycles 2, 3
and 5. We verify that the nonextensive -generalization of a Pesin-like
identity is preserved through averaging over the entire phase space. More
precisely, we computationally verify , where the entropy (), the sensitivity to the initial
conditions , and
(). The entropic index
depend on
both and the cycle. We also study the relaxation that occurs if we start
with an ensemble of initial conditions homogeneously occupying the entire phase
space. The associated Lebesgue measure asymptotically decreases as
(). These results led to (i) the first
illustration of the connection (conjectured by one of us) between sensitivity
and relaxation entropic indices, namely , where the positive numbers depend on the
cycle; (ii) an unexpected and new scaling, namely ( for , and for ).Comment: 5 pages, 5 figure
A Design of a Material Assembly in Space-Time Generating and Storing Energy
The paper introduces a theoretical background of the mechanism of electromagnetic energy and power accumulation and its focusing in narrow pulses travelling along a transmission line with material parameters variable in 1D-space and time. This mechanism may be implemented due to a special material geometry- a distribution of two different dielectrics in a spatio-temporal checkerboard. We concentrate on the practically reasonable means to bring this mechanism into action in a device that may work both as energy generator and energy storage. The basic ideas discussed below appear to be fairly general; we have chosen their electromagnetic implementation as an excellent framework for the entire concept
Physical applications of second-order linear differential equations that admit polynomial solutions
Conditions are given for the second-order linear differential equation P3 y"
+ P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of
degree n. Several application of these results to Schroedinger's equation are
discussed. Conditions under which the confluent, biconfluent, and the general
Heun equation yield polynomial solutions are explicitly given. Some new classes
of exactly solvable differential equation are also discussed. The results of
this work are expressed in such way as to allow direct use, without preliminary
analysis.Comment: 13 pages, no figure
Electron energy relaxation under terahertz excitation in (Cd1−xZnx)3As2 Dirac semimetals
We demonstrate that measurements of the photo-electromagnetic effect using terahertz laser radiation provide an argument for the existence of highly conductive surface electron states with a spin texture in Dirac semimetals (Cd₁-xZnx)₃As
Complex Scaled Spectrum Completeness for Coupled Channels
The Complex Scaling Method (CSM) provides scattering wave functions which
regularize resonances and suggest a resolution of the identity in terms of such
resonances, completed by the bound states and a smoothed continuum. But, in the
case of inelastic scattering with many channels, the existence of such a
resolution under complex scaling is still debated. Taking advantage of results
obtained earlier for the two channel case, this paper proposes a representation
in which the convergence of a resolution of the identity can be more easily
tested. The representation is valid for any finite number of coupled channels
for inelastic scattering without rearrangement.Comment: Latex file, 13 pages, 4 eps-figure
Chaotic Interaction of Langmuir Solitons and Long Wavelength Radiation
In this work we analyze the interaction of isolated solitary structures and
ion-acoustic radiation. If the radiation amplitude is small solitary structures
persists, but when the amplitude grows energy transfer towards small spatial
scales occurs. We show that transfer is particularly fast when a fixed point of
a low dimensional model is destroyed.Comment: LaTex + 4 eps file
Hamiltonian dynamics of homopolymer chain models
The Hamiltonian dynamics of chains of nonlinearly coupled particles is
numerically investigated in two and three dimensions. Simple, off-lattice
homopolymer models are used to represent the interparticle potentials. Time
averages of observables numerically computed along dynamical trajectories are
found to reproduce results given by the statistical mechanics of homopolymer
models. The dynamical treatment, however, indicates a nontrivial transition
between regimes of slow and fast phase space mixing. Such a transition is
inaccessible to a statistical mechanical treatment and reflects a bimodality in
the relaxation of time averages to corresponding ensemble averages. It is also
found that a change in the energy dependence of the largest Lyapunov exponent
indicates the theta-transition between filamentary and globular polymer
configurations, clearly detecting the transition even for a finite number of
particles.Comment: 11 pages, 8 figures, accepted for publication in Physical Review
Semi-Parametric Drift and Diffusion Estimation for Multiscale Diffusions
We consider the problem of statistical inference for the effective dynamics
of multiscale diffusion processes with (at least) two widely separated
characteristic time scales. More precisely, we seek to determine parameters in
the effective equation describing the dynamics on the longer diffusive time
scale, i.e. in a homogenization framework. We examine the case where both the
drift and the diffusion coefficients in the effective dynamics are
space-dependent and depend on multiple unknown parameters. It is known that
classical estimators, such as Maximum Likelihood and Quadratic Variation of the
Path Estimators, fail to obtain reasonable estimates for parameters in the
effective dynamics when based on observations of the underlying multiscale
diffusion. We propose a novel algorithm for estimating both the drift and
diffusion coefficients in the effective dynamics based on a semi-parametric
framework. We demonstrate by means of extensive numerical simulations of a
number of selected examples that the algorithm performs well when applied to
data from a multiscale diffusion. These examples also illustrate that the
algorithm can be used effectively to obtain accurate and unbiased estimates.Comment: 32 pages, 10 figure
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