共查询到20条相似文献,搜索用时 500 毫秒
1.
If X = X(t, ξ) is the solution to the stochastic porous media equation in O ì Rd, 1 £ d £ 3,{\mathcal{O}\subset \mathbf{R}^d, 1\le d\le 3,} modelling the self-organized criticality (Barbu et al. in Commun Math Phys 285:901–923, 2009) and X
c
is the critical state, then it is proved that
ò¥0m(O\Ot0)dt < ¥,\mathbbP-a.s.{\int^{\infty}_0m(\mathcal{O}{\setminus}\mathcal{O}^t_0)dt<{\infty},\mathbb{P}\hbox{-a.s.}} and
limt?¥ òO|X(t)-Xc|dx = l < ¥, \mathbbP-a.s.{\lim_{t\to{\infty}} \int_\mathcal{O}|X(t)-X_c|d\xi=\ell<{\infty},\ \mathbb{P}\hbox{-a.s.}} Here, m is the Lebesgue measure and Otc{\mathcal{O}^t_c} is the critical region {x ? O; X(t,x)=Xc(x)}{\{\xi\in\mathcal{O}; X(t,\xi)=X_c(\xi)\}} and X
c
(ξ) ≤ X(0, ξ) a.e. x ? O{\xi\in\mathcal{O}}. If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), limt ? ¥ òK|X(t)-Xc|dx = 0{\lim_{t \to {\infty}} \int_K|X(t)-X_c|d\xi=0} exponentially fast for all compact K ì O{K\subset\mathcal{O}} with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case ℓ = 0. 相似文献
2.
A. M. Frolov 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,61(3):571-577
The semi-exponential basis set of radial functions [A.M. Frolov, Phys.
Lett. A 374, 2361 (2010)] is used for variational computations of
bound states in three-electron atomic systems. It appears that the
semi-exponential basis set has a substantially greater potential for
accurate variational computations of bound states in three-electron atomic
systems than was originally anticipated. In particular, the 40-term
Larson’s wave function improved with the use of semi-exponential radial
basis functions now produces the total energy –7.4780581457
a.u. for the ground 12S-state in the ¥Li^\infty{\rm Li} atom (only one
spin function c1\chi_1 = aba\alpha\beta\alpha - baa\beta\alpha\alpha was used
in these calculations). This variational energy is very close to the exact
ground state energy of the ¥Li^\infty{\rm Li} atom and is substantially lower
than the total energy obtained with the original Larson’s 40-term wave
function (–7.477944869 a.u.). 相似文献
3.
In this paper, we prove a maximum principle for a frequency localized transport-diffusion equation. As an application, we
prove the local well-posedness of the supercritical quasi-geostrophic equation in the critical Besov spaces
\mathringB1-a¥,q{\mathring{B}^{1-\alpha}_{\infty,q}}, and global well-posedness of the critical quasi-geostrophic equation in
\mathringB0¥,q{\mathring{B}^{0}_{\infty,q}} for all 1 ≤ q < ∞. Here
\mathringBs¥,q {\mathring{B}^{s}_{\infty,q} } is the closure of the Schwartz functions in the norm of Bs¥,q{B^{s}_{\infty,q}}. 相似文献
4.
5.
We study the interference of resonant Higgs boson exchange in neutralino production in
m+ m-\mu^ + \mu^-
annihilation with longitudinally polarized beams. We use the energy distribution of the decay lepton in the process
[(c)\tilde]0j ? l± [(l)\tilde]-±\tilde{\chi}^0_j \to \ell^{\pm} \tilde{\ell}^\mp
to determine the polarization of the neutralinos. In the CP-conserving minimal supersymmetric standard model a non-vanishing asymmetry in the lepton energy spectrum is caused by the interference of Higgs boson exchange channels with different CP-eigenvalues. The contribution of this interference is large if the heavy neutral bosons H and A are nearly degenerate. We show that the asymmetry can be used to determine the couplings of the neutral Higgs bosons to the neutralinos. In particular, the asymmetry allows one to determine the relative phase of the couplings. We find large asymmetries and cross sections for a set of reference scenarios with nearly degenerate neutral Higgs bosons. 相似文献
6.
M. B. Ivanov S. S. Manokhin D. A. Nechaenko Yu. R. Kolobov 《Russian Physics Journal》2011,54(7):749-755
Investigations of disperse nonmetallic inclusions in unalloyed alpha titanium VT1-0 have been performed by using transmission
electron (including scanning and high-resolution) microscopy. Characteristic electron energy losses spectroscopy has shown
that these inclusions are titanium carbide particles. It has been revealed that the disperse carbides are formed in the titanium
hcp matrix as a phase based on the fcc sublattice of titanium atoms. The inclusion–matrix orientation relationship corresponds
to the well-known Kurdyumov–Sachs and Nishiyama–Wassermann relationships
[ 2[`11] 0 ]\upalpha ||[ 011 ]\updelta \text and ( 000[`1] )\upalpha ||( 1[`1] 1 )\updelta {\left[ {2\overline {11} 0} \right]_{{\upalpha }}}\parallel {\left[ {011} \right]_{{\updelta }}}{\text{ and }}{\left( {000\overline 1 } \right)_{{\upalpha }}}\parallel {\left( {1\overline 1 1} \right)_{{\updelta }}} . 相似文献
7.
The quantum effects for a physical system can be described by the set E(H)\mathcal{E(H)} of positive operators on a complex Hilbert space H\mathcal{H} that are bounded above by the identity operator I. We denote the set of sharp effects by P(H){\mathcal{P(H) }}. For A,B ? E(H)A,B\in\mathcal{E(H)}, the operation of sequential product
A°B=A\frac12BA\frac12A\circ B=A^{\frac{1}{2}}BA^{\frac{1}{2}} was proposed as a model for sequential quantum measurements. Denote by
A*B=\fracAB+BA2A\ast B=\frac{AB+BA}{2} the Jordan product of A,B ? E(H)A,B\in\mathcal{E(H)}. The main purpose of this note is to study some of the algebraic properties of the Jordan product of effects. Many of our
results show that algebraic conditions on A∗B imply that A and B commute for the usual operator product. And there are many common properties between Jordan product and sequential product
of effects. For example, if A∗B satisfies certain associative laws, then AB=BA. Moreover, A*B ? P(H)A\ast B\in{\mathcal{P(H) }} if and only if A°B ? P(H)A\circ B\in{\mathcal{P(H)}}. 相似文献
8.
This paper focuses on the issue of resilient dynamic output-feedback (DOF) control for ${{ \mathcal H }}_{\infty }$ synchronization of chaotic Hopfield networks with time-varying delay. The aim is to determine a DOF controller with gain perturbations ensuring that the ${{ \mathcal H }}_{\infty }$ norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound. A delay-dependent criterion for the ${{ \mathcal H }}_{\infty }$ synchronization is derived by employing the Lyapunov functional method together with some recent inequalities. Then, with the help of some decoupling techniques, sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases. Lastly, an example is used to illustrate the applicability of the results obtained. 相似文献
9.
Nakao Hayashi Pavel I. Naumkin Jean-Claude Saut 《Communications in Mathematical Physics》1999,201(3):577-590
We study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili (KP) equations $ \left\{\alignedat2 &u_t + u_{xxx} + \sigma\partial_x^{-1}u_{yy}= - (u^{\rho})_x, &;&;\qquad (t,x,y) \in {\bold R}\times {\bold R}^2,\\ \vspace{.5\jot} &u(0,x,y) = u_0 (x,y),&;&; \qquad (x,y) \in{\bold R}^2, \endalignedat \right. \TAG KP $ \left\{\alignedat2 &u_t + u_{xxx} + \sigma\partial_x^{-1}u_{yy}= - (u^{\rho})_x, &;&;\qquad (t,x,y) \in {\bold R}\times {\bold R}^2,\\ \vspace{.5\jot} &u(0,x,y) = u_0 (x,y),&;&; \qquad (x,y) \in{\bold R}^2, \endalignedat \right. \TAG KP where = 1 or = m 1. When = 2 and = m 1, (KP) is known as the KPI equation, while = 2, = + 1 corresponds to the KPII equation. The KP equation models the propagation along the x-axis of nonlinear dispersive long waves on the surface of a fluid, when the variation along the y-axis proceeds slowly [10]. The case = 3, = m 1 has been found in the modeling of sound waves in antiferromagnetics [15]. We prove that if S 3 is an integer and the initial data are sufficiently small, then the solution u of (KP) satisfies the following estimates: ||u(t)||¥ £ C (1 + |t|)-1 (log(2+|t|))k, ||ux(t)||¥ £ C (1 + |t|)-1 \|u(t)\|_\infty \le C (1 + |t|)^{-1} (\log (2+|t|))^{\kappa}, \|u_x(t)\|_\infty \le C (1 + |t|)^{-1} for all t ] R, where s = 1 if = 3 and s = 0 if S 4. We also find the large time asymptotics for the solution. 相似文献
10.
S. Rajesh K. P. Murali R. Ratheesh 《Applied Physics A: Materials Science & Processing》2011,104(1):159-164
Rutile filled PTFE composites have been fabricated through Sigma Mixing, Extrusion, Calendering and Hot pressing (SMECH) process.
Dielectric constant (er¢\varepsilon_{r}') and loss tangent (tan δ) of filled composites at microwave frequency region were measured by waveguide cavity perturbation technique using a Vector
Network Analyzer. The temperature coefficient of dielectric constant (ter¢\tau_{\varepsilon_{r}'}) was measured in the 0–100°C temperature range. In order to tailor the temperature coefficient of dielectric constant of
the composite, thermoplastic Poly (ether ether ketone) (PEEK) has been used as a secondary polymer. Flexible laminate having
a dielectric constant, er¢ ~ 10.4\varepsilon_{r}'\sim10.4, loss tangent tan δ∼0.0045 and ter¢ ~ -40 ppm/K\tau_{\varepsilon_{r}'}\sim-40\mbox{ ppm}/\mbox{K} was realized in Polytetrafluroethylene (PTFE)/rutile composites with the addition of 8 wt% PEEK. The reduction in ter¢\tau_{\varepsilon_{r}'} is mainly attributed to the positive ter¢\tau_{\varepsilon_{r}'} of PEEK and increased interface region in the composites as a result of the PEEK addition. 相似文献
11.
In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial
data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and
B-\frac12,\frac124{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS
ν
) has a unique global solution with initial data u0 = (u0h, u03){u_0 = (u_0^h, u_0^3)} which satisfies
||u0h||B exp(\fracCn4 ||u03||B4) £ c0n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or
||u0h||B-\frac12,\frac124 exp(\fracCn4 ||u03||B-\frac12,\frac1244) £ c0n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c
0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner
type spaces, [(Lpt)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L2t, f)\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L
1 function f(t). 相似文献
12.
Vasily Dolgushev 《Letters in Mathematical Physics》2011,97(2):109-149
We construct a 2-colored operad Ger
∞ which, on the one hand, extends the operad Ger
∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy
algebras. We show that Tamarkin’s Ger
∞-structure on the Hochschild cochain complex C
•(A, A) of an A
∞-algebra A extends naturally to a Ger+¥{{\bf Ger}^+_{\infty}}-structure on the pair (C
•(A, A), A). We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer
of this Ger+¥{{\bf Ger}^+_{\infty}}-structure to the cohomology of the pair (C
•(A, A), A). We show that Ger+¥{{\bf Ger}^+_{\infty}} is a sub DG operad of the first sheet E
1(SC) of the homology spectral sequence for the Fulton–MacPherson version SC of Voronov’s Swiss Cheese operad. Finally, we
prove that the DG operads Ger+¥{{\bf Ger}^+_{\infty}} and E
1(SC) are non-formal. 相似文献
13.
Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field
theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with
correlation function of the form μ d(t-t¢) / k^d-1+x\propto\delta(t-t') / k_{\bot}^{d-1+\xi}, where k
⊥=|k
⊥| and k
⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical
dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular
to the flow are essentially different. In contrast to the isotropic Kraichnan’s rapid-change model, the structure functions
show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary,
the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity
field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum
E μ k^1-e\mathcal{E} \propto k_{\bot}^{1-\varepsilon} and in the dispersion law w μ k^2-h\omega\propto k_{\bot}^{2-\eta}, the infrared behavior of the model is given by the limits of vanishing or infinite correlation time, with the crossover
at the ray η=0, ε>0 in the ε–η plane. The physical (Kolmogorov) point ε=8/3, η=4/3 lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point. 相似文献
14.
Krzysztof P. Wojciechowski 《Communications in Mathematical Physics》1999,201(2):423-444
In this paper we discuss the existence of the -determinant of a Dirac operator \Dd\Dd on a compact manifold with boundary. We show that the determinant is well defined in the case of the operator \Dd\Dd with a domain determined by a boundary condition from the smooth, self-adjoint Grassmannian \Grass¥*(\Dd)\Grass_{\infty}^*(\Dd) discussed in the papers [5, 13, 29]. We prove a generalization of a pasting formula for the m-invariant (see [34]). The results of the paper are used in the recent proof of the projective equality of the -determinant and Quillen determinant on \Grass¥*(\Dd)\Grass_{\infty}^*(\Dd) (see [30, 31]). 相似文献
15.
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However,
the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical
framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity
and dependency links. This formalism was applied to study Erdős-Rényi (ER) networks that include also dependency links. For
an ER network with average degree [`(k)]\bar{k} that is composed of dependency clusters of size s, the fraction of nodes that belong to the giant component, P
∞, is given by P¥=ps-1[1-exp(-[`(k)]pP¥) ]sP_{\infty}=p^{s-1}[1-\exp{(-\bar{k}pP_{\infty})} ]^{s} where 1−p is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks
and find a formula for the size of the giant component in the percolation process: P
∞=p
s−1(1−r
k
)
s
where r is the solution of r=p
s
(r
k−1−1)(1−r
k
)+1, and k is the degree of the nodes. These general results coincide, for s=1, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to s=1, where the percolation transition is second order, for s>1 it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding
their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency
clusters, removal of even a finite number (zero fraction) of the infinite network nodes will trigger a cascade of failures
that fragments the whole network. Specifically, for any given s there exists a critical degree value, [`(k)]min\bar{k}_{\min}, such that an ER network with [`(k)] £ [`(k)]min\bar{k}\leq \bar{k}_{\min} is unstable and collapse when removing even a single node. This result is in contrast to RR networks where such cascades
and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network. 相似文献
16.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
tr( (-D)2 - CHRd,2\frac1|x|4 - V(x) )-g £ Cgò\mathbbRd V(x)+g+ \fracd4 dx, g 3 1 - \frac d 4,\mathrm{tr}\left( (-\Delta)^2 - C^{\mathrm{HR}}_{d,2}\frac{1}{|x|^4} - V(x) \right)_-^{\gamma}\leq C_\gamma\int\limits_{\mathbb{R}^d} V(x)_+^{\gamma + \frac{d}{4}}\,\mathrm{d}x, \quad \gamma \geq 1 - \frac d 4, 相似文献
17.
In an addendum to the recent systematic Hermitization of certain N by N matrix Hamiltonians H
(N)(λ) (Znojil in J. Math. Phys. 50:122105, 2009) we propose an amendment H
(N)(λ,λ) of the model. The gain is threefold. Firstly, the updated model acquires a natural mathematical meaning of Runge-Kutta approximant
to a differential PT\mathcal{PT}-symmetric square well in which P\mathcal{P} is parity. Secondly, the appeal of the model in physics is enhanced since the related operator C\mathcal{C} of the so called “charge” (the requirement of observability of which defines the most popular Bender’s metric Q = PC\Theta=\mathcal{PC}) becomes also obtainable (and is constructed here) in an elementary antidiagonal matrix form at all N. Last but not least, the original phenomenological energy spectrum is not changed so that the domain of its reality (i.e.,
the interval of admissible couplings λ∈(−1,1)) remains the same. 相似文献
18.
José Ignacio Rosado 《Foundations of Physics》2011,41(7):1200-1213
The quantum state of a d-dimensional system can be represented by a probability distribution over the d
2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution
can be represented by a vector of
\mathbb Rd2-1\mathbb {R}^{d^{2}-1} in a (d
2−1)-dimensional simplex, we will call this set of vectors Q\mathcal{Q}. Other way of represent a d-dimensional system is by the corresponding Bloch vector also in
\mathbb Rd2-1\mathbb {R}^{d^{2}-1}, we will call this set of vectors B\mathcal{B}. In this paper it is proved that with the adequate scaling B=Q\mathcal{B}=\mathcal{Q}. Also we indicate some features of the shape of Q\mathcal{Q}. 相似文献
19.
Gustav Holzegel 《Communications in Mathematical Physics》2010,294(1):169-197
The massive wave equation ${\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0}
20.
The following hydrogen and oxygen concentration cells using the oxide protonic conductors,
\textCaZ\textr0.98\textI\textn0.02\textO3 - d {\text{CaZ}}{{\text{r}}_{0.98}}{\text{I}}{{\text{n}}_{0.02}}{{\text{O}}_{3 - \delta }} and
\textCaZ\textr0.9\textI\textn0.1\textO3 - d {\text{CaZ}}{{\text{r}}_{0.{9}}}{\text{I}}{{\text{n}}_{0.{1}}}{{\text{O}}_{{3} - \delta }} , as the solid electrolyte were constructed, and their polarization behavior was studied,
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