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1.
The decay of Burgers turbulence with compactly supported Gaussian “white noise” initial conditions is studied in the limit
of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and velocity differences
are computed exactly, together with the “time-like” structure functions T
n
(t,τ)≡< (u(t+τ) -u(t))
n
>.
The analysis of the answers reveals both well known features of Burgers turbulence, such as the presence of dissipative anomaly,
the extreme anomalous scaling of the velocity structure functions and self similarity of the statistics of the velocity field,
and new features such as the extreme anomalous scaling of the “time-like” structure functions and the non-existence of a global
inertial scale due to multiscaling of the Burgers velocity field.
We also observe that all the results can be recovered using the one point probability distribution function of the shock strength
and discuss the implications of this fact for Burgers turbulence in general.
Received: 4 October 1999 / Accepted: 4 February 2000 相似文献
2.
Hatem Zaag 《Communications in Mathematical Physics》2002,225(3):523-549
We consider u(x,t) a solution of u
t
=Δu+|u|
p
− 1
u that blows up at time T, where u:ℝ
N
×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)1, 1/2−η for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up
set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C
1, 1/2−η for any η>0.
Received: 20 June 2001 / Accepted: 6 October 2001 相似文献
3.
Federico Camia Luiz Renato G. Fontes Charles M. Newman 《Journal of statistical physics》2006,125(5-6):1155-1171
We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for p = p
c+λδ1/ν, with ν = 4/3, as the lattice spacing δ → 0. Our proposed framework extends previous analyses for p = p
c, based on SLE
6. It combines the continuum nonsimple loop process describing the full scaling limit at criticality with a Poissonian process
for marking double (touching) points of that (critical) loop process. The double points are exactly the continuum limits of
“macroscopically pivotal” lattice sites and the marked ones are those that actually change state as λ varies. This structure
is rich enough to yield a one-parameter family of near-critical loop processes and their associated connectivity probabilities
as well as related processes describing, e.g., the scaling limit of 2D minimal spanning trees. 相似文献
4.
Sigurd Assing 《Communications in Mathematical Physics》2002,225(3):611-632
We consider the stationarity of a Burgers equation with an external random force of gradient type in one space dimension.
The expected stationary measure is the white noise measure on the space of tempered distributions. As a consequence, the nonlinearity
of the formal equation u
t
+λu
u
x
=νu
xx
+η
x
is ill-defined. Introducing a pregenerator we can formulate a generalized martingale problem leading to a meaningful version
of the formal equation which was an open problem.
Received: 9 March 2001 / Accepted: 10 October 2001 相似文献
5.
Fabio Gavarini 《Czechoslovak Journal of Physics》2001,51(12):1330-1335
The “quantum duality principle” states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal
Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie bialgebra as
well. We extend this to a much more general result: namely, for any principal ideal domainR and for each primepεR we establish an “inner” Galois’ correspondence on the categoryHA of torsionless Hopf algebras overR, using two functors (fromHA to itself) such that the image of the first and the second is the full subcategory of those Hopf algebras which are commutative
and cocommutative, modulop, respectively (i.e., they are“quantum function algebras” (=QFA) and“quantum universal enveloping algebras” (=QUEA), atp, respectively). In particular we provide a machine to get two quantum groups — a QFA and a QUEA — out of any Hopf algebraH over a fieldk: apply the functors tok[ν] ⊗k H forp=ν.
A relevant example occurring in quantum electro-dynamics is studied in some detail.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001 相似文献
6.
The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible
to construct non-trivial Fredholm modules on post critically finite fractals by regular harmonic structures (D, r). The modules are (d
S
, ∞)–summable, the summability exponent d
S
coinciding with the spectral dimension of the generalized Laplacian operator associated with (D, r). The characteristic tools of the noncommutative infinitesimal calculus allow to define a d
S
-energy functional which is shown to be a self-similar conformal invariant.
Thiswork has been supported by the project “Teoria ellittica e forme di Dirichlet su spazi frattali” G.N.A.M.P.A. 2008 and
by the G.R.E.F.I.-G.E.N.C.O. French-Italian Research Group. 相似文献
7.
We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at least θ occupied neighbors, occupied sites remain occupied forever. It is known that, when b>θ≥2, the limiting density q=q(p) of occupied sites exhibits a jump at some p
T=p
T(b,θ)∈(0,1) from q
T:=q(p
T)<1 to q(p)=1 when p>p
T. We investigate the metastable behavior associated with this transition. Explicitly, we pick p=p
T+h with h>0 and show that, as h
↓0, the system lingers around the “critical” state for time order h
−1/2 and then passes to fully occupied state in time O(1). The law of the entire configuration observed when the occupation density is q∈(q
T,1) converges, as h
↓0, to a well-defined measure. 相似文献
8.
M.A. Koshelev M.Y. Tretyakov R.M. Lees L.-H. Xu 《Applied physics. B, Lasers and optics》2006,85(2-3):273-277
Nitrogen and oxygen pressure broadening parameters for seven r
P(J”,0) transitions of the ν1+ν3 overtone band of the main isotope of ammonia with J” varied from 2 to 9 have been measured at room temperature using an external cavity tunable diode laser spectrometer. Air-broadening parameters have also been calculated from the N2 and O2 measurements. The results are compared to previous measurements in the ν1, ν2, ν3, ν4 and ν1+ν3 bands and to the parameters for the ν3 band that are reported in the HITRAN database. PACS 33.70.Jg; 33.70.-W; 33.20.Ea; 42.62.Fi; 42.68.Ca 相似文献
9.
In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e.
“spins”) on each site of the chain and diagonal boundary matrices (K
+(u), K
−(u)). The nested Bethe ansatz applies for a general K
−(u), but a particular form of the K
+(u) matrix. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe
vectors are expressed using a trace formula 相似文献
10.
TheA
2
Π
ustate of O2
+ was earlier established as an inverted state contrary to previous assumptions. The rotational analysis of a few more bands
of theA-X system of O2
+ has now been completed. These studies show that the spin-orbit coupling constantA in theA
2
Π
ustate gradually varies with the vibrational quantum numberν and is found to be positive forν⩾6. It has also been observed that the spia-rotation interaction is not negligible in theA
2
Π
ustate. The spin splitting constantγ is reported for various vibrational levels of this electronic state. 相似文献
11.
Boundary Layer Stability¶in Real Vanishing Viscosity Limit 总被引:5,自引:0,他引:5
In the previous paper [20], an Evans function machinery for the study of boundary layer stability was developed. There,
the analysis was restricted to strongly parabolic perturbations, that is to an approximation of the form u
t
+(F(u))
x
=ν(B(u)u
x
)
x
$ (ν≪1) with an “elliptic” matrix B. However, real models, like the Navier–Stokes approximation of the Euler equations for a gas flow, involve incompletely
parabolic perturbations: B is not invertible in general.
We first adapt the Evans function to this realistic framework, assuming that the boundary is not characteristic, neither for
the hyperbolic first order system u
t
+(F(u))
x
= 0, nor for the perturbed system. We then apply it to the various kinds of boundary layers for a gas flow. We exhibit some
examples of unstable boundary layers for a perfect gas, when the viscosity dominates heat conductivity.
Received: 27 November 2000/ Accepted: 16 March 2001 相似文献
12.
C?t?lin I. Carstea 《Communications in Mathematical Physics》2010,300(2):487-528
The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from
\mathbbR2+1 ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d
ρ
2 + g(ρ)2
dθ2, g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u
tt
+ u
rr
+ r
−1
u
r
= r
−2
g(u)g′(u), λ(t) = t
−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0. 相似文献
13.
Thomas Bartsch Angela Pistoia Tobias Weth 《Communications in Mathematical Physics》2010,297(3):653-686
We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain ${\Omega\subset\mathbb{R}^2}We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain
W ì \mathbbR2{\Omega\subset\mathbb{R}^2} , which is not necessarily simply connected. On an arbitrary bounded domain we obtain new equilibria for N = 3 or N = 4. If Ω has an axial symmetry we obtain a symmetric equilibrium for each
N ? \mathbbN{N\in\mathbb{N}} . We also obtain new stream functions solving the sinh-Poisson equation -Dy = rsinhy{-\Delta\psi=\rho\sinh\psi} in Ω with Dirichlet boundary conditions for ρ > 0 small. The stream function yr{\psi_\rho} induces a stationary velocity field vr{v_\rho} solving the Euler equation in Ω. On an arbitrary bounded domain we obtain velocitiy fields having three or four counter-rotating
vortices. If Ω has an axial symmetry we obtain for each N a velocity field vr{v_\rho} that has a chain of N counter-rotating vortices, analogous to the Mallier-Maslowe row of counter-rotating vortices in the plane. Our methods also
yield new nodal solutions for other semilinear Dirichlet problems, in particular for the Lane-Emden-Fowler equation -Du=|u|p-1u{-\Delta u=|u|^{p-1}u} in Ω with p large. 相似文献
14.
M. C. Suarez 《Indian Journal of Physics》2011,85(7):1085-1089
We present an analysis of relative baryon to meson production for intermediate transverse momentum hadrons associated with
a high-p
T
trigger. The results of pion and (anti)proton spectra and ratios are presented for the “jet” and “ridge” components of the
two-dimensional Δν − Δϕ triggered correlations in central Au+Au collisions at ?{sNN }\sqrt {s_{NN} } = 200 GeV. We compare these results with the inclusive (non-triggered) measurements for the same data, and discuss our observations
in conjunction with the results from d+Au, and pp data. 相似文献
15.
Surface plasmon-phonon polaritons (SPPP’s) of types 3 and 4 are investigated in doped anisotropic single crystals of hexagonal
silicon carbide (6H-SiC) in the orientation corresponding to K⊥C and xy⊥C. It is shown that a dispersion dependence of the type-3 SPPP’s bounded by K appears in 6H-SiC when the plasmon frequency increases to ν
p⊥⩾350 cm−1. At ν
p⊥⩾400 cm−1, ν
s(K) exists for type-4 SPPP’s in the frequency range Ω
∥
+
<ν<
⊥
+
. When the concentration of free charge carriers is increased, the dispersion curves are displaced toward higher frequencies.
The conditions for the existence of type-3 and type-4 SPPP’s in 6H-SiC are determined.
Fiz. Tverd. Tela (St. Petersburg) 40, 636–639 (April 1998) 相似文献
16.
M. Vatasescu F. Masnou-Seeuws 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,21(2):191-204
The paper contains a time-dependent investigation of the tunneling effect observed in the photoassociation spectrum of Cs2 and attributed to the 0g
-(6s, 6p
3/2) double well. When by photoassociation of two cold cesium atoms a vibrational level of the outer well is populated, tunneling
is an efficient mechanism for transferring the population to the inner well (R < 15a
0), where spontaneous emission may lead to formation of cold molecules in low vibrational levels of the a
3Σ+
u(6s, 6s) electronic state. This tunneling effect is analyzed by wavepackets propagation, first considering the double well potential
alone, and following a packet made by a superposition of states initially located at large distances. Characteristic times
for the vibration dynamics, corresponding to a beating phenomenon between the two wells, to partial “revival” at large distances,
and to maxima in the population localized in the inner well are reported and discussed. Second, we simulate the two-channels
a
3Σ+
u(6s, 6s)↦0g
-(6s, 6p
3/2) photoassociation at detunings around 2.9 cm-1: the inner well can be populated either by the excitation of a vibrational level of the external well (resonant excitation),
or by tuning the photoassociation laser at the energy of the inner well level which displays tunneling (“off-resonance excitation”).
In the first case the photoassociation is efficient, while the tunneling probability is small; in the second, the tunneling
probability is large, so that despite the poor efficiency of the photoassociation process, more population can be transferred
to the inner well. This second choice is shown to be very sensitive to the laser intensity, which could be used to control
the population of the inner well and hence the formation of ultracold molecules in low vibrational levels.
Received 19 April 2002 Published online 1st October 2002
RID="a"
ID="a"e-mail: francoise.masnou@lac.u-psud.fr 相似文献
17.
A. I. Reznikov S. Ya. Umanskii Yu. F. Chaikina 《Russian Journal of Physical Chemistry B, Focus on Physics》2010,4(2):203-209
Rate constants for electron-vibrational energy exchange Ar(3
P
2) + N2(X
1Σ
g
+, ν = 0) → Ar(1
S
0) + N2(C
3Π
u
, ν′), where ν′ = 0, 1, 2, were calculated. Calculations were performed taking into account the presence of a resonance in electron scattering
by N2(X
1Σ
g
+). As a result, the interaction of Ar(3
P
2) with N2(X
1Σ
g
+, ν = 0) was characterized by attraction and, in the end, intersection of electron-vibrational potential surfaces correlating
with Ar(3
P
2) + N2(X
1Σ
g
+, ν = 0) and Ar(1
S
0) + N2(C
3Π
u
, ν′) at interparticle distances of 2.5–3.5 ?. Exchange interaction at which electron-vibrational transitions in the region of
intersection of electron-vibrational transitions in the region of intersection of electron-vibrational potential surfaces
accompanied by spin exchange were induced was calculated by the asymptotic method. The rate constants determined at 300–600
K were on the order of 10−11−10−12 cm3/s and weakly increased as the temperature grew. Mainly the C
3Π
u
, ν′ = 0 state of the N2 molecule was populated. The calculation results were in satisfactory agreement with the experimental data obtained at 300
K. 相似文献
18.
Marcelo S. Berman Luis A. Trevisan 《International Journal of Theoretical Physics》2009,48(7):1929-1932
We find a solution for exponential inflation in a Brans-Dicke generalized model, where the coupling “constant” is variable.
While in General Relativity the equation of state is p=−ρ, here we find p=α
ρ, where α<−2/3. The negativity of cosmic pressure implies acceleration of the expansion, even with Λ<0. 相似文献
19.
Yu. I. Mankov 《Technical Physics》2011,56(8):1147-1157
Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through
the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation
that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of
averaged waves, as well as position ν
m
and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of
wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities
is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively
agrees with the ν
m
behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping
and Δν are found to be similar functions of k. The results are compared to the numerical calculation data. 相似文献
20.
I. Štekl P. Čermák P. Beneš V. B. Brudanin K. N. Gusev V. G. Egorov A. A. Klimenko V. E. Kovalenko A. Kovalík N. I. Rukhadze A. V. Salamatin V. V. Timkin Ts. Vylov Ch. Briançon F. Šimkovic 《Czechoslovak Journal of Physics》2006,56(5):505-510
Present status of the experiment TGV II which is devoted to the measurement of double-beta decay of 106Cd is given. The low background spectrometer TGV II is installed in the Modane Underground Laboratory and has been running
from February 2005 with approx 10 grams of 106Cd enriched at 75%. After an analysis of 3736 hours of experimental data the new improved half-life limit for 2νEC/EC decay of 106Cd (0
g.s.
+
→ 0
g.s.
+
) is given as T
1
2/2ν
> 4.8 × 1019 years (90% CL). The search for 2νEC/EC decay of 106Cd to the excited states of 106Pd allows to determine the limits of the half-lives T
1
2/2ν
(0
g.s.
+
→ 2
1
+
) > 3.9 × 1019 years (90% CL) and T
1
2/2ν
(0
g.s.
+
→ 0
1
+
) > 5.8 × 1019 years (90% CL).
Presented by I. Štekl at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September
26–29, 2005. 相似文献