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1.
We study a reaction-diffusion system of N equations with k nonzero and N − k zero diffusion coefficients. More exactly, the first k equations of the system contain the terms a
i
Δu
i
− f
j
(u, v), i = 1, …, k, with the diffusion coefficient a
i
> 0. The right-hand sides of the other N − k equations contain only nonlinear interaction functions −h
j
(u, v), j = k + 1, …, N, with zero diffusion. Here u = (u
1, …, u
k
) and v = (υ
k+1, …, υ
N
) are unknown concentration vectors. Under appropriate assumptions on the interaction functions f(·) and h(·), we construct the trajectory attractor of this reaction-diffusion system. We also find the trajectory attractors , δ = (δ
1, …, δ
k
), for the analogous reaction-diffusion systems having the terms δ
j
Δυ
j
− h
j
(u, v), j = k + 1, …, N, with small diffusion coefficients δ
j
⩾ 0 in the last N − k equations. We prove that the trajectory attractors converge to (in an appropriate topology) as δ → 0+.
Dedicated to the memory of Vladimir Borovikov
Partially supported by the Russian Foundation for Basic Research (projects nos. 08-01-00784 and 07-01-00500). 相似文献
2.
FePS3 is a layered antiferromagnet (T
N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal
distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate5
T
2g
ground state of the Fe2+ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σi [δ(L
iz
2
−2)+|λ|L
i
.S
i
]−Σ
ij
J
ij
S
i
.S
j
. The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J
ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective
Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J
nn
k=27.7 K; andJ
nnn
k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT
N=122 K for FePS3, which is remarkably close to the observed value of theT
N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with
the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS3, for which the high temperature series expansion susceptibility is available. 相似文献
3.
We obtain bounds for the spectrum and for the total width of the spectral gaps for Jacobi matrices on ℓ2(ℤ) of the form (Hψ)
n
=a
n−1
ψ
n−1
+b
nψ
n
+a
nψ
n+1
, where a
n=a
n+q
and b
n=b
n+q
are periodic sequences of real numbers. The results are based on a study of the quasimomentum k(z) corresponding to H. We consider k(z) as a conformal mapping in the complex plane. We obtain the trace identities which connect integrals of the Lyapunov exponent
over the gaps with the normalised traces of powers of H.
Received: 17 April 2002 / Accepted: 1 October 2002 Published online: 13 January 2003
Communicated by B. Simon 相似文献
4.
Anne Boutet de Monvel Athanassis S. Fokas Dmitry Shepelsky 《Communications in Mathematical Physics》2006,263(1):133-172
Let q(x,t) satisfy an integrable nonlinear evolution PDE on the interval 0<x<L, and let the order of the highest x-derivative be n. For a problem to be at least linearly well-posed one must prescribe N boundary conditions at x=0 and n−N boundary conditions at x=L, where if n is even, N=n/2, and if n is odd, N is either (n−1)/2 or (n+1)/2, depending on the sign of ∂nxq. For example, for the sine-Gordon (sG) equation one must prescribe one boundary condition at each end, while for the modified
Korteweg-de Vries (mKdV) equations involving qt+qxxx and qt−qxxx one must prescribe one and two boundary conditions, respectively, at x=0. We will refer to these two mKdV equations as mKdV-I and mKdV-II, respectively.
Here we analyze the Dirichlet problem for the sG equation, as well as typical boundary value problems for the mKdV-I and mKdV-II
equations. We first show that the unknown boundary values at each end (for example, qx(0,t) and qx(L,t) in the case of the Dirichlet problem for the sG equation) can be expressed in terms of the given initial and boundary conditions
through a system of four nonlinear ODEs. We then show that q(x,t) can be expressed in terms of the solution of a 2×2 matrix Riemann-Hilbert problem formulated in the complex k-plane. This problem has explicit (x,t) dependence in the form of an exponential; for example, for the case of the sG this exponential is exp {i(k−1/k)x+i(k+1/k)t}. Furthermore, the relevant jump matrices are explicitly given in terms of the spectral functions {a(k),b(k)}, {A(k),B(k)}, and , which in turn are defined in terms of the initial conditions, of the boundary values of q and of its x-derivatives at x=0, and of the boundary values of q and of its x-derivatives at x=L, respectively. This Riemann-Hilbert problem has a global solution. 相似文献
5.
Lorenzo Iorio 《General Relativity and Gravitation》2011,43(6):1697-1706
The strategy followed so far in the performed or proposed tests of the general relativistic Lense-Thirring effect in the gravitational
field of the Earth with laser-ranged satellites of LAGEOS type relies upon the cancelation of the disturbing huge precessions
induced by the first even zonal harmonic coefficient J
2 of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential by means of suitably designed
linear combinations of the nodes Ω of more than one spacecraft. Actually, such a removal does depend on the accuracy with
which the coefficients of the combinations adopted can be realistically known. Uncertainties of the order of 2 cm in the semimajor
axes a and 0.5 milliarcseconds in the inclinations I of LAGEOS and LAGEOS II, entering the expression of the coefficient c
1 of the combination of their nodes used so far, yield an uncertainty δc
1 = 1.30 × 10−8. It gives an imperfectly canceled J
2 signal of 10.8 milliarcseconds per year corresponding to 23% of the Lense-Thirring signature. Uncertainties of the order
of 10–30 microarcseconds in the inclinations yield δc
1 = 7.9 × 10−9 which corresponds to an uncanceled J
2 signature of 6.5 milliarcseconds per year, i.e. 14% of the Lense-Thirring signal. Concerning a future LAGEOS-LAGEOS II-LARES
combination with coefficients k
1 and k
2, the same uncertainties in a and the less accurate uncertainties in I as before yield δk
1 = 1.1 × 10−8, δk
2 = 2 × 10−9; they imply a residual J
2 combined precession of 14.7 milliarcseconds per year corresponding to 29% of the Lense-Thirring trend. Uncertainties in the
inclinations at ≈ 10 microarcseconds level give δk
1 = 5 × 10−9, δk
2 = 2 × 10−9; the uncanceled J
2 effect is 7.9 milliarcseconds per year, i.e. 16% of the relativistic effect. 相似文献
6.
The spin-1 Ising model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated
on a cellular automaton which improved from the Creutz cellular automaton (CCA) for a simple cubic lattice. The simulations
have been made for several k=K/J and d=D/J in the 0≤d<3 and −2≤k≤0 parameter regions. We confirm the existence of the re-entrant and the successive re-entrant phase transitions near the
phase boundary. The phase diagrams characterizing phase transitions are presented for comparison with those obtained from
other calculations. The static critical exponents are estimated within the framework of the finite-size scaling theory at
d=0, 1 and 2 in the interval −2≤k≤0. The results are compatible with the universal Ising critical behavior. 相似文献
7.
Yu. V. Bogdanov S. I. Kanorskii A. A. Papchenko I. I. Sobelman V. N. Sorokin I. I. Struk E. A. Yukov 《Journal of Russian Laser Research》1994,15(6):477-492
The constants of pressure self-broadening of cesium have been measured for the transitions 6P
1/2−8D
3/2, 6P
3/2−10S
1/2, and 5D
5/2−nF(n=14−19). The constants of the resonance broadening of the 6P
1/2 and 6P
3/2 cesium levels, the constants of electron collisional broadening of thenF levels at a temperature ofT≈1500 K, and the oscillator strengths of the 5D
5/2−nF(n=14−18) transitions have been determined.
Translated from Trudy Fizicheskogo Instituta im. P. N. Lebedeva, Lebedev Physics Institute, Russian Academy of Sciences, Moscow,
Vol. 195, pp. 217–233, 1989. 相似文献
8.
The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are
calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system,
the temperature, and the parameters of the model is investigated. It is shown that a chain with N
a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational
error, this value, (t/U)c=0.300±0.005, agrees with the value (t/U)c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic
Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t
c)−1/2].
Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996) 相似文献
9.
The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized
trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space
information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as St(D) = N(a D - b lnN) S_\mathrm{t}^{(D)} = N(a D - b \ln N) , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula
and Myceilski. 相似文献
10.
The theoretical optimization of the design parametersN
A
,N
D
andW
P
has been done for efficient operation of Au-p-n Si solar cell including thermionic field emission, dependence of lifetime and mobility on impurity concentrations, dependence
of absorption coefficient on wavelength, variation of barrier height and hence the optimum thickness ofp region with illumination. The optimized design parametersN
D
=5×1020 m−3,N
A
=3×1024 m−3 andW
P
=11.8 nm yield efficiencyη=17.1% (AM0) andη=19.6% (AM1). These are reduced to 14.9% and 17.1% respectively if the metal layer series resistance and transmittance with
ZnS antireflection coating are included. A practical value ofW
P
=97.0 nm gives an efficiency of 12.2% (AM1). 相似文献
11.
We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having
anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r
2, u=4πξr
2, v
r=4πp
r
r
2, v
⊥=4πp
⊥
r
2[ρ, ξ(=−(1/2)F
14
F
14), p
r, p
⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas
ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field],
we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following
assumptions to solve the field equations (i) u=v
r=(a
2/2κ)r
n+2, v
⊥=k
1
v
r, w=k
2
v
r; a
2, n(>0), k
1, k
2 being constants with κ=((k
1+2)/3+k
2) and (ii) w+u=(b
2/2)r
n+2, u=v
r, v
⊥−v
r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as
well as physical variables for all values of n>0. Even though the second solution contains terms like k/r
2 since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing
it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior
Reissner-Nordstrom solution over a fixed boundary.
Dedicated to Prof. F A E Pirani. 相似文献
12.
ESR investigations on exchange coupled pairs of Cu ions in single crystals of Cu(dtc)2, isomorphously diluted with the corresponding diamagnetic zinc salt, are reported. The spin Hamiltonian parameters for the
coupled species (S=1) are:g
‖=2.1025,g
+=2.031,A=75.1×10−4 cm−1,B=14.8×10−4,D=276.0×10−4 cm−1 andE=46.7×10−4 cm−1. While theg andA tensors show tetragonal symmetry, the zeor-field splitting tensor is rhombic and has principal axes different from those
of theg andA tensors. Intensity measurements made down to 4.2 K indicate that the exchange is ferromagnetic with |FFF| ∼ 10 cm−1. Direct dipole-dipole interaction appears to be the major contribution to the zero-field splitting. A calculation on the
distributed point dipole model shows that dipolar interaction is considerably modified by the high covalency of the Cu-S bond
and accounts for the rhombic nature of the tensor. The possible exchange mechanisms in Cu(dtc)2—direct exchange and superexchange through the bridging sulphurs—are discussed. 相似文献
13.
We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS2. Measurements have been carried out to ascertain the spin state of Fe3+ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently
interpreted using aS=1/2 spin ground state for the Fe3+ ion. The features in the optical spectra have been assigned to transitions within thed-electron manifold of the Fe3+ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility
is typical of a low-dimensional system and exhibits a broad maximum at ∼565K. The susceptibility shows a well defined transition
to a three dimensionally ordered antiferromagnetic state atT
N=250 K. The intra and interchain exchange constants,J andJ′, have been evaluated from the experimental susceptibilities using the relationship between these quantities, andχ
max,T
max, andT
N for a spin 1/2 one-dimensional chain. The values areJ=−440.71 K, andJ′=53.94 K. Using these values ofJ andJ′, the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used belowT
N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infiniteS=1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS2. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility
at 0K (2.75×10−4 emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected
value (2.7×10−4 emu/mol) obtained from the experimental data. 相似文献
14.
N-m-tolyl phthalimide, C15NO2H11 crystallizes in the space group Cc with unit cell dimensions,a=8·54(1),b=19·89(2),c = 7·59(1)A, β=114·53(1)° andZ=4.V=1173(2)A3,D
m
=1·35(1),D
c
= 1·344 mg.m−3,M
r
=237 λCoKa=1·7903A. The structure was solved byMULTAN and refined to an R-factor of 0·116 for 632 counter reflections. The molecules are held together by van der Waal’s forces.
The angle between the tolyl plane and the plane through the phthalimide group is 53·4(4)°.
Contribution No. 607. 相似文献
15.
We consider the harmonic superspaces associated with SU(2,2/N) superconformal algebras. For arbitrary N, we show that massless representations, other than the chiral ones, correspond to [N/2] elementary ultrashort analytic superfields whose first component is a scalar in the k antisymmetric irrep of SU(N) (k=1...[N/2]) with top spin J
top=(N/2–k/2,0). For N=2n, we analyze UIR's obtained by tensoring the self-conjugate ultrashort multiplet J
top=(n/2,0) and show that N–1 different basic products give rise to all possible UIR's with residual shortening. 相似文献
16.
A new dark energy model called “ghost dark energy” was recently suggested to explain the observed accelerating expansion of
the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter,
ρ
D
= α H, where α is a constant of order LQCD3{\Lambda_{\rm QCD}^3} and ΛQCD ~ 100 MeV is QCD mass scale. In this Letter, we extend the ghost dark energy model to the universe with spatial curvature
in the presence of interaction between dark matter and dark energy. We study cosmological implications of this model in detail.
In the absence of interaction the equation of state parameter of ghost dark energy is always w
D
> −1 and mimics a cosmological constant in the late time, while it is possible to have w
D
< −1 provided the interaction is taken into account. When k = 0, all previous results of ghost dark energy in flat universe are recovered. For the observational test, we use Supernova
type Ia Gold sample, shift parameter of cosmic microwave background radiation and the correlation of acoustic oscillation
on the last scattering surface and the baryonic acoustic peak from Sloan Digital Sky Survey are used to confine the value
of free parameter of mentioned model. 相似文献
17.
Masayoshi Senba Alicia C. Gonzalez James R. Kempton Donald J. Arseneau James J. Pan Alexandra Tempelmann Donald G. Fleming 《Hyperfine Interactions》1991,65(1-4):979-986
The addition reaction Mu+NO+M→MuNO+M and the spin exchange reaction Mu(↑) +MO(↓)→Mu(↓)+NO(↑) have been measured by longitudinal
field μSR at room temperature in the presence of up to 58 atm of N2 as inert collider. The pressure dependence of the longitudinal relaxation rate due to the addition reaction (λc) demostrates that the system is still in the low pressure regime in this pressure range. The corresponding termolecular rate
constant has been determined ask
0,Mu
=(1.10±0.25)×10−32 cm6 molecules−2 s−1, almost 4 times smaller than the corresponding H atom reactionk
0,H=3.90×10−32 cm6 molecules−2 s−1 [I.M. Campbell et al., J. Chem. Soc. Faraday Trans. 1.71 (1975) 2097]. The average value of the spin exchange rate constants
in the 2.5–58 atm pressure range,k
SE=(3.16±0.06)×10−10 cm3 molecule−1 s−1, is in good agreement with previous values obtained by transverse field μSR [D.G. Fleming et al., J. Chem. Phys. 73 (1980)
2751]. 相似文献
18.
The mass spectrum of pure Yang–Mills theory in 3+1 dimensions is discussed for an arbitrary simple gauge algebra within a
quasigluon picture. The general structure of the low-lying gluelump and two-quasigluon glueball spectrum is shown to be common
to all algebras, while the lightest C=− three-quasigluon glueballs only exist when the gauge algebra is A
r≥2, that is, in particular,
\mathfraksu(N 3 3)\mathfrak{su}(N\geq3). Higher-lying C=− glueballs are shown to exist only for the A
r≥2, Dodd−r≥4 and E6 gauge algebras. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis
and a funnel form; it appears to be gauge-algebra dependent when at least three sources are considered. As a main result,
the present framework’s predictions are shown to be consistent with available lattice data in the particular case of an
\mathfraksu(N)\mathfrak{su}(N) gauge algebra within ’t Hooft’s large-N limit. 相似文献
19.
We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO4 single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio
of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian
corresponding to axial symmetry with the parameters g
∥1=1.9305, g
⊥1=1.9565, A
∥1=−168.2×10−4cm−1, and A
⊥1=−54.3×10−4cm−1 for V1 centers and g
∥2=1.9340, g
⊥2=1.9523, A
∥2=−169.0×10−4cm−1, and A
⊥2=−55.2×10−4cm−1 for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally
distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO2+ ion forms when α-RbTiOPO4 crystals and crystals of the KTP group (KTiOPO4, NaTiOPO4, α-and β-LiTiOPO4), studied earlier, are doped with vanadium is discussed.
Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998) 相似文献
20.
The static conductivity σ(E) and photoconductivity (PC) at radiation frequencies ħω=10 and 15 meV in Si doped with shallow impurities (density N=1016−6×1016 cm−3, ionization energy ε1≃45 meV) with compensation K=10−4−10−5 in electric fields E=10–250 V/cm are measured at liquid-helium temperatures T. Special measures are taken to prevent the high-frequency part of the background radiation (ħω>16 meV) from striking the
sample. It is found that the conductivity σ(E) is due to carrier motion along the D
− band, which is filled with carriers under the influence of the field E. In fields E<E
q
(E
q
≃100–200 V/cm) the carrier motion consists of hops along localized D
− states in a 10–15 meV energy band below the bottom of the free band (energy ε=ε1); for E>E
q
carriers drift along localized D
− states with energy ε∞ε1−10 meV. An explanation is proposed for the threshold behavior of the field dependence of the photo-and static conductivities.
Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 232–236 (25 August 1997) 相似文献