共查询到20条相似文献,搜索用时 31 毫秒
1.
Theoretical expressions of 〈y
N〉, 〈|y
N − σ1
y
P
c
|〉 and 〈|y
N
2
−σ
1
2
(y
P
c
)2|〉 (wherey
N andy
P
c
are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom
contributionσ
1
2
for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained
for both the related and unrelated cases. The local values of 〈y
N〉 and 〈|y
N
n
− σ
1
n
(y
P
c
)
n
|〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located
in the structure.
Contribution No. 550 相似文献
2.
The present paper reports that triboluminescence (TBL) does not appear at the instant of impact of the load but a certain
time lag is required for its appearance which depends on the value of the stress applied to the crystal. Since TBL appears
in sugar crystals during the creation of new surfaces, the fracture-initiation time of the crystal has been taken to be the
delay time in observing TBL pulse after the application of stress. The dependence of fracture-initiation time,t
f
σ
, of crystals on the stress, σ, may be expressed ast
f
σ
=t
o exp (− ασ), wheret
o and α are constants. The values of the lattice energy, and the change in lattice energy per unit stress, of sugar crystals
have been calculated from TBL measurements and they have been found to be 21·2 kcal mole−1 and 0·41 × 10−8 kcal mole−1 dyne−1 cm2 respectively. 相似文献
3.
Electrical resistance measurements are reported on the binary liquid mixtures CS2 + CH3CN and CS2 + CH3NO2 with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport.
For the liquid mixture filled at the critical composition, the resistance of the system aboveT
c follows the relationR=R
c−A(T−T
c)
b
withb=0·6±0·1. BelowT
c the conductivities of the two phases obey a relation σ2−σ1=B(T
c−T)β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium
property. 相似文献
4.
N. A. Silant’ev 《Journal of Experimental and Theoretical Physics》1997,85(4):712-723
An analysis is made of the relation between accurate formulas for the coefficients of turbulent diffusion D
T and the alpha effect α
T for a magnetic field in the Lagrange and Euler representations. It is shown that the quadratic term with respect to α
T in the diffusion coefficient derived by Moffatt and Kraichnan is incorrect and should be dropped. First, a numerical solution
of the nonlinear equation (DIA equation) for the Green function is presented, describing the transport of a magnetic field
for the case of incompressible, uniform, isotropic, steady-state turbulence possessing helicity. These solutions are used
to calculate the steady-state coefficients D
T and α
T for various values of the parameters ξ
0=u
0
σ
0/R
0, a=H
0/u
0
2
p
0, σ
0/σ
1, and R
0/R
1, where u
0, σ
0, and R
0 are the characteristic velocity, lifetime, and scale of the turbulent pulsations, and H
0, σ
1, and R
1 are similar values describing the helicity of the medium h(1,2)=〈u(1)· (∇×u(2))〉, and the parameter α characterizes the degree of helicity. The DIA values of D
T and α
T and the self-consistent values of these quantities calculated using the Green tensor in the diffusion approximation are in
qualitative agreement. It is shown that the coefficient of turbulent diffusion is always positive for all the types of turbulence
studied. Nonsteady-state values of D
T(t) and α
T(t) calculated by a self-consistent method are given.
Zh. éksp. Teor. Fiz. 112, 1312–1331 (October 1997) 相似文献
5.
This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy
t
=dω
t
−∇Γ(y
t
) dt, y
0=0 and d=2. Γ is a 2 &\times; 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales
Γ12=−Γ21=h(x
1), with h(x
1)=∑
n
=0
∞γ
n
h
n
(x
1/R
n
), where h
n
are smooth functions of period 1, h
n
(0)=0, γ
n
and
R
n
grow exponentially fast with n. We can show that y
t
has an anomalous fast behavior (?[|y
t
|2]∼t
1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization.
Received: 1 June 2001 / Accepted: 11 January 2002 相似文献
6.
Andre Toom 《Journal of statistical physics》1997,88(1-2):347-364
We consider space- and time-uniformd-dimensional random processes with linear local interaction, which we call harnesses and which may be used as discrete mathematical
models of random interfaces. Their components are rea random variablesa
s
t
, wheres ∈ Z
d
andt=0, 1, 2.,... At every time step two events occur: first, every component turns into a linear combination of itsN neighbors, and second, a symmetric random i.i.d. “noise”v is added to every component. For any σ ∈Z
d
+
define Δσ
a′
s
as follows. If σ=(0,...,0), σ=(0,...,0), Δσ
a
s
t
=a
s
t
. Then by induction,
wheree
i is thed-dimensional vector, whoseith component is one and other components are zeros. Denote |σ| the sum of components of σ. Call a real random variable ϕ symmetric
if it is distributed as −ϕ. For any symmetric random variable ϕpower decay or P-decay is defined as the supremum of thoser for which therth absolute moment of ϕ is finite. Convergence a.s., in probability and in law whent→∞ is examined in terms of P-decay(v): Ifd=1, σ=0 ord=2, σ=(0,0), Δσ
a
s
t
diverges. In all the other cases: If P-decay(v)<(d+2)/(d+|σ|), Δσ
a
s
t
diverges; if P-decay(v)>(d+2)/(d+|σ|), Δσ
a
s
t
, converges and P-decay(ν) For any symmetric random variable ϕexponential decay or E-decay is defined as the supremum of thoser for which the expectation of exp(|x|r) is finite. Let E-decay(v)>0. Whenever Δσ
a
s
t
converges (that is, ifd>2 or |σ|>0: Ifd>2, E-decay(lima
s
t
)=min(E-decay(v),d+2/2); if |σ|=1, E-decay (lim Δσ
a
s
t
)=min(E-decay(ν),d+2); if |σ| ⩾, E-decay (lim Δσ
a
s
t
)=E-decay(ν). 相似文献
7.
The joint probability density functions of the normalized structure amplitudes of the structure and the model (i.e.,y
N andy
p
c
) are derived for triclinic crystals containing heavy atoms (1, 2 and many) by taking the model to consist of the heavy atoms
and a part of the light atoms in the unit cell. These functions are derived for the two cases where the model is completely
correct (i.e., the related case) and where the model is completely wrong (i.e., the unrelated case) in terms of the fractional contributions to the local mean intensity from the heavy atoms and all known
atoms (i.e., σ
1h
/2
and σ
1
2
) as parameters. These functions are then used to obtain the theoretical local values of 〈y
N〉 and 〈|y
N
n
− σ
1
n
(y
P
c
)
n
|〉,n=1, 2. A method of using these results to compute the theoretical overall values ofR(F) andR(I) for the related and unrelated cases is briefly described. A comparison of the observed values of these indices with their
theoretical values for the related and unrelated cases would help in determining the correctness of the proposed trial structure.
Contribution No. 548 相似文献
8.
In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t
n
f(t, u(t)), where A is the generator of a C
0-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C
0-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S
p-A defined similarly to the case of S
p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A
u:= A ∩ BUC(ℝ, X) if n = 0 and to t
n
A
u ⊕ w
n
C
0 (ℝ, X) if n ∈ ℕ, where w
n(t) = (1 + |t|)n. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0.
Dedicated to the memory of B. M. Levitan 相似文献
9.
Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves
a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition
for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization
(one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent
state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution.
Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M
* (M* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find
that: 1) for M
* ≪ M ≪ M
*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t1, t2, t3 and t*; 2) there are transient regimes (t
1 ≲ t ≲ t
3) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter
than t2. The chain growth is auto-accelerated for t
1 ≲ t ≲ t
2 : the cut-off chain length (= polymerization degree 〈n〉w
N
1 ∝ t
2 in this regime. 4) For t
2 < t < t
3 the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N1 is decreasing with time in this regime, while the length scale N2 of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t*, shows a sharp maximum in the vicinity of M*; the effective exponent
is as high as ∼ σ-1/3 just above M*. 相似文献
10.
We examine the predictions of gauge theories with colour excitation for the processpp →μ
+
μ
−
X. Relative to the predictions of quark parton model (with three colours) we find enhancements as large as a factor 3 – 4 for
the cross-sectionM
3
d
2
σ/dMdy|y=0 in the region 0·03 ≲M/√s ≲ 0·2 at √s=62 GeV,M being the invariant mass andy the rapidity of the muon pair. We study the sensitivity of this result to the colour gluon mass and the underlying parametrisation
of the quark and gluon distribution functions. 相似文献
11.
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
12.
I. S. Dmitriev Ya. A. Teplova Yu. A. Fainberg 《Journal of Experimental and Theoretical Physics》1999,89(5):830-836
The electron loss and electron capture cross sections σ
i,i+m and σ
i,i−m for boron ions and atoms traveling at the velocities V=1.19 and 1.83 a.u. in H2, He, N2, Ne, Ar, and Xe are measured. The known experimental data on these cross sections at velocities near the cross-section maximum
are analyzed. It is found that the electron loss cross sections can be described by a formula which was previously derived
in the free-collision approximation and takes into account features of both the ions and the ambient atoms. As the nuclear
charge Z
t of the ambient atoms increases, the cross sections vary nonmonotonically, increasing on average as Zt
t
1/2
. A formula based on the model of independent electrons is proposed for electron capture by ions with small values of the
charge i. It describes the dependence of the electron capture cross section σ
i,i−1 on the mean binding energy of an electron in an ion with the charge i−1. The total electron capture cross section σ
i,i−1 is proportional to the number of vacancies in the unfilled electron shell nearest the nucleus. The cross sections 0σ
i,i−1 exhibit substantially nonmonotonic variation with Z
t, increasing on average as Z
t
1/3
.
Zh. éksp. Teor. Fiz. 116, 1539–1550 (November 1999) 相似文献
13.
W. J. Kossler X. H. Yu A. Greer H. E. Schone C. E. Stronach M. Davis R. S. Cary J. E. Crow W. F. Lankford J. Oostens 《Hyperfine Interactions》1991,63(1-4):81-86
Transverse and zero-field μSR measurements were made on YBa2(Cu1−xNix)3O7−y withx=0.1 and 0.2, and YBa2(Cu1−x
Zn
x
)3O7−y
withx=0.03, 0.06, 0.1, and 0.16, wherey≈0.1. Since doping may lead to magnetic ordering this was searched for with both zero and transverse field μSR, but no evidence
was found over the temperature range studied: 10–100 K. However, depolarization rates as functions of temperature were obtained,
and the low temperature values of these are σ=3.2 μs−1.1.6μs−1, and 1 μs−1 forx=0.01, and 0.2 Ni, respectively, and σ=0.8 μs−1, 0.75 μs−1, 0.65 μs−1, and 0.4 μs−1 forx=0.03, 0.06, 0.1, and 0.16 Zn, respectively. Estimates for the effect of decreasing electron concentration for Zn are made,
but these alone do not account for the drop in σ. Estimates for the effect of scattering on λ and hence σ are made. The reduction
in σ for Ni dopant is in surprisingly good agreement with these estimates. For Zn the order of magnitude is correct, but the
relative lack of further change in σ after the effect of the first 0.03 addition seems to imply a saturation of the effect
of scattering. 相似文献
14.
S N Bhatia 《Pramana》1982,18(3):249-259
Heat capacity of MnBr2·4H2O has been measured in the critical region around the Neel temperature. The data can be fitted, over a restricted range of
|t|⩽10−2, to the asymptotic power law. The critical exponents and the amplitudesA andA′ are not consistent with any theoretic predictions. However when scaling constraints are imposed, their values agree with
the parameters of Ising model. Corrections to scaling are necessary to extend the range of the fit to |t|>10−2. The correction terms are asymmetric giving −1·15±0·25 as the ratio of the amplitudes of the lowest order correction terms,D andD′ above and belowT
c. This value is in agreement with the recent predictions of the renormalisation group theory. 相似文献
15.
We study zero-temperature, stochastic Ising models σ
t
on Z
d
with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every
x in Z
d
, σ
x
t
flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”.
For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ
J
+(1-α)δ-
J
) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous
disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem.
Received: 3 November 1999 / Accepted: 10 April 2000 相似文献
16.
V. Batusov Yu. Budagov M. Lyablin A. Sissakian 《Physics of Particles and Nuclei Letters》2010,7(5):359-363
The laser beam space uncertainty σ was measured during ray propagation in atmospheric air (a) and in atmospheric air inside the tube (t) with both ends closed by optically transparent windows. For the studied case of the 70 m passed distance, the sigma values
were discovered to differ greatly: σ
a
/σ
t
≈ 100
x
. The observed effect may represent a physical basis for the creation of an extended laser ray to be used as a coordinate
axis in the high-precision metrology when assembling a big-length research equipment (accelerators, detectors, etc.) or in
civil engineering tasks. 相似文献
17.
Viktor Bezák 《Czechoslovak Journal of Physics》1999,49(7):1017-1025
The time evolution of a random surfacez=h(r, t) (r=x, y) formed by a deposition process of the Edwards-Wilkinson type is discussed. The discussion is based on the author’s former
derivation of the autocorrelation functionA
h(|r − r′|,t, t′)=〈h(r,t)h(r′,t′)〉 of the height functionh(r,t) under the assumption of a stochastic initial condition [V. Bezák: Acta Physica Univ. Comenianae39 (1998) 135]. Under the assumption of a steady (non-zero) deposition rate, the varianceσ
h
2
(t)=〈[h(r,t)]2〉 increases logarithmically in time whilst the correlation lengthl
h(t) of the height functionh(r,t) increases as ∼t
1/2. Therefore, the ratioσ
h(t)/l
h
(t) tends to zero and the surfacez=h(r,t) does always tend towards a smoothened appearance.
This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97. 相似文献
18.
An electron paramagnetic resonance (EPR) line shape simulation for nitroxide spin probes in the motional narrowing region
was carried out assuming axially symmetricg andA tensors and with different anisotropies of rotationN (=R
∥/R
⊥) whereR
∥ andR
⊥ are, respectively, elements of the diffusion tensor along and perpendicular to its principal axisz′. In addition, it was assumed that the principal axes of the diffusion tensor coincide with the molecular axes. Each of three
casesz′=x,z′=y andz′=z, which result from cyclic permutations of the molecular axesx, y andz with thez′,y′ andx′ axes of the diffusion tensor, yields its typical EPR spectrum characterized by the relative intensities of the low-, center-
and high-field lines. The parameter δ defined by and calculable from the intensities of the three lines was found to vary
linearly withN for thez′=x andz′=y cases and, as anticipated, to be practically constant at a value of 1 for thez′=z case. This suggested a method for estimatingN for a probe from its EPR spectrum. Experimental spectra over a narrow temperature range (1°C) in the vicinity of the nematic-to-isotropic
transition (about 34.6°C) ofN-(4-n-butylbenzilidene)-4-amino-2,2,6,6-tetramethylpiperidine-1-oxide at a mole fraction of 1·10−3 in 4-n-pentyl-4′-cyanobiphenyl showed a pattern of peak heights characteristic of thez′=x case with δ values that gave, neglecting effects of the mean field, higher and lowerN values in the nematic and isotropic regions, respectively. Analysis of other similar systems in the literature gave similar
results. 相似文献
19.
Evgeni Korotyaev 《Communications in Mathematical Physics》2000,213(2):471-489
The spectral properties of the Schr?dinger operator T(t)=−d
2/dx
2+q(x,t) in L
2(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ
ac
(T(t))=σ
ac
(T(0)) consists of intervals, which are separated by the gaps γ
n
(T(t))=γ
n
(T(0))=(α
n
−,α
n
+), n≥1. We prove: in each gap γ
n
≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ
n
±(t) of the dislocation operator, such that λ
n
±(0)=α
n
± and the point λ
n
±(t) runs clockwise around the gap γ
n
changing the energy sheet whenever it hits α
n
±, making n/2 complete revolutions in unit time. On the first sheet λ
n
±(t) is an eigenvalue and on the second sheet λ
n
±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ0(t) in the basic gap
γ0(T(t))=γ0(T(0))=(−∞ ,α0
+). The asymptotics of λ
n
±(t) as n→∞ is determined.
Received: 5 April 1999 / Accepted: 3 March 2000 相似文献
20.
K.C. Chung C.S. Wang A.J. Santiago J.W. Zhang 《The European Physical Journal A - Hadrons and Nuclei》2001,12(2):161-167
The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined
by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models.
The values of the relevant parameters are C
σ
2∼ 94, C
ω
2∼ 32, C
ρ
2∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m
σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole
parameter region with positive c. On the other hand, the effective nucleon mass M* is larger than 0.73M, if the symmetry incompressibility Ks is assumed to be negative and the nuclear-matter incompressibility K0 is kept less than 300 MeV.
Received: 27 June 2001 / Accepted: 5 October 2001 相似文献