共查询到20条相似文献,搜索用时 31 毫秒
1.
We study the acoustic behavior of critical percolation network within a real-space renormalization group framework recently proposed by Ohtsuki and Keyes. Using large cell Monte Carlo renormalization group calculations, we obtain the exponent for anomalous sound dispersion K
1+x/v
. Our estimate 2 x/v0.80 is in agreement with the exponent for anomalous diffusion in percolation clusters =(–)/ v. 相似文献
2.
For the zero-temperature Glauber dynamics of the q-state Potts model, the fraction r(q, t) of spins which never flip up to time t decays like a power law r(q, t)t
–(q)
when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model ( A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of ( q) for all values of q. The exponent ( q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception of q=2 and q=, for which (2)=3/8 and ()=1. 相似文献
3.
For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability is strictly less than 1. The same argument is applied to prove that if L( ):={( x, y): x=r cos , y=r sin for some r0, or } and ( ):=lim pp
c
[log( p– p
c
)] –1 log P cr {itO is connected to by an occupied path in L()}, then ( ) is strictly decreasing in on [0, 2 ]. Similarly, lim n [–log n] –1 log P
cr {itO is connected by an occupied path in L()( ) to the exterior of [– n, n]×[– n, n] is strictly decreasing in on [0, 2 ]. 相似文献
4.
This article is a study of the mapping from a potential q( x) on R
3 to the backscattering amplitude associated with the Hamiltonian –+ q( x). The backscattering amplitude is the restriction of the scattering amplitude a(, , k), (, , k) S
2× S
2× +, to a(,–, k). We show that in suitable (complex) Banach spaces the map from q( x) to a( x/| x|, – x/| x|, | x|) is usually a local diffeomorphism. Hence in contrast to the overdetermined problem of recovering q from the full scattering amplitude the inverse backscattering problem is well posed. 相似文献
5.
We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies ( r)=
AW( r)–
BW( r) of the two phases behaves like ( r) r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos ( r) r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate 相似文献
6.
Let A
be the irrational rotation algebra, i.e. the C
*-algebra generated by two unitaries U, V satisfying VU=e
2i
UV, with irrational, and consider the fixed point subalgebra B
under the flip automorphism UU
–1, VV
–1. We prove that B
is an AF-algebra.Dedicated to Professor Huzihiro Araki on the occasion of his 60'th birthday 相似文献
7.
A thin film of NbN (thickness t = 300 Å), has been deposited on an MgO and a Si wafer. Both samples have been studied by transmission from 10 or 20 to 120 cm –1, and have exhibited one maximum of transmission at a given frequency like the classical superconductors as Pb, Sn or Hg in the superconductive state. From the Far IR experimental data, the characteristic temperature c, and the gap frequency ( gap () = 2 (), () being the energy gap) are immediately obtained (for instance for the NbN / MgO sample, c = 15.5 K; g (5 K) = 39.7 cm –1), and it is seen that
as expected from the BCS theory for a weak coupling. To fit the data we had to adjust only two additionnal parameters: collision and plasma frequency, c () and p (including all carriers). At = 5 K, thebest fit for the NbN / MgO sample is obtained with c = 371 cm –1 and p = 12,600cm –1. 相似文献
8.
We study ergodic Jacobi matrices on l
2( Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: ( H
, ,
u)(n)=u(n+1)+u(n–1)+ cos(2 n+) u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: | ac|=||=4 –2.Work partially supported by the US-Israel BSF 相似文献
9.
It is shown that the chiral angle, ( r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, ( r) is strictly convex or concave. As r, ( r) and ( r) approach their limit values at the rate O r
-
for any (0,2). 相似文献
10.
The number of n-site lattice trees (up to translation) is believed to behave asymptotically as Cn
–0
n
, where is a critical exponent dependent only on the dimension d of the lattice. We present a rigorous proof that ( d–1)/ d for any d2. The method also applies to lattice animals, site animals, and two-dimensional self-avoiding polygons. We also prove that v when d=2, where v is the exponent for the radius of gyration. 相似文献
11.
We prove that for any diophantine rotation angle and a.e. phase the almost Mathieu operator ( H( ) )
n
=
n–1
+
n+1
+ cos(2( + n))
n
has pure point spectrum with exponentially decaying eigenfunctions for 15. We also prove the existence of some pure point spectrum for any 5.4. 相似文献
12.
Let u() be an absolutely integrable function and define the random process where the t
i are Poisson arrivals and the s
i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum of n(t), S
n(), in terms of the probability density of s, p s(). If any probability density p s() having the property p s() I for small is substituted into this formula, the calculated S n() is such that S n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed a limit spectrum. If a probability density having the property p s( )
for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p s is suitably close to the former p s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/ f noise with low-frequency turnover, and also strict 1/ f
1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis. 相似文献
13.
We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent . We find -0.640±0.004 and =0.87±0.07 for isotropic animals in 2 d, and =0.64±0.06 in 3 d. For directed lattice animals we argue that the leading correction has =
or =
; we also estimate
=0.82±0.01 and 0.69 ±0.01 in d=2, 3 respectively. For percolation clusters at and above p
c, we find ( p
c) =0.58±0.06 and ( p> p
c)=0.84±0.09 in 2 d, and ( p
c)=0.42±0.11 and ( p> p
c)=0.41 ±0.09 in 3 d. 相似文献
14.
We consider percolation on the sites of a graph G, e.g., a regular d-dimensional lattice. All sites of G are occupied (vacant) with probability p (respectively, q=1–p), independently of each other. W denotes the cluster of occupied sites containing a fixed site (which will usually be taken to be the origin) and W the cardinality of W. The percolation probability is the probability that # W=, i.e., (p)=P
p{# W=}. Some critical values of p,p
H and p
T, are defined, respectively, as the smallest value of p for which (p)> 0, and for which the expectation of # W is infinite. Formally, p
H=inf { p(p)>0} and p
T=inf{ p E
p{# W}=}. We show for fairly general graphs Gthat if p
T, thenP
P{#W n} decreases exponentially inn. For the special casesG =G
0= the simple quadratic lattice andG
1= the graph which corresponds to bond-percolation on 2, we obtain upper and lower bounds for(p) of the formC¦p¦-P
H¦, and bounds forEp{#W} of the formC¦p–p
H¦–. We also investigate smoothness properties of (p)=E
p{number of clusters per site} =E
p {(#W)–1; (#W) 1}. This function was introduced by Sykes and Essam, who assumed that (·) has exactly one singularity, namely, atp=p
H. For the graphsG
0 andG
1, (i.e., site or bond percolation on 2) we show that (p) is analytic atp p
H and has two continuous derivatives atp=p
H. The emphasis is on rigorous proofs.Research supported by the NSF through a grant to Cornell University. 相似文献
15.
We have studied the various nonlinear optical processes that can be described by a fourth-rank (3)-tensor: signals of frequency in degenerate four-wave mixing (DFWM), harmonics of frequency 2 and 3, and (3)-type difference-frequency generation (DFG) with observation of anti-Stokes emission of a signal of frequency 2 1 — 2. Structural information in terms of normalized anisotropies is derived in all frequency domains by analysis of the elements of the respective orientation-dependent susceptibility tensor. A novel laser-based technique for the remote orientation analysis of crystalline structures is introduced. 相似文献
16.
Following earlier work of Masood-ul-Alam, we consider a uniqueness problem for non-rotating stellar models. Given a static, asymptotically flat perfectfluid spacetime with barotropic equation of state ( p), and given another such spacetime which is spherically symmetric and has the same ( p) and the same surface potential: we prove that both are identical provided ( p) satisfies a certain differential inequality. This inequality is more natural and less restrictive than the conditions required by Masood-ul-Alam.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, project P-7197 相似文献
17.
The decay of periodic surface profiles by surface self-diffusion is simulated by numerically solving the phenomenological equations for this process. The crystalline nature of the surface is taken into account by introducing an anisotropic surface free energy, (). Depending on the degree of anisotropy of (), the decay kinetics and the shapes of the profiles are largely different. A comparison with measurements of profile decay on Pt(l10) single crystal surfaces shows that the anisotropy in () along the [1¯10] azimuth should be about 2–3%, while that along the [001] azimuth is expected near 8%. In the latter case large amplitude profiles exhibit (111) faceting and slow decay kinetics which are non-exponential. The rate of surface self-diffusion on Pt(110) is anisotropic with the [1¯10] direction being faster than the [001] direction. 相似文献
18.
The 2H( d, ) 4He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between cm=45° and cm=135°. At E
d
=28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratio R= d/ d ( cm=90°)/ d/ d ( cm=135°) was measured for each deuteron energy. 相似文献
19.
We study a class of twist maps where the function g( )= (1–|2 |
z–1) is nonanalytic ( C
1) and endowed with a varying degree of inflection z. When z>3, reappearance of a KAM torus after its breakup has been observed. We introduce an inverse residue criterion to determine the reappearance point. Scaling behavior at the transition points is also studied. For 2 z<3 the scaling exponents are found to vary with z, whereas for z3 they are independent of z. In this sense z=3 plays a role quite similar to that of the upper critical dimension in phase transitions. 相似文献
20.
Parabolic triples of the form ( E*,,) are considered, where ( E*,) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle ( E*,) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bundles is obtained. The pull back, by this map, of the symplectic form on the moduli space of stable parabolic Higgs bundles will be denoted by d . On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme Hilb ( Z), where Z denotes the total space of the line bundle KX X( S), that sends a triple ( E*,,) to the divisor defined by the section on the spectral curve corresponding to the parabolic Higgs bundle ( E*,). Using this map and a meromorphic one–form on Hilb ( Z), a natural two–form on the moduli space of stable parabolic triples is constructed. It is shown here that this form coincides with the above mentioned form d . 相似文献
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