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1.
We derive, from conformal invariance and quantum gravity, the multifractal spectrum f() of the harmonic measure (i.e., electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions. It gives the Hausdorff dimension of the set of points where the potential varies with distance r to the fractal frontier as r . First examples are a random walk, i.e., a Brownian motion, a self-avoiding walk, or a critical percolation cluster. The generalized dimensions D(n) as well as the multifractal functions f() are derived, and are all identical for these three cases. The external frontiers of a Brownian motion and of a percolation cluster are thus identical to a self-avoiding walk in the scaling limit. The multifractal (MF) function f(,c) of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is given as a function of the central charge c of the associated conformal field theory. The dimensions D EP of the external perimeter and D H of the hull of a critical scaling curve or cluster obey the superuniversal duality equation . Finally, for a conformally invariant scaling curve which is simple, i.e., without double points, we derive higher multifractal functions, like the universal function f 2(,) which gives the Hausdorff dimension of the points where the potential varies jointly with distance r as r on one side of the curve, and as r on the other. The general case of the potential distribution between the branches of a star made of an arbitrary number of scaling paths is also treated. The results apply to critical O(N) loops, Potts clusters, and to the SLE process. We present a duality between external perimeters of Potts clusters and O(N) loops at their critical point, as well as the corresponding duality in the SLE process for =16.  相似文献   

2.
The high-spin states of 93Mo have been studied by a 82Se( 16O, 5n) 93Mo reaction at a beam energy of 100 MeV using techniques of in-beam -ray spectroscopy. Measurements of -t, --t coincidences, -ray angular distributions and -ray linear polarizations were performed. The high-spin isomer was found as a (39/2-) state at about 9.7 MeV. The near-yrast states in 93Mo were interpreted using the weak-coupling picture of a d5/2 neutron to a neutron magic core nucleus 92Mo.  相似文献   

3.
In the present article, undoped and Codoped Mtype Srhexaferrites have been prepared at low temperatures down to 980 C for the first time by the usual ceramic procedure and sintering technique. On these materials, a CoK Xray diffraction analysis and the room temperature 57Fe Mössbauer spectroscopy (MES) were carefully performed. The results obtained are described and interpreted. The mechanism of Co substitution partially in place of iron and the site of its occupancy were proposed and established.  相似文献   

4.
A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr d , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL d–d× d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.  相似文献   

5.
The statistical mechanics is considered of any polymer network with a prescribed topology, in dimensiond, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made toO(2), whered=4–, of the basic critical dimensions L associated with anyL-leg vertex (L1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent G of any networkG toO(2), includingL-leg star polymers. The infinite sets of contact critical exponents between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents 0, 1, 2 calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimensiond=4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constitutingL-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled.  相似文献   

6.
Using methods of emission spectroscopy, we have determined the gaskinetic temperature fields of planar highfrequency capacitive discharge plasma in N2/CO2/He gas mixtures depending on the excitation frequency, discharge current, pressure, and chemical composition of the mixture. It is shown that the dominant contribution to the neutral component heating in the center of the discharge chamber is made by the processes of VT relaxation of vibrationally excited molecules N2(X 1, V) and CO2(X 1, V), whereas in the zones near the electrodes an important role in the heating is played, along with the VT relaxation of the N2(X 1, V) and CO2(X 1, V) molecules, by the processes of deactivation of the metastable states A 3 of the N2 molecule.  相似文献   

7.
8.
A phase diagram of pinned soliton structures in two dimensions has been found for a repulsive interactionU(x) between solitons withU(x)>0. The critical fugacity of the commensurate soliton structure is shown to be proportional toU(l), wherel is the period of this structure.  相似文献   

9.
The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&k, is found to scale with the linear sizeL as (InL)(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y), yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.  相似文献   

10.
The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents (l) and (nl) increase on dilution to (l)/(1–) and (nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher (nl)= (l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).  相似文献   

11.
The correlation function and the correlation length are discussed in the theoretical framework of the Wilson-Feynman diagram expansion for small =4–d. It is shown explicitly that to order 2 the scaling relation = (2–) is satisfied and that the correlation function is a homogeneous function ofk and . The explicit form of the scaled correlation function is exhibited.  相似文献   

12.
Recently, a class of -invariant scalar quantum field theories described by the non-Hermitian Lagrangian = () 2 +g 2 (i) was studied. It was found that there are two regions of . For <0 the -invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For 0 the -invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle transition at =0 is not well understood. In this paper we initiate an investigation of this transition by carrying out a detailed numerical study of the effective potential V eff (c) in zero-dimensional spacetime. Although this numerical work reveals some differences between the <0 and the >0 regimes, we cannot yet see convincing evidence of the transition at =0 in the structure of the effective potential for -symmetric quantum field theories.  相似文献   

13.
The influence of the concentration of an activator (C NaI) and of plastic deformation on a change in the contribution of a slow component to the decay of the -scintillations of CsI–Na crystals was investigated, as well as the influence of C NaI on a change in the shape of the luminescence excitation spectrum in the region of absorption of activator centers (AC) and of vacancy-related centers (VRC) and also on a change in the intercenter time of deexcitation of the centers indicated. It is shown that AC and VRC participate in the photoluminescence and -scintillations of CsI–Na crystals. In the -scintillations, AC are responsible for the component 1 = 370 nsec, whereas the components 1 = 460 nsec and 2 2 sec are associated with VRC. The reduction of 1 from 770 to 560 nsec with an increase in C NaI from 2·10–3 to 3·10–2 mole% and from 570 to 470 nsec after plastic deformation of the crystals ( = 5%) along the 111 axis is caused by a decrease in the number of VRC. The mechanisms underlying the -scintillations of the CaI–Na crystals containing AC and VRC and also the decrease in the number of VRC are discussed.  相似文献   

14.
We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/r d+2–2,0+,0+. Renormalization group calculations ind=d u are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.  相似文献   

15.
We investigate the structure of scaling solutions of Smoluchowski's coagulation equation, of the formc k (t)s(t) (k/s(t)), wherec k (t) is the concentration of clusters of sizek at timet,s(t) is the average cluster size, and(x) is a scaling function. For the rate constantK(i, j) in Smoluchowski's equation, we make the very general assumption thatK(i, j) is a homogeneous function of the cluster sizesi andj:K(i,j)=a K(ai,aj) for alla>0, but we restrict ourselves to kernels satisfyingK(i, j)/j0 asj. We show that gelation occurs if>1, and does not occur if1. For all gelling and nongelling models, we calculate the time dependence ofs(t), and we derive an equation for(x). We present a detailed analysis of the behavior of(x) at large and small values ofx. For all models, we find exponential large-x behavior: (x)A x e x asx and, for different kernelsK(i, j), algebraic or exponential small-x behavior: (x)Bx or (x)=exp(–Cx –|| + ...) asx0.  相似文献   

16.
Hydrogen molecules are excited by two 193 nm-photons [X1 g + E,F1 g + ;Q02(1)] generated with a commerical oscillator-amplifier ArF laser. Stimulated emission is subsequently observed in the IR (=752.4 nm to 836.6 nm;E, FB) and in the VUV (=134.0 nm to 160.9 nm;BX) with a VUV conversion efficiency of 0.2%. The rotational fine-structure, the saturation behaviour, pump depletion as well as SRS-onset on and off two-photon resonance are investigated.  相似文献   

17.
Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianH(n)=(n+1)+(n–1)+v(n) (n),n,l 2(),, wherev(n)=[(n+1)]–[n],[x] denoting the integer part ofx and the golden mean , give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal.  相似文献   

18.
In order to indentity the corrosion products formed on steel surfaces from 57Fe Mössbauer spectroscopy, detailed Mössbauer parameters have been determined for various kinds of iron-oxyhydroxides: -FeOOH, -FeOOH, -FeOOH and -FeOOH. 57Fe Mössbauer measurements of the iron oxyhydroxides indicate the following results. Fe occupies a single site in -FeOOH, but below the Néel temperature as at e.g., 300 K the Mössbauer spectrum is always broad, showing a distribution of the strength of the magnetic exchange interactions. Its shape depends on the grain-size and synthetic methods of the specimen. Fe occupies 3 sites in -FeOOH. High-purity reagents of -FeOOH always contain small amounts of -FeOOH and their Néel temperatures depend on the synthetic methods of the specimen. Mössbauer spectroscopy of the synthetic -FeOOH shows very broad distribution of the hyperfine magnetic fields.  相似文献   

19.
The collective structures of 131Cs have been investigated by in-beam -ray spectroscopic techniques following the 124Sn (^11B , 4n) reaction at a beam energy Elab = 57MeV. The previously established rotational bands, built on g7/2, d5/2 and the unique-parity h11/2 orbitals, have been extended and evolve into new bands involving rotationally aligned (h11/2)2 and (h11/2)2 quasiparticles. In addition, a new multiquasiparticle band based on the g7/2 g7/2 h11/2 configuration has also been observed. Theoretical interpretations for the assigned configurations are discussed in the framework of Total Routhian Surface (TRS) and Tilted Axis Cranking (TAC) model calculations. TAC model calculations predict a decrease in the B(M1) values with increasing rotational frequency for the g7/2/d5/2 (h11/2)2 and h11/2 (h11/2)2 bands, thus indicating a magnetic rotation character for these bands.  相似文献   

20.
Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentrationp, we show that the-point size exponent p 0 of polymer chains remains unchanged for small disorder concentration (p>p c ). At the percolation thresholdp=p c , using a Flory-type approximation, we conjecture that pc 0 =5/(d B +7), whered B is the percolation backbone dimension. It shows that the upper critical dimensionality for the-point transition atp=p c shifts to a dimensiond c >3. We also propose that the-point varies practically linearly withp for 1>pp c .  相似文献   

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