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1.
Comparing mean field and Euclidean matching problems 总被引:1,自引:0,他引:1
J. Houdayer J.H. Boutet de Monvel O.C. Martin 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(3):383-393
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered
systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems.
Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered.
We first study a mean field model taking the link lengths between points to be independent random variables. For this model
we find perfect agreement with the results of a replica calculation, and give a conjecture. Then we study the case where the
points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that
the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d
2
). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among
k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than
at . However, we argue that the dimensional dependence of the Euclidean model's energy density is non-perturbative, i.e., it is beyond all orders in k of the expansion in k-link correlations.
Received: 1st December 1997 / Revised: 6 May 1998 / Accepted: 30 June 1998 相似文献
2.
D. Monier L. Fruchter 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(2):143-148
We have studied the occurrence of magnetothermal instabilities in a single crystal during field sweep magnetization experiments, equivalent to short time relaxation studies. We find instability
behaviour in good agreement with a recent model by Mints, for a non-linear E(J) characteristic. In particular, we find that a decrease of the dynamic relaxation rate, characterizing the effective activation
energy, precedes the unstable regime. We point out formal analogies between such instabilities and the general predictions
for flux avalanches.
Received: 11 December 1997 / Revised: 15 January 1998 / Accepted: 31 March 1998 相似文献
3.
P.A. Marcos J.A. Alonso A. Rubio M.J. López 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1999,6(2):221-233
The thermal stability, phases and phase changes of small carbon clusters and fullerenes are investigated by constant energy
Molecular Dynamics simulations performed over a wide range of temperatures, i.e., from to above the melting point of graphitic carbon. The covalent bonds between the carbon atoms in the clusters are represented
by the many-body Tersoff potential. The zero temperature structural characteristics of the clusters, i.e., the minimum energy structures as well as the isomer hierarchy can be rationalized in terms of the interplay between the
strain energy (due to the surface curvature) and the number of dangling bonds in the cluster. Minimization of the strain energy
opposes the formation of cage structures whereas minimization of the number of dangling bonds favors it. To obtain a reliable
picture of the processes experienced by carbon clusters as a function of temperature, both thermal and dynamical characteristics
of the clusters are carefully analyzed. We find that higher excitation temperatures are required for producing structural
transformations in the minimum energy structures than in higher lying isomers. We have also been able to unambiguously identify
some structural changes of the clusters occurring at temperatures well below the melting-like transition. On the other hand,
the melting-like transition is interrupted before completion, i.e., the thermal decomposition of the clusters (evaporation or ejection of or units) occurs, from highly excited configurations, before the clusters have fully developed a liquid-like phase. Comparison
with experiments on the thermal decomposition of and a discussion of the possible implications of our results on the growth mechanisms leading to the formation of different
carbon structures are included.
Received: 25 March 1998 / Received in final form: 30 October 1998 相似文献
4.
H. Stark J. Stelzer R. Bernhard 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(3):515-523
Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a
point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes
a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For
such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental
observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets,
but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order
phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two
boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a
defect between them.
Received 11 December 1998 相似文献
5.
L. Bongini M. Degli Esposti C. Giardinà A. Schianchi 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(2):263-272
In this paper, we solve a general problem of optimizing a portfolio in a futures markets framework, extending the previous
work of Galluccio et al. [Physica A 259, 449 (1998)]. We allow for long buying/short selling of a relatively large number of assets, assuming a fixed level of margin
requirement. Because of non-linearity in the constraint, we derive a multiple equilibrium solution, in a size exponential
respect to the number of assets. That means that we can not obtain the unique efficiency frontier, but many of them and each
one is related to different levels of risk. Such a problem is analogous to that of finding the ground state in long-ranged
Ising spin glass with external field. In order to get the best portfolio (i.e. that is along the best efficiency frontier), we have to implement a two-step procedure, performing the exhaustive enumeration
of all local minima. We develop a concrete application, where the different part of the proposed solution are computed.
Received 31 December 2001 相似文献
6.
M.G. Kozlov S.G. Porsev 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1999,5(1):59-63
The results of ab initio calculation of energies, hyperfine structure constants and static polarizabilities for several low-lying levels of barium
are reported. The effective Hamiltonian for the valence electrons has been constructed in the frame of CI+MBPT method and solutions of many electron equation were found. Using the wave functions obtained the hyperfine structure constants and static polarizabilities were calculated.
Received: 22 June 1998 / Revised: 2 September 1998 / Accepted: 15 September
1998 相似文献
7.
G. Filatrella A. Petraglia G. Rotoli 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(1):23-30
In this paper we investigate the behavior of moderate size two-dimensional classical arrays of Josephson junctions in presence
of an external oscillating field. We have included in the model the effects due to mutual inductance terms, and we have employed
an explicit set of differential equations. We have found that the discretization parameter - i.e. the coupling term due to the inductance of the loops - is the most important parameter to determine the height of the Shapiro
steps for a given amplitude and frequency of the rf-bias. The amplitude of the Shapiro steps in the case of zero frustration
as a function of the coupling term shows a remarkable minimum for intermediate values when we retain all terms of the full
model with mutual inductances, while the limits for very large and very small values of they are the same of the single Josephson junction. For the case of frustration 1/2 the Shapiro step becomes smaller in the
rigid limit (i.e., small ) as expected for the XY model, and tends to the limit value of the single junctions for the decoupled case (i.e., large ).
Received 9 November 1998 and Received in final form 6 April 1999 相似文献
8.
A. Desaix O. Roubeau J. Jeftic J.G. Haasnoot K. Boukheddaden E. Codjovi J. Linarès M. Noguès F. Varret 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(2):183-193
We investigate the behaviour of photo-excitable, bistable systems, under permanent light irradiation, in presence of relaxation
towards the non-excited state. Cooperativity causes bistability of the steady state, leading to light-induced thermal and
optical hysteresis (LITH and LIOH). The light-induced instability is expected to induce demixtion, i.e. the coexistence of domains of the two stable steady states. Such effects are evidenced by magnetic and reflectivity measurements
on the spin-crossover solid solution: , with x= 0.3, 0.5, 0.85. Experimental data are in quantitative agreement with a simple macroscopic model which includes a non-linear
relaxation term in the master equation.
Received: 5 June 1997 / Accepted: 17 July 1998 相似文献
9.
S. Franz T. Garel H. Orland 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(3):463-468
We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains
are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use
a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle
point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the
other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds
between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems.
Received 4 December 1998 and Received in final form 10 March 1999 相似文献
10.
K. Suematsu 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(1):93-100
We develop a new theory of gelation which takes into account (i) delay of the gel point and (ii) change of functionality due
to ring formation. We show that the problem of finding the gel point in real polymer solutions reduces to the problem of calculating
the total ring concentration and the extent of reaction of intermolecular reaction at the gel point. In this paper, we solve
a special case of this problem, on the basis of the independence assumption between intermolecular reaction and cyclization
which takes into account only (i) the delay of the gel point: making use of the asymptotic equality of the total ring concentration,
we acquire an approximate solution for the gel point Dc as a function of the inverse concentration , the relative frequency of cyclization and dimension d. Applying the observed values of in linear polyesters, the theoretical result reproduces well the Wile and the Gordon-Scantlebury observations, showing the
existence of a critical dilution beyond which gelation can not occur, and an asymptote . As the classical gel point is approached, the present theory reduces to the linear equation, which makes one-to-one correspondence
with the real slope , suggesting the inequality which is just what polymer chemists have quested for so far, with the physical meaning having remained unknown.
Receveid: 30 December 1997 / Revised: 28 May 1998 / Accepted: 12 June 1998 相似文献
11.
A. Dutta J.K. Bhattacharjee B.K. Chakrabarti 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(1):97-103
We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists
of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at
a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point
in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation
technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d
u
= 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the
quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian
model by Fisher renormalisation.
Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998 相似文献
12.
P.M.C. de Oliveira 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(1):111-115
The Broad Histogram is a method designed to calculate the energy degeneracy g(E) from microcanonical averages of certain macroscopic quantities N up and N dn. These particular quantities are defined within the method, and their averages must be measured at constant energy values,
i.e. within the microcanonical ensemble. Monte-Carlo simulational methods are used in order to perform these measurements. Here,
the mathematical relation allowing one to determine g(E) from these averages is shown to be exact for any statistical model, i.e. any energy spectrum, under completely general conditions. We also comment about some troubles concerning the measurement
of the quoted microcanonical averages, when one uses a particular approach, namely the energy random walk dynamics. These
troubles appear when movements corresponding to different energy jumps are performed using the same probability, and also
when the correlations between successive averaging states are not adequately treated: they have nothing to do with the method
itself.
Received: 29 May 1998 / Received in final form: 12 June 1998 / Accepted: 13 June 1998 相似文献
13.
J.M. Luck T.M. Nieuwenhuizen 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(3):483-500
No direct imaging is possible in turbid media, where light propagates diffusively over length scales larger than the mean
free path .The diffuse intensity is, however, sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects in an otherwise homogeneous, non-absorbing medium can be
described by a stationary diffusion equation. In analogy with electrostatics, the influence of a single embedded object on
the intensity field is parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative
charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics
of the object are its capacitance Q or its effective radius ,and its polarizability P. These quantities can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic
objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework
is provided by radiative transfer theory. This formalism is worked out in detail, in the case of spherical and cylindrical
objects of radius R, of the following kinds: (i) totally absorbing (black), (ii) transparent, (iii) totally reflecting. The capacitance, effective
radius, and polarizability of these objects differ from the predictions of the diffusion approximation by a size factor, which
only depends on the ratio .The analytic form of the size factors is derived for small and large objects, while accurate numerical results are obtained
for objects of intermediate size .For cases (i) and (ii) the size factor is smaller than one and monotonically increasing with ,while for case (iii) it is larger than one and decreasing with .
Received: 7 August 1998 / Accepted: 3 September 1998 相似文献
14.
B. Reusch R. Blümel 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1998,3(2):123-127
Numerical simulations of the equations of motion of 300 charged particles confined to a plane with an additional magnetic
field orthogonal to the plane reproduce recently observed self-organization of non-neutral plasmas into a small number of
interacting vortices. In the presence of damping we observe crystallized vortices, i.e. vortices with regular internal structure. We also observe crystallized vortex crystals, i.e. geometric patterns of crystallized vortices. Fractal vortex arrangements are investigated and found to be stable. Our results
are relevant for quantum dots and artificial atoms.
Received: 24 February 1998 / Revised: 4 March 1998 / Accepted: 4 May
1998 相似文献
15.
We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains
intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in
balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release
of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point.
We apply the theory to a discussion of the results of Radler et al.
Received: 21 July 1997 / Received in final form: 19 January 1998 /Accepted: 5 March 1998 相似文献
16.
M. Brut A. Estève G. Landa G. Renvez M. Djafari Rouhani 《The European physical journal. E, Soft matter》2009,28(1):17-25
We present a new competitive method for the atomic scale treatment of macromolecular flexibility called Static Mode method.
This method is based on the “induced-fit” concept, i.e. it maps the intrinsic deformations of a macromolecule subject to diverse external excitations. The algorithm makes it possible
to obtain a set of deformations, each one corresponding to a specific interaction on a specific molecular site, in terms of
force constants contained in the energy model. In this frame, the docking problem can be expressed in terms of interaction
sites between the two molecules, the molecular deformations being extracted from the pre-calculated Static Modes of each molecule.
Some preliminary basic examples aimed at illustrating potential applications where macro- or bio-molecular flexibility is
of key importance are given: flexibility inducing conformational changes in the case of furanose ring and flexibility for
the characterization, including allostery, of poly(N-isopropylacrylamide)(P-NIPAM) active sites. We also discuss how this
procedure allows “induced-fit” flexible molecular docking, beyond state-of-the-art semi-rigid methods. 相似文献
17.
Alessandro Michelangeli Alessandro Olgiati Raffaele Scandone 《Journal of Nonlinear Mathematical Physics》2018,25(4):558-588
We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space. 相似文献
18.
Georg Hoever 《Communications in Mathematical Physics》1997,189(3):879-890
We investigate the spectrum of the two-dimensional Schr?dinger operator , where the magnetic field and the electric potential V are spherically symmetric, i.e., , , and b is p-periodic, similarly for V. By considering two different gauges we get the following results: In case the spectrum contains a semi-axis that consists alternately of intervals of absolutely continuous and dense point spectrum.
In case the essential spectrum is purely dense point spectrum and possibly there are spectral gaps.
Received: 12 March 1997 / Accepted: 2 April 1997 相似文献
19.
We consider certain two-dimensional systems with self-dual points including uniform and disordered q-state Potts models. For systems with continuous energy density (such as the disordered versions) it is established that the
self-dual point exhibits critical behavior: Infinite susceptibility, vanishing magnetization and power law bounds for the
decay of correlations.
Received: 16 November 1998 / Accepted: 28 January 1999 相似文献
20.
S. Bottin H. Chaté 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(1):143-155
We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical
level. We present such a statistical analysis of experimental data guided by a parallel investigation of a simple coupled
map lattice model for spatiotemporal intermittency. We confirm that this generic type of spatiotemporal chaos is relevant
in the context of plane Couette flow, where the linear stability of the laminar regime at all Reynolds numbers insures the
necessary local subcriticality. Using large ensembles of similar experiments, we show the existence of a well-defined threshold
Reynolds number above which a unique, turbulent, intermittent attractor coexists with the laminar flow. Furthermore, our data
reveals that this transition to spatiotemporal intermittency is discontinuous, i.e. akin to a first-order phase transition.
Received: 10 April 1998 / Revised: 22 June 1998 / Accepted: 24 June 1998 相似文献