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## The range of interaction between DNA-bending proteins is controlled by the second-longest correlation length for bending fluctuations

Zhang, Houyin; Marko, John F.
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
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When a DNA molecule is stretched, the zero-force correlation length for its bending fluctuations – the persistence length A – bifurcates into two different correlation lengths - the shorter “longitudinal” correlation length ξ‖(f) and the longer “transverse” correlation length ξ⊥(f). In the high-force limit, ξ‖(f)=ξ⊥(f)/2=kBTA/f/2. When DNA-bending proteins bind to the DNA molecule, there is an effective interaction between the protein-generated bends mediated by DNA elasticity and bending fluctuations. Surprisingly, the range of this interaction is not the longest correlation length associated with transverse fluctuations of the tangent vector along the polymer, but instead is the second longest longitudinal correlation length ξ‖ (f, μ). The effect arises from the protein-bend contribution to the Hamiltonian having an axial rotational symmetry which eliminates its coupling to the transverse fluctuations.

## The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation

Napiórkowski, Marek; Piasecki, Jarosław
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.981694%
The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length and the correlation length are the same, equal to 1/2 for the perfect gas, and 1 for the imperfect gas.

## Dependence of extensive chaos on the spatial correlation length (substantial revision)

Egolf, David A.; Greenside, Henry S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.00262%
We consider spatiotemporal chaotic systems for which spatial correlation functions decay substantially over a length scale xi (the spatial correlation length) that is small compared to the system size L. Numerical simulations suggest that such systems generally will be extensive, with the fractal dimension D growing in proportion to the system volume for sufficiently large systems (L >> xi). Intuitively, extensive chaos arises because of spatial disorder. Subsystems that are sufficiently separated in space should be uncorrelated and so contribute to the fractal dimension in proportion to their number. We report here the first numerical calculation that examines quantitatively how one important characterization of extensive chaos---the Lyapunov dimension density---depends on spatial disorder, as measured by the spatial correlation length xi. Surprisingly, we find that a representative extensively chaotic system does not act dynamically as many weakly interacting regions of size xi.; Comment: 14 pages including 3 figures (Postscript files separate from the main text), uses equations.sty and aip.sty macros. Submitted to Nature

## Characterization of relaxation processes in interacting vortex matter through a time-dependent correlation length

Pleimling, Michel; Tauber, Uwe C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.929824%
Vortex lines in type-II superconductors display complicated relaxation processes due to the intricate competition between their mutual repulsive interactions and pinning to attractive point or extended defects. We perform extensive Monte Carlo simulations for an interacting elastic line model with either point-like or columnar pinning centers. From measurements of the space- and time-dependent height-height correlation function for lateral flux line fluctuations, we extract a characteristic correlation length that we use to investigate different non-equilibrium relaxation regimes. The specific time dependence of this correlation length for different disorder configurations displays characteristic features that provide a novel diagnostic tool to distinguish between point-like pinning centers and extended columnar defects.; Comment: 12 pages, 3 figures, version to appear in J. Stat. Mech

## The Growing Correlation Length in Glasses

Fullerton, Christopher J.; Moore, M. A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.00262%
The growing correlation length observed in supercooled liquids as their temperature is lowered has been studied with the aid of a single occupancy cell model. This model becomes more accurate as the density of the system is increased. One of its advantages is that it permits a simple mapping to a spin system and the effective spin Hamiltonian is easily obtained for smooth interparticle potentials. For a binary liquid mixture the effective spin Hamiltonian is in the universality class of the Ising spin glass in a field. No phase transition at finite temperatures is therefore expected and the correlation length will stay finite right down to zero temperature. For binary mixtures of hard disks and spheres we were not able to obtain the effective spin Hamiltonian analytically, but have done simulations to obtain its form. It again is in the universality class of the Ising spin glass in a field. However, in this case the effective field can be shown to go to zero at the density of maximum packing in the model, (which is close to that of random close packing), which means that the correlation length will diverge as the density approaches its maximum. The exponent nu describing the divergence is related in d dimensions to the Ising spin glass domain wall energy exponent theta.; Comment: 16 pages...

## Depolarization volume and correlation length in the homogenization of anisotropic dielectric composites

Mackay, Tom G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.929824%
In conventional approaches to the homogenization of random particulate composites, both the distribution and size of the component phase particles are often inadequately taken into account. Commonly, the spatial distributions are characterized by volume fraction alone, while the electromagnetic response of each component particle is represented as a vanishingly small depolarization volume. The strong-permittivity-fluctuation theory (SPFT) provides an alternative approach to homogenization wherein a comprehensive description of distributional statistics of the component phases is accommodated. The bilocally-approximated SPFT is presented here for the anisotropic homogenized composite which arises from component phases comprising ellipsoidal particles. The distribution of the component phases is characterized by a two-point correlation function and its associated correlation length. Each component phase particle is represented as an ellipsoidal depolarization region of nonzero volume. The effects of depolarization volume and correlation length are investigated through considering representative numerical examples. It is demonstrated that both the spatial extent of the component phase particles and their spatial distributions are important factors in estimating coherent scattering losses of the macroscopic field.; Comment: Typographical error in eqn. 16 in WRM version is corrected in arxiv version

## Effect of attractions on correlation length scales in a glass-forming liquid

Xu, Wen-Sheng; Sun, Zhao-Yan; An, Li-Jia
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.09952%
There is growing evidence that slow dynamics and dynamic heterogeneity possess structural signatures in glass-forming liquids. However, even in the weakly frustrated glass-forming liquids, whether or not the dynamic heterogeneity has a structural origin is a matter of debate. Via molecular dynamics simulation, we present a study of examining the connection between dynamic heterogeneity and bond orientational order in a weakly frustrated glass-forming liquid in two dimensions by taking advantage of assessing the effect of attractions on the correlation length scales. We find that attractions can strongly affect relaxation dynamics, dynamic heterogeneity and the associated dynamic correlation length of the liquid, but their influence on bond orientational order and the associated static correlation length shows a manner reminiscent of the effect of attractions on the thermodynamics of liquids. This implies that the growth of bond orientational order and static correlation length scale might be merely a manifestation of favoring the configurational entropy in weakly frustrated glass-forming liquids. Thus, our results lead strong evidence that bond orientational order cannot provide a complete description of dynamic heterogeneity even in weakly frustrated glass-forming systems.; Comment: 8 pages...

## Large-q expansion of the correlation length in the two-dimensional q-state Potts model

Arisue, H.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.05021%
The large-q expansions of the exponential correlation length and the second moment correlation length for the q-state Potts model in two dimensions are calculated at the first order phase transition point both in the ordered and disordered phases. The expansion coefficients in the ordered and disordered phases coincide in lower orders for both of the two types of the correlation lengths, but they differ a little from each other in higher orders for the second moment correlation length. The second largest eigenvalues of the transfer matrix have the continuum spectrum both in the ordered and disordered phases in the large-q region, which is suggested to be maintained even in the limit of $q\to 4$ from the analysis of the expansion series.; Comment: 3 pages, LaTeX, 2 figures, Talk presented at LATTICE99(spin models), Pisa, 29 June - 3 July 1999, to appear in Nucl. Phys. B (Proc.Suppl.)

## Determination of electron-hole correlation length in CdSe quantum dots using explicitly correlated two-particle cumulant

Blanton, Christopher J.; Chakraborty, Arindam
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.169507%
The electron-hole correlation length serves as an intrinsic length scale for analyzing excitonic interactions in semiconductor nanoparticles. In this work, the derivation of electron-hole correlation length using the two-particle reduced density is presented. The correlation length was obtained by first calculating the electron-hole cumulant from the pair density,and then transforming the cumulant into intracular coordinates, and finally then imposing exact sum-rule conditions on the radial integral of the cumulant. The excitonic wave function for the calculation was obtained variationally using the electron-hole explicitly correlated Hartree-Fock method. As a consequence, both the pair density and the cumulant were explicit functions of the electron-hole separation distance. The use of explicitly correlated wave function and the integral sum-rule condition are the two key features of this derivation. The method was applied to a series of CdSe quantum dots with diameters 1-20 nm and the effect of dot size on the correlation length was analyzed.; Comment: keywords: explicitly correlated, Gaussian-type geminal, electron-hole correlation, reduced density matrix, cumulant, transition density matrix

## Correlation length versus gap in frustration-free systems

Gosset, David; Huang, Yichen
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.929824%
Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap $\epsilon$ has correlation length $\xi$ upper bounded as $\xi=O(1/\epsilon)$. In general this bound cannot be improved. Here we study the scaling of the correlation length as a function of the spectral gap in frustration-free local Hamiltonians, and we prove a tight bound $\xi=O(1/\sqrt\epsilon)$ in this setting. This highlights a fundamental difference between frustration-free and frustrated systems near criticality. The result is obtained using an improved version of the combinatorial proof of correlation decay due to Aharonov et al.; Comment: v2: corrected one reference

## Measuring the correlation length of intergalactic magnetic fields from observations of gamma-ray induced cascades

Neronov, A.; Taylor, A. M.; Tchernin, C.; Vovk, Ie.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.05021%
Context. The imaging and timing properties of {\gamma}-ray emission from electromagnetic cascades initiated by very-high-energy (VHE) {\gamma}-rays in the intergalactic medium depend on the strength B and correlation length {\lambda}B of intergalactic magnetic fields (IGMF). Aims. We study the possibility of measuring both B and {\lambda}B via observations of the cascade emission with {\gamma}-ray telescopes. Methods. For each measurement method, we find two characteristics of the cascade signal, which are sensitive to the IGMF B and {\lambda}B values in different combinations. For the case of IGMF measurement using the observation of extended emission around extragalactic VHE {\gamma}-ray sources, the two characteristics are the slope of the surface brightness profile and the overall size of the cascade source. For the case of IGMF measurement from the time delayed emission, these two characteristics are the initial slope of the cascade emission light curve and the overall duration of the cascade signal. Results. We show that measurement of the slope of the cascade induced extended emission and/or light curve can both potentially provide measure of the IGMF correlation length, provided it lies within the range 10 kpc< {\lambda}B <1 Mpc. For correlation lengths outside this range...

## Nonequilibrium dynamic-correlation-length scaling method

Nakamura, Tota
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.00262%
The finite-size scaling method in the equilibrium Monte Carlo(MC) simulations and the finite-time scaling method in the nonequilibrium-relaxation simulations are compromised. MC time data of various physical quantities are scaled by the MC time data of the dynamic correlation length, which corresponds to changing the system size in the finite-size scaling method. This scaling method is tested in the three-dimensional ferromagnetic Ising spin model and in the three dimensional $\pm J$ Ising spin-glass model. The transition temperature and the critical exponents, $\eta$ and $\nu$, are obtained by the nonequilibrium relaxation data of the susceptibility and the dynamic correlation length apart from the dynamic exponent. We also comment on the definition of the dynamic correlation length in the nonequilibrium relaxation process. The Ornstein-Zernike formula is not always appropriate.; Comment: 7 pages, 10 figures

## Random wetting transition on the Cayley tree : a disordered first-order transition with two correlation length exponents

Monthus, Cecile; Garel, Thomas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.08756%
We consider the random wetting transition on the Cayley tree, i.e. the problem of a directed polymer on the Cayley tree in the presence of random energies along the left-most bonds. In the pure case, there exists a first-order transition between a localized phase and a delocalized phase, with a correlation length exponent $\nu_{pure}=1$. In the disordered case, we find that the transition remains first-order, but that there exists two diverging length scales in the critical region : the typical correlation length diverges with the exponent $\nu_{typ}=1$, whereas the averaged correlation length diverges with the bigger exponent $\nu_{av}=2$ and governs the finite-size scaling properties. We describe the relations with previously studied models that are governed by the same "Infinite Disorder Fixed Point". For the present model, where the order parameter is the contact density $\theta_L=l_a/L$ (defined as the ratio of the number $l_a$ of contacts over the total length $L$), the notion of "infinite disorder fixed point" means that the thermal fluctuations of $\theta_L$ within a given sample, become negligeable at large scale with respect to sample-to-sample fluctuations. We characterize the statistics over the samples of the free-energy and of the contact density. In particular...

## Dynamical heterogeneity in a highly supercooled liquid: Consistent calculations of correlation length, intensity, and lifetime

Mizuno, Hideyuki; Yamamoto, Ryoichi
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.084575%
We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length $\xi_4$, intensity $\chi_4$, and lifetime $\tau_{\text{hetero}}$. We evaluated all three quantities consistently from a single order parameter. In a previous study (H. Mizuno and R. Yamamoto, Phys. Rev. E {\bf 82}, 030501(R) (2010)), we examined the lifetime $\tau_{\text{hetero}}(t)$ in two time intervals $t=\tau_\alpha$ and $\tau_{\text{ngp}}$, where $\tau_\alpha$ is the $\alpha$-relaxation time and $\tau_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime $\tau_{\text{hetero}}(t)$, we evaluated the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ from the same order parameter used for the lifetime $\tau_{\text{hetero}}(t)$. We found that as the temperature decreases, the lifetime $\tau_{\text{hetero}}(t)$ grows dramatically, whereas the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ increase slowly compared to $\tau_{\text{hetero}}(t)$ or plateaus. Furthermore, we investigated the lifetime $\tau_{\text{hetero}}(t)$ in more detail. We examined the time-interval dependence of the lifetime $\tau_{\text{hetero}}(t)$ and found that as the time interval $t$ increases...

## Master singular behavior from correlation length measurements for seven one-component fluids near their gas-liquid critical point

Garrabos, Yves; Palencia, Fabien; Lecoutre-Chabot, Carole; John, Erkey Can; Neindre, Bernard Le
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.929824%
We present the master (i.e. unique) behavior of the correlation length, as a function of the thermal field along the critical isochore, asymptotically close to the gas-liquid critical point of xenon, krypton, argon, helium 3, sulfur hexafluoride, carbon dioxide and heavy water. It is remarkable that this unicity extends to the correction-to-scaling terms. The critical parameter set which contains all the needed information to reveal the master behavior, is composed of four thermodynamic coordinates of the critical point and one adjustable parameter which accounts for quantum effects in the helium 3 case. We use a scale dilatation method applied to the relevant physical variables of the onecomponent fluid subclass, in analogy with the basic hypothesis of the renormalization theory. This master behavior for the correlation length satisfies hyperscaling. We finally estimate the thermal field extent, where the critical crossover of the singular thermodynamic and correlation functions deviate from the theoretical crossover function obtained from field theory.; Comment: Submitted to Physical Review E

## Fracture Roughness and Correlation Length in the Central Force Model

Bakke, Jan Øystein Haavig; Ramstad, Thomas; Hansen, Alex
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.00262%
We measure the roughness exponent and the correlation length exponent of a stress-weighted percolation process in the central force model in 2D. The roughness exponent is found to be zeta = 0.75 \pm 0.03 and the correlation length exponent is found to be nu = 1.7 \pm 0.3. This result supports a conjecture that the fracture roughness for large scales is controlled by a stress weighted percolation process, and the fracture roughness can by calculated from the correlation length exponent by zeta = 2*nu/(1+2*nu). We also compare global and local measurements of the fracture roughness and do not find sign of anomalous scaling in the central force model.; Comment: 4 pages, 4 figures

## Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function

Umeno, Y.; Shiroishi, M.; Kluemper, A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.09952%
The asymptotics of the equal-time one-particle Green's function for the half-filled one-dimensional Hubbard model is studied at finite temperature. We calculate its correlation length by evaluating the largest and the second largest eigenvalues of the Quantum Transfer Matrix (QTM). In order to allow for the genuinely fermionic nature of the one-particle Green's function, we employ the fermionic formulation of the QTM based on the fermionic R-operator of the Hubbard model. The purely imaginary value of the second largest eigenvalue reflects the k_F (= pi/2) oscillations of the one-particle Green's function at half-filling. By solving numerically the Bethe Ansatz equations with Trotter numbers up to N=10240, we obtain accurate data for the correlation length at finite temperatures down into the very low temperature region. The correlation length remains finite even at T=0 due to the existence of the charge gap. Our numerical data confirm Stafford and Millis' conjecture regarding an analytic expression for the correlation length at T=0.; Comment: 7 pages, 6 figures

## Extracting the dynamic correlation length of actin networks from microrheology experiments

Sonn-Segev, Adar; Bernheim-Groswasser, Anne; Roichman, Yael
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.26001%
The mechanical properties of polymer gels based on cytoskeleton proteins (e.g. actin) have been studied extensively due to their significant role in biological cell motility and in maintaining the cell's structural integrity. Microrheology is the natural method of choice for such studies due to its economy in sample volume, its wide frequency range, and its spatial sensitivity. In microrheology, the thermal motion of tracer particles embedded in a complex fluid is used to extract the fluid's viscoelastic properties. Comparing the motion of a single particle to the correlated motion of particle pairs, it is possible to extract viscoelastic properties at different length scales. In a recent study, a crossover between intermediate and bulk response of complex fluids was discovered in microrheology measurements of reconstituted actin networks. This crossover length was related to structural and mechanical properties of the networks, such as their mesh size and dynamic correlation length. Here we capitalize on this result giving a detailed description of our analysis scheme, and demonstrating how this relation can be used to extract the dynamic correlation length of a polymer network. We further study the relation between the dynamic correlation length and the structure of the network...

## Large-q expansion for the second moment correlation length in the two-dimensional q-state Potts model

Arisue, H.
Tipo: Artigo de Revista Científica
We calculate the large-q expansion of the second moment correlation length at the first order phase transition point of the q-state Potts model in two dimensions both in the ordered and disordered phases to order 21 in $1/\sqrt{q}$. They coincide with each other to the third term of the series but differ a little in higher orders. Numerically the ratio of the second moment correlation length in the two phases is not far from unity in all region of q>4. The ratio of the second moment correlation length to the standard correlation length in the disordered phase is far from unity, which suggests that the second largest and smaller eigenvalues of the transfer matrix form a continuum spectrum not only in the large-q region but also in all the region of q>4.; Comment: 12 pages, 2 figures included
We numerically study dynamics and correlation length scales of a colloidal liquid in both quiescent and sheared conditions to further understand the origin of slow dynamics and dynamic heterogeneity in glass-forming systems. The simulation is performed in a weakly frustrated two-dimensional liquid, where locally preferred order is allowed to develop with increasing density. The four-point density correlations and bond-orientation correlations, which have been frequently used to capture dynamic and static length scales $\xi$ in a quiescent condition, can be readily extended to a system under steady shear in this case. In the absence of shear, we confirmed the previous findings that the dynamic slowing down accompanies the development of dynamic heterogeneity. The dynamic and static length scales increase with $\alpha$-relaxation time $\tau_{\alpha}$ as power-law $\xi\sim\tau_{\alpha}^{\mu}$ with $\mu>0$. In the presence of shear, both viscosity and $\tau_{\alpha}$ have power-law dependence on shear rate in the marked shear thinning regime. However, dependence of correlation lengths cannot be described by power laws in the same regime. Furthermore, the relation $\xi\sim\tau_{\alpha}^{\mu}$ between length scales and dynamics holds for not too strong shear where thermal fluctuations and external forces are both important in determining the properties of dense liquids. Thus...