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

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

EN

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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.

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/06/2012

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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.

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Nonlinear Sciences - Chaotic Dynamics#Nonlinear Sciences - Cellular Automata and Lattice Gases#Nonlinear Sciences - Pattern Formation and Solitons

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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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

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## The Growing Correlation Length in Glasses

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/04/2013

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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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/10/2012

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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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/09/1999

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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.)

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/05/2014

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#Physics - Atomic and Molecular Clusters#Condensed Matter - Mesoscale and Nanoscale Physics#Physics - Chemical Physics

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

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## Correlation length versus gap in frustration-free systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Quantum Physics#Condensed Matter - Statistical Mechanics#Condensed Matter - Strongly Correlated Electrons#Mathematical Physics

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/07/2013

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...

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## Nonequilibrium dynamic-correlation-length scaling method

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/02/2010

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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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/01/2009

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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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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#Condensed Matter - Soft Condensed Matter#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics

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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/12/2005

Relevância na Pesquisa

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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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/07/2005

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/10/2002

Relevância na Pesquisa

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#Condensed Matter - Strongly Correlated Electrons#Condensed Matter - Statistical Mechanics#Nonlinear Sciences - Exactly Solvable and Integrable Systems

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/08/2014

Relevância na Pesquisa

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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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/01/2000

Relevância na Pesquisa

47.09952%

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

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## Dynamics and correlation length scales of a glass-forming liquid in quiescent and sheared conditions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/05/2012

Relevância na Pesquisa

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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...

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