907 research outputs found
Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems
The renormalization-group (RG) functions for the three-dimensional n-vector
cubic model are calculated in the five-loop approximation. High-precision
numerical estimates for the asymptotic critical exponents of the
three-dimensional impure Ising systems are extracted from the five-loop RG
series by means of the Pade-Borel-Leroy resummation under n = 0. These
exponents are found to be: \gamma = 1.325 +/- 0.003, \eta = 0.025 +/- 0.01, \nu
= 0.671 +/- 0.005, \alpha = - 0.0125 +/- 0.008, \beta = 0.344 +/- 0.006. For
the correction-to-scaling exponent, the less accurate estimate \omega = 0.32
+/- 0.06 is obtained.Comment: 11 pages, LaTeX, no figures, published versio
Extensive Modeling of a Coaxial Stub Resonator for Online Fingerprinting of Fluids
A straightforward method of extensive modeling of a lossy stub resonator system for online fingerprinting of fluids is presented in this paper. The proposed model solves the telegrapher's equations including the skin effect and dielectric losses and describes the amplitude versus frequency response of lossy coaxial stub resonators with a fluid under investigation as dielectric. The adequacy of the method is demonstrated by comparing simulations with experimentally obtained data. Even though we applied the model to a coaxial stub resonator for the online fingerprinting of fluids (e.g., for water quality monitoring), the potential applicability of the method reaches further. Indeed, the method introduced here may be useful for different types of sensors based on lossy transmission line theor
Anomalous Dynamics of Forced Translocation
We consider the passage of long polymers of length N through a hole in a
membrane. If the process is slow, it is in principle possible to focus on the
dynamics of the number of monomers s on one side of the membrane, assuming that
the two segments are in equilibrium. The dynamics of s(t) in such a limit would
be diffusive, with a mean translocation time scaling as N^2 in the absence of a
force, and proportional to N when a force is applied. We demonstrate that the
assumption of equilibrium must break down for sufficiently long polymers (more
easily when forced), and provide lower bounds for the translocation time by
comparison to unimpeded motion of the polymer. These lower bounds exceed the
time scales calculated on the basis of equilibrium, and point to anomalous
(sub-diffusive) character of translocation dynamics. This is explicitly
verified by numerical simulations of the unforced translocation of a
self-avoiding polymer. Forced translocation times are shown to strongly depend
on the method by which the force is applied. In particular, pulling the polymer
by the end leads to much longer times than when a chemical potential difference
is applied across the membrane. The bounds in these cases grow as N^2 and
N^{1+\nu}, respectively, where \nu is the exponent that relates the scaling of
the radius of gyration to N. Our simulations demonstrate that the actual
translocation times scale in the same manner as the bounds, although influenced
by strong finite size effects which persist even for the longest polymers that
we considered (N=512).Comment: 13 pages, RevTeX4, 16 eps figure
Critical equation of state of randomly dilute Ising systems
We determine the critical equation of state of three-dimensional randomly
dilute Ising systems, i.e. of the random-exchange Ising universality class. We
first consider the small-magnetization expansion of the Helmholtz free energy
in the high-temperature phase. Then, we apply a systematic approximation scheme
of the equation of state in the whole critical regime, that is based on
polynomial parametric representations matching the small-magnetization of the
Helmholtz free energy and satisfying a global stationarity condition. These
results allow us to estimate several universal amplitude ratios, such as the
ratio A^+/A^- of the specific-heat amplitudes. Our best estimate A^+/A^-=1.6(3)
is in good agreement with experimental results on dilute uniaxial
antiferromagnets.Comment: 21 pages, 1 figure, refs adde
Critical behavior of weakly-disordered anisotropic systems in two dimensions
The critical behavior of two-dimensional (2D) anisotropic systems with weak
quenched disorder described by the so-called generalized Ashkin-Teller model
(GATM) is studied. In the critical region this model is shown to be described
by a multifermion field theory similar to the Gross-Neveu model with a few
independent quartic coupling constants. Renormalization group calculations are
used to obtain the temperature dependence near the critical point of some
thermodynamic quantities and the large distance behavior of the two-spin
correlation function. The equation of state at criticality is also obtained in
this framework. We find that random models described by the GATM belong to the
same universality class as that of the two-dimensional Ising model. The
critical exponent of the correlation length for the 3- and 4-state
random-bond Potts models is also calculated in a 3-loop approximation. We show
that this exponent is given by an apparently convergent series in
(with the central charge of the Potts model) and
that the numerical values of are very close to that of the 2D Ising
model. This work therefore supports the conjecture (valid only approximately
for the 3- and 4-state Potts models) of a superuniversality for the 2D
disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.
Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy
We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with
cubic anisotropy. We compute and analyze the fixed-dimension perturbative
expansion of the renormalization-group functions to four loops. The relations
of these models with N-color Ashkin-Teller models, discrete cubic models,
planar model with fourth order anisotropy, and structural phase transition in
adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic
anisotropy) are compatible with the existence of a line of fixed points joining
the Ising and the O(2) fixed points. Along this line the exponent has
the constant value 1/4, while the exponent runs in a continuous and
monotonic way from 1 to (from Ising to O(2)). For N\geq 3 we find a
cubic fixed point in the region , which is marginally stable or
unstable according to the sign of the perturbation. For the physical relevant
case of N=3 we find the exponents and at the cubic
transition.Comment: 14 pages, 9 figure
Possible origins of macroscopic left-right asymmetry in organisms
I consider the microscopic mechanisms by which a particular left-right (L/R)
asymmetry is generated at the organism level from the microscopic handedness of
cytoskeletal molecules. In light of a fundamental symmetry principle, the
typical pattern-formation mechanisms of diffusion plus regulation cannot
implement the "right-hand rule"; at the microscopic level, the cell's
cytoskeleton of chiral filaments seems always to be involved, usually in
collective states driven by polymerization forces or molecular motors. It seems
particularly easy for handedness to emerge in a shear or rotation in the
background of an effectively two-dimensional system, such as the cell membrane
or a layer of cells, as this requires no pre-existing axis apart from the layer
normal. I detail a scenario involving actin/myosin layers in snails and in C.
elegans, and also one about the microtubule layer in plant cells. I also survey
the other examples that I am aware of, such as the emergence of handedness such
as the emergence of handedness in neurons, in eukaryote cell motility, and in
non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue.
Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in
Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec
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