836 research outputs found
Collapse of a semiflexible polymer in poor solvent
We investigate the dynamics and the pathways of the collapse of a single,
semiflexible polymer in a poor solvent via 3-D Brownian Dynamics simulations.
Earlier work indicates that the condensation of semiflexible polymers
generically proceeds via a cascade through metastable racquet-shaped,
long-lived intermediates towards the stable torus state. We investigate the
rate of decay of uncollapsed states, analyze the preferential pathways of
condensation, and describe likelihood and lifespan of the different metastable
states. The simulation are performed with a bead-stiff spring model with
excluded volume interaction and exponentially decaying attractive potential.
The semiflexible chain collapse is studied as functions of the three relevant
length scales of the phenomenon, i.e., the total chain length , the
persistence length and the condensation length , where is a measure of the attractive potential per unit
length. Two dimensionless ratios, and , suffice to describe
the decay rate of uncollapsed states, which appears to scale as . The condensation sequence is described in terms of the time series
of the well separated energy levels associated with each metastable collapsed
state. The collapsed states are described quantitatively through the spatial
correlation of tangent vectors along the chain. We also compare the results
obtained with a locally inextensible bead-rod chain and with a phantom
bead-spring model. Finally, we show preliminary results on the effects of
steady shear flow on the kinetics of collapse.Comment: 9 pages, 8 figure
Early Stages of Homopolymer Collapse
Interest in the protein folding problem has motivated a wide range of
theoretical and experimental studies of the kinetics of the collapse of
flexible homopolymers. In this Paper a phenomenological model is proposed for
the kinetics of the early stages of homopolymer collapse following a quench
from temperatures above to below the theta temperature. In the first stage,
nascent droplets of the dense phase are formed, with little effect on the
configurations of the bridges that join them. The droplets then grow by
accreting monomers from the bridges, thus causing the bridges to stretch.
During these two stages the overall dimensions of the chain decrease only
weakly. Further growth of the droplets is accomplished by the shortening of the
bridges, which causes the shrinking of the overall dimensions of the chain. The
characteristic times of the three stages respectively scale as the zeroth, 1/5
and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure
Twist Deformations of the Supersymmetric Quantum Mechanics
The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian
twist which preserves the super-Hopf algebra structure of its Universal
Enveloping Superalgebra. Two constructions are possible. For even N one can
identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra.
Alternatively, supersymmetry generators can be realized as operators belonging
to the Universal Enveloping Superalgebra of one bosonic and several fermionic
oscillators. The deformed system is described in terms of twisted operators
satisfying twist-deformed (anti)commutators. The main differences between an
abelian twist defined in terms of fermionic operators and an abelian twist
defined in terms of bosonic operators are discussed.Comment: 18 pages; two references adde
Effects of Long-Range Nonlinear Interactions in Double-Well Potentials
We consider the interplay of linear double-well-potential (DWP) structures
and nonlinear longrange interactions of different types, motivated by
applications to nonlinear optics and matter waves. We find that, while the
basic spontaneous-symmetry-breaking (SSB) bifurcation structure in the DWP
persists in the presence of the long-range interactions, the critical points at
which the SSB emerges are sensitive to the range of the nonlocal interaction.
We quantify the dynamics by developing a few-mode approximation corresponding
to the DWP structure, and analyze the resulting system of ordinary differential
equations and its bifurcations in detail. We compare results of this analysis
with those produced by the full partial differential equation, finding good
agreement between the two approaches. Effects of the competition between the
local self-attraction and nonlocal repulsion on the SSB are studied too. A far
more complex bifurcation structure involving the possibility for not only
supercritical but also subcritical bifurcations and even bifurcation loops is
identified in that case.Comment: 12 pages, 9 figure
On the Bohr inequality
The Bohr inequality, first introduced by Harald Bohr in 1914, deals with
finding the largest radius , , such that holds whenever in the unit disk
of the complex plane. The exact value of this largest radius,
known as the \emph{Bohr radius}, has been established to be This paper
surveys recent advances and generalizations on the Bohr inequality. It
discusses the Bohr radius for certain power series in as well as
for analytic functions from into particular domains. These domains
include the punctured unit disk, the exterior of the closed unit disk, and
concave wedge-domains. The analogous Bohr radius is also studied for harmonic
and starlike logharmonic mappings in The Bohr phenomenon which is
described in terms of the Euclidean distance is further investigated using the
spherical chordal metric and the hyperbolic metric. The exposition concludes
with a discussion on the -dimensional Bohr radius
Comparison of some Reduced Representation Approximations
In the field of numerical approximation, specialists considering highly
complex problems have recently proposed various ways to simplify their
underlying problems. In this field, depending on the problem they were tackling
and the community that are at work, different approaches have been developed
with some success and have even gained some maturity, the applications can now
be applied to information analysis or for numerical simulation of PDE's. At
this point, a crossed analysis and effort for understanding the similarities
and the differences between these approaches that found their starting points
in different backgrounds is of interest. It is the purpose of this paper to
contribute to this effort by comparing some constructive reduced
representations of complex functions. We present here in full details the
Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM)
together with other approaches that enter in the same category
Symmetry-breaking Effects for Polariton Condensates in Double-Well Potentials
We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in the atomic condensate case is that the bifurcation for attractive interactions is slightly sub-critical instead of supercritical. These conclusions of the bifurcation analysis are corroborated by direct numerical simulations examining the dynamics of the system in the unstable regime.MICINN (Spain) project FIS2008- 0484
Generalized Contour Dynamics: A Review
Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow
Two-Component Nonlinear Schrodinger Models with a Double-Well Potential
We introduce a model motivated by studies of Bose-Einstein condensates (BECs)
trapped in double-well potentials. We assume that a mixture of two hyperfine
states of the same atomic species is loaded in such a trap.The analysis is
focused on symmetry-breaking bifurcations in the system, starting at the linear
limit and gradually increasing the nonlinearity. Depending on values of the
chemical potentials of the two species, we find numerous states, as well as
symmetry-breaking bifurcations, in addition to those known in the
single-component setting. These branches, which include all relevant stationary
solutions of the problem, are predicted analytically by means of a two-mode
approximation, and confirmed numerically. For unstable branches, outcomes of
the instability development are explored in direct simulations.Comment: 17 pages, 12 figures, Physica D, in pres
Off-pump coronary artery bypass grafting provides complete revascularization with reduced myocardial injury, transfusion requirements, and length of stay: A prospective randomized comparison of two hundred unselected patients undergoing off-pump versus conventional coronary artery bypass grafting
AbstractObjective: Retrospective comparisons of selected patients undergoing off-pump versus conventional on-pump coronary artery bypass grafting have yielded inconsistent results and raised concerns about completeness of revascularization in off-pump coronary artery bypass grafting. Methods: Two hundred unselected patients referred for elective primary coronary artery bypass grafting were randomly assigned to undergo off-pump coronary artery bypass grafting with an Octopus tissue stabilizer (Medtronic, Inc, Minneapolis, Minn) or conventional coronary artery bypass grafting with cardiopulmonary bypass by a single surgeon. Revascularization intent determined before random assignment was compared with the revascularization performed. All management followed strict, unbiased, criteria-driven protocols. Patients and nonoperative care providers were blinded to surgical group. Results: Baseline characteristics were similar. The number of grafts performed per patient (mean ± SD 3.39 ± 1.04 for off-pump coronary artery bypass grafting, 3.40 ± 1.08 for conventional coronary artery bypass grafting) and the index of completeness of revascularization (number of grafts performed/number of grafts intended, 1.00 ± 0.18 for off-pump coronary artery bypass grafting, 1.01 ± 0.09 for conventional coronary artery bypass grafting) were similar. Likewise, the index of completeness of revascularization was similar between groups for the lateral wall. Combined hospital and 30-day mortalities and stroke rates were similar. Postoperative myocardial serum enzyme measures were significantly lower after off-pump coronary artery bypass grafting, suggesting less myocardial injury. Adjusted postoperative thromboelastogram indices, fibrinogen, international normalized ratio, and platelet levels all showed significantly less coagulopathy after off-pump coronary artery bypass grafting. Patients undergoing off-pump coronary artery bypass grafting received fewer units of blood, were more likely to avoid transfusion altogether, and had a higher hematocrit at discharge. Cardiopulmonary bypass was an independent predictor of transfusion (odds ratio 2.42, P =.0073) by multivariate analysis. More patients undergoing off-pump coronary artery bypass grafting were extubated in the operating room and within 4 hours. Postoperative length of stay (in days) was shorter for off-pump coronary artery bypass grafting (5.1 ± 6.5 for off-pump coronary artery bypass grafting, 6.1 ± 8.2 for conventional coronary artery bypass grafting, P =.005 by Wilcoxon test). One patient (in the conventional coronary artery bypass grafting group) required angioplasty for graft closure within 30 days. Conclusions: When compared with conventional coronary artery bypass grafting with cardiopulmonary bypass, off-pump coronary artery bypass grafting achieved similar completeness of revascularization, similar in-hospital and 30-day outcomes, shorter length of stay, reduced transfusion requirement, and less myocardial injury.J Thorac Cardiovasc Surg 2003;125:797-80
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