997 research outputs found

### Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

We develop powerful numerical and analytical techniques for the solution of
the Helmholtz equation on general domains. We prove two theorems: the first
theorem provides an exact formula for the ground state of an arbirtrary
membrane, while the second theorem generalizes this result to any excited state
of the membrane. We also develop a systematic perturbative scheme which can be
used to study the small deformations of a membrane of circular or square
shapes. We discuss several applications, obtaining numerical and analytical
results.Comment: 29 pages, 12 figures, 7 tabl

### Scale-Free topologies and Activatory-Inhibitory interactions

A simple model of activatory-inhibitory interactions controlling the activity
of agents (substrates) through a "saturated response" dynamical rule in a
scale-free network is thoroughly studied. After discussing the most remarkable
dynamical features of the model, namely fragmentation and multistability, we
present a characterization of the temporal (periodic and chaotic) fluctuations
of the quasi-stasis asymptotic states of network activity. The double (both
structural and dynamical) source of entangled complexity of the system temporal
fluctuations, as an important partial aspect of the Correlation
Structure-Function problem, is further discussed to the light of the numerical
results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major
revision and new results incorporated. To appear in Chaos (2006

### Systematic derivation of a rotationally covariant extension of the 2-dimensional Newell-Whitehead-Segel equation

An extension of the Newell-Whitehead-Segel amplitude equation covariant under
abritrary rotations is derived systematically by the renormalization group
method.Comment: 8 pages, to appear in Phys. Rev. Letters, March 18, 199

### Kink Arrays and Solitary Structures in Optically Biased Phase Transition

An interphase boundary may be immobilized due to nonlinear diffractional
interactions in a feedback optical device. This effect reminds of the Turing
mechanism, with the optical field playing the role of a diffusive inhibitor.
Two examples of pattern formation are considered in detail: arrays of kinks in
1d, and solitary spots in 2d. In both cases, a large number of equilibrium
solutions is possible due to the oscillatory character of diffractional
interaction.Comment: RevTeX 13 pages, 3 PS-figure

### Shear induced grain boundary motion for lamellar phases in the weakly nonlinear regime

We study the effect of an externally imposed oscillatory shear on the motion
of a grain boundary that separates differently oriented domains of the lamellar
phase of a diblock copolymer. A direct numerical solution of the
Swift-Hohenberg equation in shear flow is used for the case of a
transverse/parallel grain boundary in the limits of weak nonlinearity and low
shear frequency. We focus on the region of parameters in which both transverse
and parallel lamellae are linearly stable. Shearing leads to excess free energy
in the transverse region relative to the parallel region, which is in turn
dissipated by net motion of the boundary toward the transverse region. The
observed boundary motion is a combination of rigid advection by the flow and
order parameter diffusion. The latter includes break up and reconnection of
lamellae, as well as a weak Eckhaus instability in the boundary region for
sufficiently large strain amplitude that leads to slow wavenumber readjustment.
The net average velocity is seen to increase with frequency and strain
amplitude, and can be obtained by a multiple scale expansion of the governing
equations

### Thermodynamic Limit Of The Ginzburg-Landau Equations

We investigate the existence of a global semiflow for the complex
Ginzburg-Landau equation on the space of bounded functions in unbounded domain.
This semiflow is proven to exist in dimension 1 and 2 for any parameter values
of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some
restrictions on the parameters but cover nevertheless some part of the
Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]

### Michaelis-Menten Relations for Complex Enzymatic Networks

All biological processes are controlled by complex systems of enzymatic
chemical reactions. Although the majority of enzymatic networks have very
elaborate structures, there are many experimental observations indicating that
some turnover rates still follow a simple Michaelis-Menten relation with a
hyperbolic dependence on a substrate concentration. The original
Michaelis-Menten mechanism has been derived as a steady-state approximation for
a single-pathway enzymatic chain. The validity of this mechanism for many
complex enzymatic systems is surprising. To determine general conditions when
this relation might be observed in experiments, enzymatic networks consisting
of coupled parallel pathways are investigated theoretically. It is found that
the Michaelis-Menten equation is satisfied for specific relations between
chemical rates, and it also corresponds to the situation with no fluxes between
parallel pathways. Our results are illustrated for simple models. The
importance of the Michaelis-Menten relationship and derived criteria for
single-molecule experimental studies of enzymatic processes are discussed.Comment: 10 pages, 4 figure

### Blood coagulation dynamics: mathematical modeling and stability results

The hemostatic system is a highly complex multicomponent biosystem that under normal physiologic conditions maintains the fluidity of blood. Coagulation is initiated in response to endothelial surface vascular injury or certain biochemical stimuli, by the exposure of plasma to Tissue Factor (TF), that activates platelets and the coagulation cascade, inducing clot formation, growth and lysis. In recent years considerable advances have contributed to understand this highly complex process and some mathematical and numerical models have been developed. However, mathematical models that are both rigorous and comprehensive in terms of meaningful experimental data, are not available yet. In this paper a mathematical model of coagulation and fibrinolysis in flowing blood that integrates biochemical, physiologic and rheological factors, is revisited. Three-dimensional numerical simulations are performed in an idealized stenosed blood vessel where clot formation and growth are initialized through appropriate boundary conditions on a prescribed region of the vessel wall. Stability results are obtained for a simplified version of the clot model in quiescent plasma, involving some of the most relevant enzymatic reactions that follow Michaelis-Menten kinetics, and having a continuum of equilibria.CEMAT/IST through FCT [PTDC/MAT/68166/2006]; Czech Science Foundation [201/09/0917]; Grant Agency of the Academy of Sciences of the CR [IAA100190804]; Ministry of Education of Czech Republic [6840770010]info:eu-repo/semantics/publishedVersio

### Unstable decay and state selection II

The decay of unstable states when several metastable states are available for
occupation is investigated using path-integral techniques. Specifically, a
method is described which allows the probabilities with which the metastable
states are occupied to be calculated by finding optimal paths, and fluctuations
about them, in the weak noise limit. The method is illustrated on a system
described by two coupled Langevin equations, which are found in the study of
instabilities in fluid dynamics and superconductivity. The problem involves a
subtle interplay between non-linearities and noise, and a naive approximation
scheme which does not take this into account is shown to be unsatisfactory. The
use of optimal paths is briefly reviewed and then applied to finding the
conditional probability of ending up in one of the metastable states, having
begun in the unstable state. There are several aspects of the calculation which
distinguish it from most others involving optimal paths: (i) the paths do not
begin and end on an attractor, and moreover, the final point is to a large
extent arbitrary, (ii) the interplay between the fluctuations and the leading
order contribution are at the heart of the method, and (iii) the final result
involves quantities which are not exponentially small in the noise strength.
This final result, which gives the probability of a particular state being
selected in terms of the parameters of the dynamics, is remarkably simple and
agrees well with the results of numerical simulations. The method should be
applicable to similar problems in a number of other areas such as state
selection in lasers, activationless chemical reactions and population dynamics
in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.

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