1,267 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
Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
Enyzme kinetics are cyclic. We study a Markov renewal process model of
single-enzyme turnover in nonequilibrium steady-state (NESS) with sustained
concentrations for substrates and products. We show that the forward and
backward cycle times have idential non-exponential distributions:
\QQ_+(t)=\QQ_-(t). This equation generalizes the Haldane relation in
reversible enzyme kinetics. In terms of the probabilities for the forward
() and backward () cycles, is shown to be the
chemical driving force of the NESS, . More interestingly, the moment
generating function of the stochastic number of substrate cycle ,
follows the fluctuation theorem in the form of
Kurchan-Lebowitz-Spohn-type symmetry. When $\lambda$ = $\Delta\mu/k_BT$, we
obtain the Jarzynski-Hatano-Sasa-type equality:
1 for all , where is the fluctuating chemical work
done for sustaining the NESS. This theory suggests possible methods to
experimentally determine the nonequilibrium driving force {\it in situ} from
turnover data via single-molecule enzymology.Comment: 4 pages, 3 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
Longitudinal response functions of 3H and 3He
Trinucleon longitudinal response functions R_L(q,omega) are calculated for q
values up to 500 MeV/c. These are the first calculations beyond the threshold
region in which both three-nucleon (3N) and Coulomb forces are fully included.
We employ two realistic NN potentials (configuration space BonnA, AV18) and two
3N potentials (UrbanaIX, Tucson-Melbourne). Complete final state interactions
are taken into account via the Lorentz integral transform technique. We study
relativistic corrections arising from first order corrections to the nuclear
charge operator. In addition the reference frame dependence due to our
non-relativistic framework is investigated. For q less equal 350 MeV/c we find
a 3N force effect between 5 and 15 %, while the dependence on other theoretical
ingredients is small. At q greater equal 400 MeV/c relativistic corrections to
the charge operator and effects of frame dependence, especially for large
omega, become more important. In comparison with experimental data there is
generally a rather good agreement. Exceptions are the responses at excitation
energies close to threshold, where there exists a large discrepancy with
experiment at higher q. Concerning the effect of 3N forces there are a few
cases, in particular for the R_L of 3He, where one finds a much improved
agreement with experiment if 3N forces are included.Comment: 26 pages, 9 figure
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
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]
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