1,245 research outputs found
Hybrid-Model Calculations of the Nucleon Removal by 80-164 MeV Protons from Medium-Mass Nuclei
This work was supported by National Science Foundation Grant PHY 75-00289 and Indiana Universit
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
Coarse graining of master equations with fast and slow states
We propose a general method for simplifying master equations by eliminating
from the description rapidly evolving states. The physical recipe we impose is
the suppression of these states and a renormalization of the rates of all the
surviving states. In some cases, this decimation procedure can be analytically
carried out and is consistent with other analytical approaches, like in the
problem of the random walk in a double-well potential. We discuss the
application of our method to nontrivial examples: diffusion in a lattice with
defects and a model of an enzymatic reaction outside the steady state regime.Comment: 9 pages, 9 figures, final version (new subsection and many minor
improvements
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
Systematics of Inclusive Charged Particles Production with Medium Energy Protons
This work was supported by National Science Foundation Grants PHY 76-84033A01, PHY 78-22774, and Indiana Universit
Selection of the scaling solution in a cluster coalescence model
The scaling properties of the cluster size distribution of a system of
diffusing clusters is studied in terms of a simple kinetic mean field model. It
is shown that a one parameter family of mathematically valid scaling solutions
exists. Despite this, the kinetics reaches a unique scaling solution
independent of initial conditions. This selected scaling solution is marginally
physical; i.e., it is the borderline solution between the unphysical and
physical branches of the family of solutions.Comment: 4 pages, 5 figure
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
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
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Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area
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