摘要:

A model is presented for the contraction of vertebrate striated muscle which is predicated largely on structural grounds and ascribes to the binding of myosin and actin subunits the primary element of force generation. The dynamics of the model is realized as a series of ’’states’’ and transitions among them which can be characterized as a biased random walk in one dimension. Two modes are described for the motion of the myosin subunits (HMM‐1): (1) ’’inchworm,’’ where the relative configuration of the two elements of the duplex head remains unchanged, and (2) ’’flip‐flop,’’ where the heads are free to undergo reversal of ordinal position. The master equation is solved in some detail for the ’’inchworm’’ mode and the solutions displayed. The mean first passage time (MFPT) is computed for the ’’inchworm’’ mode and related to the velocity of muscle contraction. For the case where both modes operate the MFPT is computed by a perturbation procedure and the effects of the ’’flip‐flop’’ mode are shown to decrease the MFPT. When load dependence is included in the characterization of the elementary rates (attachment/detachment), it is shown that the stochastic theory agrees, for small loads, with the phenomenological equation of A. V. Hill relating velocity and load. A brief discussion is made of the length‐tension isotherm and estimates made for the force generated per crossbridge and for the energy release necessary for unit displacement by a myosin head along the actin polymer (force &angupr;10−7dynes; energy &angupr;3 kcal mole−1).

ISSN:0094-243X    

DOI:10.1063/1.30360

出版商:AIP    

年代:1976

数据来源: AIP

摘要:

A class of renormalization groups characterized as the general Gaussian renormalization group is defined. It includes the sharp cutoff renormalization group of Wilson, the linear renormalization group of Bell and Wilson, and the incomplete‐integration renormalization group of Wilson. The renormalization group approach to critical phenomena and the expansion around four dimensions is reviewed. The fixed point of the general Gaussian renormalization group is determined to order &egr;2, where &egr;=4−d(dis the dimensionality of the system), and the critical exponents are determined to the same order. The main conclusion is that the exponents do not depend on the cutoff functions of the renormalization group.

ISSN:0094-243X    

DOI:10.1063/1.30359

出版商:AIP    

年代:1976

数据来源: AIP

摘要:

C. Eminhizer and the authors1have recently developed iterative methods for solving the dynamics of extremely nonlinear anharmonic oscillators. These methods are re‐examined here in a formalism proposed by Carleman2for the embedding of nonlinear dynamical equations in an infinite set of linear equations.The methods are based on recursion formulae for the Fourier coefficients of Fourier series solutions of the dynamical equations and for coefficients of expansions of Fourier frequencies.The series solutions avoid ’’Secular Terms’’ and ’’Small Denominators’’ and converge rapidly in large regimes of highly nonlinear behaviour.

ISSN:0094-243X    

DOI:10.1063/1.30362

出版商:AIP    

年代:1976

数据来源: AIP

摘要:

A careful study of the derivation of the non‐linear hydrodynamic equations using generalized response theory is presented. There is a correspondence between the results of response theory and the use of local equilibrium distribution functions but it is not direct. The general forms of the transport equations for the densities of conserved variables are presented and discussed.

ISSN:0094-243X    

DOI:10.1063/1.30355

出版商:AIP    

年代:1976

数据来源: AIP

摘要:

In the basic predator‐prey model under investigation, growth rates of both species are influenced by both predator and prey population levels. Random dispersal is modelled by diffusion‐like terms in both discrete and continuous situations. Application of a combined successive‐approximations multiple‐scale approach to stability theory shows that under some circumstances uniform conditions will be succeeded by a new steady state wherein predator and prey are more concentrated in certain regions. Under other circumstances (in the discrete case only), although uniform conditions are stable according to linear theory, nevertheless sufficiently large pertubations are destabilizing. The biological implications of the results are discussed.

ISSN:0094-243X    

DOI:10.1063/1.30356

出版商:AIP    

年代:1976

数据来源: AIP

摘要:

The density of particles in space or in phase space varies in time through continuous flow and through discrete jumps, due to collisions, chemical reactions, radio‐active decay, or births and deaths. A method is developed for computing the fluctuations arising from the random jumps and influenced by the flow. It equally applies to equilibrium, stationary states, and time‐dependent situations, both in linear and nonlinear systems. The method is based on the master equation and does not require the additional assumptions needed for the Langevin approach, although the correct form of the Langevin force can be deduced from it a posteriori. Factorial cumulants turn out to be a convenient tool. As applications the fluctuations inherent in the diffusion process are computed and a controversial chemical reaction is discussed.

ISSN:0094-243X    

DOI:10.1063/1.30357

出版商:AIP    

年代:1976

数据来源: AIP

摘要:

Phenomena arising from the interaction of non‐linear limit cycle oscillators are discussed. The individual oscillators are piecewise linear and discontinuous (the ’’playground swing’’ model). A special interaction is chosen, which allows much of the analysis to be performed algebraically rather than by solving differential equations. The model is well adapted to efficient numerical computation. Examples are discussed for which various types of synchronization are found.

ISSN:0094-243X    

DOI:10.1063/1.30358

出版商:AIP    

年代:1976

数据来源: AIP

ISSN:0094-243X    

DOI:10.1063/1.30361

出版商:AIP    

年代:1976

数据来源: AIP