1,721,023 research outputs found
An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach
Get PDFWe summarise the properties and the fundamental mathematical results
associated with basic models which describe
coagulation and fragmentation processes in a deterministic manner
and in which cluster size is a discrete quantity (an integer
multiple of some basic unit size).
In particular, we discuss Smoluchowski's equation for aggregation,
the Becker-Döring model of simultaneous aggregation and fragmentation,
and more general models involving coagulation and fragmentation
Exact solutions for cluster-growth kinetics with evolving size and shape profiles
Get PDFIn this paper we construct a model for the simultaneous
compaction by which clusters are restructured, and growth
of clusters by pairwise coagulation. The model has the form
of a multicomponent aggregation problem in which the
components are cluster mass and cluster diameter.
Following suitable approximations, exact explicit solutions
are derived which may be useful for the verification of
simulations of such systems. Numerical simulations are
presented to illustrate typical behaviour and to show the
accuracy of approximations made in deriving the model.
The solutions are then simplified using asymptotic
techniques to show the relevant timescales of the kinetic
processes and elucidate the shape of the cluster distribution
functions at large times
An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach
No full textWe summarise the properties and the fundamental mathematical results
associated with basic models which describe
coagulation and fragmentation processes in a deterministic manner
and in which cluster size is a discrete quantity (an integer
multiple of some basic unit size).
In particular, we discuss Smoluchowski's equation for aggregation,
the Becker-Döring model of simultaneous aggregation and fragmentation,
and more general models involving coagulation and fragmentation
An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach
Get PDFWe summarise the properties and the fundamental mathematical resultsassociated with basic models which describecoagulation and fragmentation processes in a deterministic mannerand in which cluster size is a discrete quantity (an integermultiple of some basic unit size).In particular, we discuss Smoluchowski's equation for aggregation,the Becker-Döring model of simultaneous aggregation and fragmentation,and more general models involving coagulation and fragmentation
Exact solutions for cluster-growth kinetics with evolving size and shape profiles
Get PDFIn this paper we construct a model for the simultaneouscompaction by which clusters are restructured, and growthof clusters by pairwise coagulation. The model has the formof a multicomponent aggregation problem in which thecomponents are cluster mass and cluster diameter.Following suitable approximations, exact explicit solutionsare derived which may be useful for the verification ofsimulations of such systems. Numerical simulations arepresented to illustrate typical behaviour and to show theaccuracy of approximations made in deriving the model.The solutions are then simplified using asymptotictechniques to show the relevant timescales of the kineticprocesses and elucidate the shape of the cluster distributionfunctions at large times
Nonlinear breathing modes at a defect
Get PDFRecent molecular dynamics (MD) simulations of Cubero et al (1999) of
a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a
thymine (T) base show that breathing events can occur on the nanosecond
timescale, whereas breathing events in a normal DNA duplex take place on the microsecond timescale.
The main aim of this paper is to analyse a nonlinear Klein-Gordon lattice
model of the DNA duplex including both nonlinear interactions between
opposing bases and a defect in the interaction at one lattice site;
each of which can cause localisation of energy.
Solutions for a breather mode either side of the defect are derived using
multiple-scales asymptotics and are pieced together across the defect to
form a solution which includes the effects of the nonlinearity and the defect.
We consider defects in the
inter-chain interactions and in the along chain interactions.
In most cases we find in-phase breather modes and/or out-of-phase
breather modes, with one case displaying a shifted mode
Exact solutions for cluster-growth kinetics with evolving size and shape profiles
No full textIn this paper we construct a model for the simultaneous
compaction by which clusters are restructured, and growth
of clusters by pairwise coagulation. The model has the form
of a multicomponent aggregation problem in which the
components are cluster mass and cluster diameter.
Following suitable approximations, exact explicit solutions
are derived which may be useful for the verification of
simulations of such systems. Numerical simulations are
presented to illustrate typical behaviour and to show the
accuracy of approximations made in deriving the model.
The solutions are then simplified using asymptotic
techniques to show the relevant timescales of the kinetic
processes and elucidate the shape of the cluster distribution
functions at large times
Similarity solutions of a Becker-Döring system with time-dependent monomer input
Get PDFWe formulate the Becker-Döring equations for cluster growth in the presence of a time-dependent source of monomer input.
In the case of size-independent aggregation and ragmentation
rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found
Asymptotic approximations to travelling waves in the diatomic Fermi-Pasta-Ulam lattice
Get PDFWe construct high-order approximate travelling waves solutions of the diatomic Fermi-Pasta-Ulam lattice using asymptotic techniques which are valid for arbitrary mass ratios. Separately small amplitude ansatzs are made for the motion of the lighter and heavier particles, which are coupled The Fredholm alternative is used to derive consistency conditions, whose solution generates small amplitude expansions for both sets of particles
Similarity solutions of a Becker-Döring system with time-dependent monomer input
No full textWe formulate the Becker-Döring equations for cluster growth in the presence of a time-dependent source of monomer input.
In the case of size-independent aggregation and ragmentation
rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found
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