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DCDSS is indexed by Science Citation Index Expanded, ISI Alerting Services and Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES).
Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDSS is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.
DCDSS publishes only Theme Issues: issues with a coherent topic proposed by guest editors. Click here to learn how to submit a theme issue proposal. Occasionally, proposals of an important current topic that is also the main theme of a high quality workshop/meeting are also considered, however, the same rigorous editorial process is applied.
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TOP 10 Most Read Articles in DCDSS, January 2015
1 
Turing instability in a coupled predatorprey
model with different Holling type functional responses
Volume 4, Number 6, Pages: 1621  1628, 2010
Zhifu Xie
Abstract
References
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In a reactiondiffusion system, diffusion can induce the instability
of a positive equilibrium which is stable with respect to a
constant perturbation, therefore, the diffusion may create new
patterns when the corresponding system without diffusion fails,
as shown by Turing in 1950s. In this paper we study a coupled
predatorprey model with different Holling type functional
responses, where crossdiffusions are included in such a way that
the prey runs away from predator and the predator chase preys. We
conduct the Turing instability analysis for each Holling functional response.
We prove that if a positive equilibrium solution is linearly stable with respect to the ODE system of
the predatorprey model, then it is
also linearly stable with respect to the model. So diffusion and
crossdiffusion in the predatorprey model with Holling type
functional responses given in this paper can not drive Turing
instability. However, diffusion and crossdiffusion can still create
nonconstant positive solutions for the model.

2 
Boolean models of bistable biological systems
Volume 4, Number 6, Pages: 1443  1456, 2010
Franziska Hinkelmann
and Reinhard Laubenbacher
Abstract
References
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This paper presents an algorithm for approximating certain types of dynamical
systems given by a system of ordinary delay differential equations by
a Boolean network model. Often Boolean models are much simpler to understand than
complex differential equations models. The motivation for this work comes
from mathematical systems biology. While Boolean mechanisms do not provide information about exact
concentration rates or time scales, they are often sufficient to
capture steady states and other key dynamics. Due to their intuitive nature, such
models are very appealing to researchers in the life sciences.
This paper is focused on dynamical systems that exhibit bistability and are described
by delay equations. It is shown that if a certain motif
including a feedback loop is present in the wiring diagram of the system, the
Boolean model captures the bistability of molecular switches. The method is applied to
two examples from biology, the lac operon and the phage $\lambda$
lysis/lysogeny switch.

3 
Reaction diffusion equation with nonlocal term arises as a mean field limit of the master equation
Volume 5, Number 1, Pages: 115  126, 2011
Kazuhisa Ichikawa,
Mahemauti Rouzimaimaiti
and Takashi Suzuki
Abstract
References
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We formulate a reaction diffusion equation with nonlocal term as a mean field equation of the master equation where the particle density is defined continuously in space and time. In the case of the constant mean waiting time, this limit equation is associated with the diffusion coefficient of A. Einstein, the reaction rate in phenomenology, and the Debye term under the presence of potential.

4 
Modeling drugprotein dynamics
Volume 5, Number 1, Pages: 191  207, 2011
Lambertus A. Peletier
Abstract
References
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In this paper we discuss two models involving protein binding. The first model describes a system involving a drug,
a receptor and a protein, and the question is to what extent the affinity of the drug to the protein affects the drugreceptor binding and thereby the efficiency of the drug. The second model is the basic model underlying TargetMediated Drug Disposition, which describes the pharmacokinetics of a drug in the presence of a target, often a receptor.

5 
On the existence of a weak solution to a free boundary problem for a model of a shape memory alloy spring
Volume 5, Number 1, Pages: 1  13, 2011
Toyohiko Aiki
Abstract
References
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In our previous works we proposed and studied the mathematical model for the position of the joint of a shape memory alloy and a bias springs in case the temperature is known. The purpose of this paper is to establish a mathematical model with unknown temperature and to show a local existence of a solution to the model in time.

6 
A relation between crossdiffusion and reactiondiffusion
Volume 5, Number 1, Pages: 147  158, 2011
Hideki Murakawa
Abstract
References
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Reactiondiffusion system approximations to a crossdiffusion system are investigated.
Iida and Ninomiya~[Recent Advances on Elliptic and Parabolic Issues, 145164 (2006)] proposed a semilinear reactiondiffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled crossdiffusion system provided that solutions of both the reactiondiffusion and the crossdiffusion systems are sufficiently smooth.
In this paper, the results are extended to a more general crossdiffusion problem involving strongly coupled systems.
It is shown that a solution of the problem can be approximated by that of a semilinear reactiondiffusion system without any assumptions on the solutions.
This indicates that the mechanism of crossdiffusion might be captured by
reactiondiffusion interaction.

7 
Experimental data for solid tumor cells: Proliferation curves and timechanges of heat shock proteins
Volume 5, Number 1, Pages: 235  244, 2011
Kazuhiko Yamamoto,
Kiyoshi Hosono,
Hiroko Nakayama,
Akio Ito
and Yuichi Yanagi
Abstract
References
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We consider a relation between proliferation of solid tumor cells and timechanges of the quantities of heat
shock proteins in them.
To do so, in the present paper we start to obtain some experimental data of the proliferation curves of solid tumor cells,
actually, A549 and HepG2, as well as the timechanges of proteins, especially HSP90 and HSP72, in them.
And we propose a mathematical model to recreate the experimental data of the proliferation curves and the timechanges
of the quantities of heat shock proteins, which is described by ODE systems.
Finally, we discuss a problem which exists between mitosis of solid tumor cells and timechanges of the quantities of
heat shock proteins, from the viewpoint of biotechnology.

8 
On a onedimensional shapememory alloy model in its fasttemperatureactivation limit
Volume 5, Number 1, Pages: 15  28, 2011
Toyohiko Aiki,
Martijn Anthonissen
and Adrian Muntean
Abstract
References
Full Text
Related Articles
We study a onedimensional model describing the motion of a shapememory alloy spring at a small characteristic time scale, called here fasttemperatureactivation limit. At this level, the standard Falk's model reduces to a nonlinear elliptic partial differential equation (PDE) with Newton boundary condition. We show existence and uniqueness of a bounded weak solution and approximate this numerically. Interestingly, in spite of the nonlinearity of the model, the approximate solution exhibits nearly a linear profile. Finally, we extend the reduced model to the simplest PDE system for shape memory alloys that can capture oscillations and then damp out these oscillations numerically. The numerical results for both limiting cases show excellent agreement. The graphs show that the valve opens in an instant, which is realistic behavior of the free boundary.

9 
The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics
Volume 3, Number 3, Pages: 409  427, 2010
Luis A. Caffarelli
and Alexis F. Vasseur
Abstract
Full Text
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This paper is dedicated to the application of the De GiorgiNashMoser
kind of techniques to regularity issues in fluid mechanics. In a first
section, we recall the original method introduced by De Giorgi to prove
$C^\alpha$regularity of solutions to elliptic problems with rough
coefficients. In a second part, we give the main ideas to apply those
techniques in the case of parabolic equations with fractional Laplacian.
This allows, in particular, to show the global regularity of the
Surface QuasiGeostrophic equation in the critical case. Finally, a last
section is dedicated to the application of this method to the 3D
NavierStokes equation.

10 
Modelling phase transitions via Young measures
Volume 5, Number 1, Pages: 29  48, 2011
Steffen Arnrich
Abstract
References
Full Text
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We consider the elastic theory of single crystals at constant temperature
where the free energy density depends on the local concentration of one or
more species of particles in such a way that for a given local concentration
vector certain lattice geometries (phases) are preferred. Furthermore we consider possible large deformations of the crystal lattice.
After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measurevalued solutions that relies on a new existence theorem for Young measures in infinite settings. This article is an overview of [2].

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