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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.
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TOP 10 Most Read Articles in DCDSS, February 2017
1 
A framework for the development of implicit solvers for incompressible flow problems
Volume 5, Number 6, Pages: 1195  1221, 2012
David J. Silvester,
Alex Bespalov
and Catherine E. Powell
Abstract
References
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This survey paper reviews some recent developments in the design of
robust solution methods for the NavierStokes equations
modelling incompressible fluid flow. There are two
building blocks in our solution strategy. First, an implicit time integrator that uses
a stabilized trapezoid rule with an explicit
AdamsBashforth method for error control, and second, a
robust Krylov subspace solver for the spatially discretized system.
Numerical experiments are presented that illustrate the effectiveness
of our generic approach. It is further shown that the basic solution strategy can be
readily extended to more complicated models, including
unsteady flow problems with coupled physics and steady flow problems that
are nondeterministic in the sense that they have uncertain input data.

2 
Annihilation of two interfaces in a hybrid system
Volume 8, Number 5, Pages: 857  869, 2015
ShinIchiro Ei,
Kei Nishi,
Yasumasa Nishiura
and Takashi Teramoto
Abstract
References
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We consider the mixed ODEPDE system called a hybrid system,
in which the two interfaces interact with each other through a
continuous medium and their equations of motion are derived
in a weak interaction framework.
We study the bifurcation property of the resulting hybrid system
and construct an unstable standing pulse solution, which plays
the role of a separator
for dynamic transition from standing breather to annihilation behavior
between two interfaces.

3 
Dynamics of two phytoplankton species
competing for light and nutrient with internal storage
Volume 7, Number 6, Pages: 1259  1285, 2014
SzeBi Hsu
and ChiuJu Lin
Abstract
References
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We analyze a competition model of two phytoplankton species for a
single nutrient with internal storage and light in a well mixed
aquatic environment. We apply the theory of monotone dynamical
system to determine the outcomes of competition: extinction of two
species, competitive exclusion, stable coexistence and bistability
of two species. We also present the graphical presentation to
classify the competition outcomes and to compare outcome of models with
and without internal storage.

4 
Phasefield models for transition phenomena in materials with hysteresis
Volume 8, Number 4, Pages: 693  722, 2014
Claudio Giorgi
Abstract
References
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Nonisothermal phasefield models of transition phenomena in materials with hysteresis are considered within the framework of the GinzburgLandau theory. Our attempt is to capture the relation between phasetransition and hysteresis (either mechanical or magnetic). All models are required to be compatible with thermodynamics and to fit well the shape of the major hysteresis loop. Focusing on uniform cyclic processes, numerical simulations at different temperatures are performed.

5 
Rateindependent memory in magnetoelastic materials
Volume 8, Number 4, Pages: 649  691, 2014
Daniele Davino
and Ciro Visone
Abstract
References
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These notes origin from a group of lectures given at the Spring School on ``Rateindependent evolutions and hysteresis modelling'' (Hystry 2013), held at Politecnico di Milano and at Università degli Studi di Milano, from May 27 until May 31, 2013. They are addressed to Graduate students in mathematics and applied science, interested in modeling rateindependent effects in smart systems. Therefore, they aim to provide the basic issues concerning modeling of multifunctional materials showing memory phenomena, with emphasis to magnetostrictives, in view of their application to the design of smart devices. Such tutorial summarizes several years activity on these issues that involved the cooperation with several colleagues, among all Dr. P. Krejčí, with whom the authors are indebted.

6 
Discussion about traffic junction modelling: Conservation laws VS HamiltonJacobi equations
Volume 7, Number 3, Pages: 411  433, 2014
Guillaume Costeseque
and JeanPatrick Lebacque
Abstract
References
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In this paper, we consider a numerical scheme to solve first order HamiltonJacobi (HJ) equations posed on a junction. The main mathematical properties of the scheme are first recalled and then we give a traffic flow interpretation of the key elements. The scheme formulation is also adapted to compute the vehicles densities on a junction. The equivalent scheme for densities recovers the wellknown Godunov scheme outside the junction point. We give two numerical illustrations for a merge and a diverge which are the two main types of traffic junctions. Some extensions to the junction model are finally discussed.

7 
Some uniqueness result of the Stokes flow in a half space in a space of bounded functions
Volume 7, Number 5, Pages: 887  900, 2014
Ken Abe
Abstract
References
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This paper presents a uniqueness theorem for the Stokes equations in a half space in a space of bounded functions. The Stokes equations is well understood for decaying velocity as $x\to\infty$, but less known for nondecaying velocity even for a half space. This paper presents a uniqueness theorem on $L^{\infty}(\mathbb{R}_+^n)$ for unbounded velocity as $t\downarrow 0$. Under suitable supbounds both for velocity and pressure gradient, a uniqueness theorem for nondecaying velocity is proved.

8 
Numerical simulation of flow in fluidized beds
Volume 8, Number 5, Pages: 833  846, 2015
Petr Bauer,
Michal Beneš,
Radek Fučík,
Hung Hoang Dieu,
Vladimír Klement,
Radek Máca,
Jan Mach,
Tomáš Oberhuber,
Pavel Strachota,
Vítězslav Žabka
and Vladimír Havlena
Abstract
References
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The article provides a brief overview of a onedimensional model of twophase flow in the geometry of a circulating fluidized bed combustor exhibiting vertical variability of crosssection.
The model is based on numerical solution of conservation laws for mass, momentum and energy
of gas and solid components of the fluidizedbed system by means of the finitevolume method in space and of a multistep higherorder solver in time.
The presented computational results reproduce characteristic behavior of fluidized beds in the given geometry.

9 
Hopf fibration and singularly perturbed elliptic equations
Volume 7, Number 4, Pages: 823  838, 2014
Bernhard Ruf
and P. N. Srikanth
Abstract
References
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In this article we show how the Hopf fibration can be used to generate special solutions of singularly perturbed elliptic equations on annuli. Indeed, by the Hopf fibration the equation can be reduced to a lower dimensional problem, to which known results on single (or multiple point) concentration can be applied. Reversing the reduction process, one obtains solutions concentrating on circles and spheres, which are given as the fibres of the Hopf fibration.

10 
A new "flexible" 3D macroscopic model for shape memory alloys
Volume 6, Number 2, Pages: 277  291, 2012
Ferdinando Auricchio
and Elena Bonetti
Abstract
References
Full Text
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In this paper we introduce a 3D phenomenological model for shape memory behavior, accounting for: martensite
reorientation, asymmetric response of the material to tension/compression, different kinetics between forward and reverse phase transformation.
We combine two modeling approaches using scalar and tensorial internal variables. Indeed,
we use volume proportions of different configurations of the crystal lattice
(austenite and two variants of martensite) as scalar internal variables and
the preferred direction of stressinduced martensite as tensorial internal variable.
Then, we derive evolution equations by a generalization of the principle of virtual powers, including
microforces and micromovements responsible for phase transformations.
In addition, we prescribe an evolution law for phase proportions ensuring different
kinetics
during forward and reverse transformation of the oriented martensite.

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