9,176 research outputs found
Multiphase modelling of vascular tumour growth in two spatial dimensions
In this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model. Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters are investigated
Cumulant expansion of the periodic Anderson model in infinite dimension
The diagrammatic cumulant expansion for the periodic Anderson model with
infinite Coulomb repulsion () is considered here for an hypercubic
lattice of infinite dimension (). The same type of simplifications
obtained by Metzner for the cumulant expansion of the Hubbard model in the
limit of , are shown to be also valid for the periodic Anderson
model.Comment: 13 pages, 7 figures.ps. To be published in J. Phys. A: Mathematical
and General (1997
Many-body approach to the nonlinear interaction of charged particles with an interacting free electron gas
We report various many-body theoretical approaches to the nonlinear decay
rate and energy loss of charged particles moving in an interacting free
electron gas. These include perturbative formulations of the scattering matrix,
the self-energy, and the induced electron density. Explicit expressions for
these quantities are obtained, with inclusion of exchange and correlation
effects.Comment: 11 pages, 5 figures. To appear in Journal of Physics
Fractional Aharonov-Bohm effect in mesoscopic rings
We study the effects of correlations on a one dimensional ring threaded by a
uniform magnetic flux. In order to describe the interaction between particles,
we work in the framework of the U Hubbard and - models. We focus
on the dilute limit. Our results suggest the posibility that the persistent
current has an anomalous periodicity , where is an integer in
the range ( is the number of particles in the ring
and is the flux quantum). We found that this result depends neither
on disorder nor on the detailed form of the interaction, while remains the on
site infinite repulsion.Comment: 14 pages (Revtex), 5 postscript figures. Send e-mail to:
[email protected]
Variational cluster approach to correlated electron systems in low dimensions
A self-energy-functional approach is applied to construct cluster
approximations for correlated lattice models. It turns out that the
cluster-perturbation theory (Senechal et al, PRL 84, 522 (2000)) and the
cellular dynamical mean-field theory (Kotliar et al, PRL 87, 186401 (2001)) are
limiting cases of a more general cluster method. Results for the
one-dimensional Hubbard model are discussed with regard to boundary conditions,
bath degrees of freedom and cluster size.Comment: 4 pages, final version with minor change
Slow-string limit and "antiferromagnetic" state in AdS/CFT
We discuss a slow-moving limit of a rigid circular equal-spin solution on R x
S^3. We suggest that the solution with the winding number equal to the total
spin approximates the quantum string state dual to the maximal-dimension
``antiferromagnetic'' state of the SU(2) spin chain on the gauge theory side.
An expansion of the string action near this solution leads to a weakly coupled
system of a sine-Gordon model and a free field. We show that a similar
effective Hamiltonian appears in a certain continuum limit from the half-filled
Hubbard model that was recently suggested to describe the all-order dilatation
operator of the dual gauge theory in the SU(2) sector. We also discuss some
other slow-string solutions with one spin component in AdS_5 and one in S^5.Comment: 32 pages, Latex v2: one footnote and references adde
Strong-Coupling Expansion for the Hubbard Model
A strong-coupling expansion for models of correlated electrons in any
dimension is presented. The method is applied to the Hubbard model in
dimensions and compared with numerical results in . Third order expansion
of the Green function suffices to exhibit both the Mott metal-insulator
transition and a low-temperature regime where antiferromagnetic correlations
are strong. It is predicted that some of the weak photoemission signals
observed in one-dimensional systems such as should become stronger as
temperature increases away from the spin-charge separated state.Comment: 4 pages, RevTex, 3 epsf figures include
Cluster coherent potential approximation for electronic structure of disordered alloys
We extend the single-site coherent potential approximation (CPA) to include
the effects of non-local disorder correlations (alloy short-range order) on the
electronic structure of random alloy systems. This is achieved by mapping the
original Anderson disorder problem to that of a selfconsistently embedded
cluster. This cluster problem is then solved using the equations of motion
technique. The CPA is recovered for cluster size , and the disorder
averaged density-of-states (DOS) is always positive definite. Various new
features, compared to those observed in CPA, and related to repeated scattering
on pairs of sites, reflecting the effect of SRO are clearly visible in the DOS.
It is explicitly shown that the cluster-CPA method always yields
positive-definite DOS. Anderson localization effects have been investigated
within this approach. In general, we find that Anderson localization sets in
before band splitting occurs, and that increasing partial order drives a
continuous transition from an Anderson insulator to an incoherent metal.Comment: 7 pages, 6 figures. submitted to PR
A Velocity-based Moving Mesh Virtual Element Method
We present a velocity-based moving mesh virtual element method for the
numerical solution of PDEs involving moving boundaries. The virtual element
method is used for computing both the mesh velocity and a conservative
Arbitrary Lagrangian-Eulerian solution transfer on general polygonal meshes.
The approach extends the linear finite element method to polygonal mesh
structures, achieving the same degree of accuracy. In the context of moving
meshes, a major advantage of the virtual element approach is the ease with
which nodes can be inserted on mesh edges. Demonstrations of node insertion
techniques are presented to show that moving polygonal meshes can be simply
adapted for situations where a boundary encounters a solid object or another
moving boundary, without reduction in degree of accuracy
Climate or rural development policy?
Being heavily energy dependent, it is not much of a surprise that Europe pays special attention to reducing the use of fossil fuels. Each one of the ten new member states is characterized by relatively low per capita energy consumption and relatively low energy efficiency, and the share of renewables in their energy mix tends to be low, too. The paper examines the problem when policy measures create a decrease in environmental capital instead of an increase. In this case it hardly seems justified to talk about environmental protection. The authors describe a case of a Hungarian rapeseed oil mill which would not be of too much interest on its own but given that almost all similar plants went bankrupt, there are some important lessons to learn from its survival. The enterprise the authors examined aimed at establishing a micro-regional network. They completed a brown-field development to establish a small plant on the premises of a former large agricultural cooperative. By partnering with the former employees and suppliers of the sometime cooperative, they enjoyed some benefits which all the other green-field businesses focusing on fuel production could not. The project improved food security, energy security and population retention as well
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