4,382 research outputs found
A continuum treatment of growth in biological tissue: The coupling of mass transport and mechanics
Growth (and resorption) of biological tissue is formulated in the continuum
setting. The treatment is macroscopic, rather than cellular or sub-cellular.
Certain assumptions that are central to classical continuum mechanics are
revisited, the theory is reformulated, and consequences for balance laws and
constitutive relations are deduced. The treatment incorporates multiple
species. Sources and fluxes of mass, and terms for momentum and energy transfer
between species are introduced to enhance the classical balance laws. The
transported species include: (\romannumeral 1) a fluid phase, and
(\romannumeral 2) the precursors and byproducts of the reactions that create
and break down tissue. A notable feature is that the full extent of coupling
between mass transport and mechanics emerges from the thermodynamics.
Contributions to fluxes from the concentration gradient, chemical potential
gradient, stress gradient, body force and inertia have not emerged in a unified
fashion from previous formulations of the problem. The present work
demonstrates these effects via a physically-consistent treatment. The presence
of multiple, interacting species requires that the formulation be consistent
with mixture theory. This requirement has far-reaching consequences. A
preliminary numerical example is included to demonstrate some aspects of the
coupled formulation.Comment: 29 pages, 11 figures, accepted for publication in Journal of the
Mechanics and Physics of Solids. See journal for final versio
Biological remodelling: Stationary energy, configurational change, internal variables and dissipation
Remodelling is defined as an evolution of microstructure or variations in the
configuration of the underlying manifold. The manner in which a biological
tissue and its subsystems remodel their structure is treated in a continuum
mechanical setting. While some examples of remodelling are conveniently
modelled as evolution of the reference configuration (Case I), others are more
suited to an internal variable description (Case II). In this paper we explore
the applicability of stationary energy states to remodelled systems. A
variational treatment is introduced by assuming that stationary energy states
are attained by changes in microstructure via one of the two mechanisms--Cases
I and II. An example is presented to illustrate each case. The example
illustrating Case II is further studied in the context of the thermodynamic
dissipation inequality.Comment: 24 pages, 4 figures. Replaced version has corrections to typos in
equations, and the corresponding correct plot of the solution--all in Section
Heisenberg model in a random field: phase diagram and tricritical behavior
By using the differential operator technique and the effective field theory
scheme we study the tricritical behavior of Heisenberg classical model of
spin-1/2 in a random field. The phase diagram in the T-h plane on a square and
simple cubic lattice for a cluster with two spins is obtained when the random
field is bimodal distributed.Comment: 10 pages, 1 figur
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