2,200 research outputs found
Quasichemical Models of Multicomponent Nonlinear Diffusion
Diffusion preserves the positivity of concentrations, therefore,
multicomponent diffusion should be nonlinear if there exist non-diagonal terms.
The vast variety of nonlinear multicomponent diffusion equations should be
ordered and special tools are needed to provide the systematic construction of
the nonlinear diffusion equations for multicomponent mixtures with significant
interaction between components. We develop an approach to nonlinear
multicomponent diffusion based on the idea of the reaction mechanism borrowed
from chemical kinetics.
Chemical kinetics gave rise to very seminal tools for the modeling of
processes. This is the stoichiometric algebra supplemented by the simple
kinetic law. The results of this invention are now applied in many areas of
science, from particle physics to sociology. In our work we extend the area of
applications onto nonlinear multicomponent diffusion.
We demonstrate, how the mechanism based approach to multicomponent diffusion
can be included into the general thermodynamic framework, and prove the
corresponding dissipation inequalities. To satisfy thermodynamic restrictions,
the kinetic law of an elementary process cannot have an arbitrary form. For the
general kinetic law (the generalized Mass Action Law), additional conditions
are proved. The cell--jump formalism gives an intuitively clear representation
of the elementary transport processes and, at the same time, produces kinetic
finite elements, a tool for numerical simulation.Comment: 81 pages, Bibliography 118 references, a review paper (v4: the final
published version
Chemical and hydrodynamic alignment of an enzyme
Motivated by the implications of the complex and dynamic modular geometry of
an enzyme on its motion, we investigate the effect of combining long-range
internal and external hydrodynamic interactions due to thermal fluctuations
with short-range surface interactions. An asymmetric dumbbell consisting of two
unequal subunits, in a nonuniform suspension of a solute with which it
interacts via hydrodynamic interactions as well as non-contact surface
interactions, is shown to have two alignment mechanisms due to the two types of
interactions. In addition to alignment, the chemical gradient results in a
drift velocity that is modified by hydrodynamic interactions between the
constituents of the enzyme.Comment: 7+4 pages, 3 figure
A Predictive Model for Convective Flows Induced by Surface Reactivity Contrast
Concentration gradients in a fluid along a reactive surface due to contrast
in surface reactivity generate convective flows. These flows result from
contributions by electro and diffusio osmotic phenomena. In this study we have
analyzed reactive patterns that release and consume protons, analogous to
bimetallic catalytic conversion of peroxide. Here, we present a simple
analytical model that accurately predicts the induced potentials and consequent
velocities in such systems over a wide range of input parameters. Our model is
tested against direct numerical solutions to the coupled Poisson,
Nernst-Planck, and Navier-Stokes equations. Our analysis can be used to predict
enhancement of mass transport and the resulting impact on overall catalytic
conversion, and is also applicable to predicting the speed of catalytic
nanomotors
Self-propulsion of a catalytically active particle near a planar wall: from reflection to sliding and hovering
Micron-sized particles moving through solution in response to self-generated
chemical gradients serve as model systems for studying active matter. Their
far-reaching potential applications will require the particles to sense and
respond to their local environment in a robust manner. The self-generated
hydrodynamic and chemical fields, which induce particle motion, probe and are
modified by that very environment, including confining boundaries. Focusing on
a catalytically active Janus particle as a paradigmatic example, we predict
that near a hard planar wall such a particle exhibits several scenarios of
motion: reflection from the wall, motion at a steady-state orientation and
height above the wall, or motionless, steady "hovering." Concerning the steady
states, the height and the orientation are determined both by the proportion of
catalyst coverage and the interactions of the solutes with the different
"faces" of the particle. Accordingly, we propose that a desired behavior can be
selected by tuning these parameters via a judicious design of the particle
surface chemistry
Derandomization with Minimal Memory Footprint
Existing proofs that deduce BPL = ? from circuit lower bounds convert randomized algorithms into deterministic algorithms with large constant overhead in space. We study space-bounded derandomization with minimal footprint, and ask what is the minimal possible space overhead for derandomization. We show that BPSPACE[S] ? DSPACE[c ? S] for c ? 2, assuming space-efficient cryptographic PRGs, and, either: (1) lower bounds against bounded-space algorithms with advice, or: (2) lower bounds against certain uniform compression algorithms. Under additional assumptions regarding the power of catalytic computation, in a new setting of parameters that was not studied before, we are even able to get c ? 1.
Our results are constructive: Given a candidate hard function (and a candidate cryptographic PRG) we show how to transform the randomized algorithm into an efficient deterministic one. This follows from new PRGs and targeted PRGs for space-bounded algorithms, which we combine with novel space-efficient evaluation methods. A central ingredient in all our constructions is hardness amplification reductions in logspace-uniform TC?, that were not known before
Experimental evaluation of high-thrust, throttleable, monopropellant hydrazine reactors
Throttleable monopropellant hydrazine catalytic reactors of a size applicable to a planetary landing vehicle were designed, fabricated, and tested. An experimental evaluation of two 2670-N reactor designs was conducted. The steady state and dynamic characteristics of the thruster/valve combinations were determined. The results of the testing, including the engine characteristic velocity, smoothness of combustion, insensitivity to heat sterilization, and response during various simulated duty cycles are presented and discussed. No problems of a fundamental nature were encountered as a result of rapid dynamic throttling of these large hydrazine reactors
Scaled free energies, power-law potentials, strain pseudospins and quasi-universality for first-order structural transitions
We consider ferroelastic first-order phase transitions with
order-parameter strains entering Landau free energies as invariant polynomials,
that have structural-variant Landau minima. The total free energy
includes (seemingly innocuous) harmonic terms, in the {\it
non}-order-parameter strains. Four 3D transitions are considered,
tetragonal/orthorhombic, cubic/tetragonal, cubic/trigonal and
cubic/orthorhombic unit-cell distortions, with respectively, and 2; and and 6. Five 2D transitions are also considered, as
simpler examples. Following Barsch and Krumhansl, we scale the free energy to
absorb most material-dependent elastic coefficients into an overall prefactor,
by scaling in an overall elastic energy density; a dimensionless temperature
variable; and the spontaneous-strain magnitude at transition .
To leading order in the scaled Landau minima become
material-independent, in a kind of 'quasi-universality'. The scaled minima in
-dimensional order-parameter space, fall at the centre and at the
corners, of a transition-specific polyhedron inscribed in a sphere, whose
radius is unity at transition. The `polyhedra' for the four 3D transitions are
respectively, a line, a triangle, a tetrahedron, and a hexagon. We minimize the
terms harmonic in the non-order-parameter strains, by substituting
solutions of the 'no dislocation' St Venant compatibility constraints, and
explicitly obtain powerlaw anisotropic, order-parameter interactions, for all
transitions. In a reduced discrete-variable description, the competing minima
of the Landau free energies induce unit-magnitude pseudospin vectors, with values, pointing to the polyhedra corners and the (zero-value) center.Comment: submitted to PR
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