5,084 research outputs found
Effective interactions and phase behaviour for a model clay suspension in an electrolyte
Since the early observation of nematic phases of disc-like clay colloids by
Langmuir in 1938, the phase behaviour of such systems has resisted theoretical
understanding. The main reason is that there is no satisfactory generalization
for charged discs of the isotropic DLVO potential describing the effective
interactions between a pair of spherical colloids in an electrolyte. In this
contribution, we show how to construct such a pair potential, incorporating
approximately both the non-linear effects of counter-ion condensation (charge
renormalization) and the anisotropy of the charged platelets. The consequences
on the phase behaviour of Laponite dispersions (thin discs of 30 nm diameter
and 1 nm thickness) are discussed, and investigation into the mesostructure via
Monte Carlo simulations are presented.Comment: LaTeX, 12 pages, 11 figure
Hypocrisy At The Lectern Do Our Personal Lifestyle Choices Reflect Our Spoken Commitment To Global Sustainabilty?
Do our actions model a genuine commitment to global sustainability? Or do they belie that spoken commitment? These questions are addressed in this article, drawing on bodies of substantive research tying personal behavioral choices to global warming, fresh water scarcity, energy resource management, the absorptive capacity of the earth to sustain life, and a viable sharing of the earth’s resources to assure a basic level of social justice. A compelling case is made that our personal lifestyles are not incongruence with our avowed concerns for an environmentally sustainable earth and a just sharing of its bounties. The article treats environmental sustainability and social justice as co-imperatives, thereby offering a future scenario that demands lifestyle adjustments and shared sacrifices
Stochastic integration in UMD Banach spaces
In this paper we construct a theory of stochastic integration of processes
with values in , where is a separable Hilbert space and
is a UMD Banach space (i.e., a space in which martingale differences are
unconditional). The integrator is an -cylindrical Brownian motion. Our
approach is based on a two-sided -decoupling inequality for UMD spaces due
to Garling, which is combined with the theory of stochastic integration of
-valued functions introduced recently by two of the authors.
We obtain various characterizations of the stochastic integral and prove
versions of the It\^{o} isometry, the Burkholder--Davis--Gundy inequalities,
and the representation theorem for Brownian martingales.Comment: Published at http://dx.doi.org/10.1214/009117906000001006 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stochastic evolution equations in UMD Banach spaces
We discuss existence, uniqueness, and space-time H\"older regularity for
solutions of the parabolic stochastic evolution equation dU(t) = (AU(t) +
F(t,U(t))) dt + B(t,U(t)) dW_H(t), t\in [0,\Tend], U(0) = u_0, where
generates an analytic -semigroup on a UMD Banach space and is a
cylindrical Brownian motion with values in a Hilbert space . We prove that
if the mappings and satisfy suitable Lipschitz conditions and is
\F_0-measurable and bounded, then this problem has a unique mild solution,
which has trajectories in C^\l([0,T];\D((-A)^\theta) provided
and satisfy \l+\theta<\frac12. Various extensions of this
result are given and the results are applied to parabolic stochastic partial
differential equations.Comment: Accepted for publication in Journal of Functional Analysi
Mechano-transduction: from molecules to tissues.
External forces play complex roles in cell organization, fate, and homeostasis. Changes in these forces, or how cells respond to them, can result in abnormal embryonic development and diseases in adults. How cells sense and respond to these mechanical stimuli requires an understanding of the biophysical principles that underlie changes in protein conformation and result in alterations in the organization and function of cells and tissues. Here, we discuss mechano-transduction as it applies to protein conformation, cellular organization, and multi-cell (tissue) function
Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation
Using the theory of stochastic integration for processes with values in a UMD
Banach space developed recently by the authors, an Ito formula is proved which
is applied to prove the existence of strong solutions for a class of stochastic
evolution equations in UMD Banach spaces. The abstract results are applied to
prove regularity in space and time of the solutions of the Zakai equation.Comment: Accepted for publication in Journal of Differential Equation
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