Working seminar — Stochastic techniques in
microbiology
Thursdays at 2:00 pm
Lind Hall Room 409
Organizer: Peter R. Kramer
(Department of Mathematical Sciences,
Rensselaer Polytechnic Institute)
upcoming
March 27, 2008, 2:00 pm, Lind Hall
409 Simple stochastic models for
water dynamics near a solute
Abstract:
I will present some work (which I originally intended to
include in last Wednesday's
seminar) which concerns the mathematical issues involved in
constructing a simple
stochastic model for water near a solute for the eventual goal
of developing a means
for accelerating molecular dynamics simulations through a
simplified statistical description
of the water molecules. So far only the most basic stochastic
techniques have been used
— the main issue has more been the distinction between
mathematical and engineeringbased
views of the problem, a distinction upon which I will
elaborate. In particular, the
mathematics will be much less technical than for the stochastic
immersed boundary method,
and I will strive to explain the approach from an elementary
standpoint. Indeed we use a very simple toy problem to help us
figure out what's going on in molecular dynamics. As this
general research program is at a rather early stage, I would be
particularly interested
in feedback from other mathematicians and scientists as we
move forward.
April 3, 2008, 2:00 pm, Lind Hall
409 Informal working seminar on stochastic techniques in
microbiology
Abstract:
Based on the response I received, I propose to do the
following:
I'll begin by briefly advertising the various projects in which
I am
actively interested since
several new people have arrived since I did this before.
For most of the hour,
I will again discuss the stochastic immersed boundary method
for simulating
microbiological systems, but the emphasis
will not be so much on the method itself, but on more general
issues raised in the
design and analysis of the method. Possible topics for
discussion include:
1) How do you add noise in a "correct" way to a physical
system?
2) How can you check that a stochastic numerical method is
simulating the
correct statisical physics?
3) How can you use the method of stochastic mode reduction to
analyze the
effective coarsegrained behavior of a complex stochastic
systems when
a separation of time scales can be exploited. If desired, I
can illustrate the
stochastic mode reduction approach on the simple equation I
described
last week (showing that, on longtime scales, thermally driven
Newton's law
for particle motion (second order stochastic differential
equation) can
be approximated by a first order driftdiffusion model).
I'll direct the discussion as best I can toward the interests
of those who choose to
attend, and pitch the technical level accordingly.
May 1, 2008, 2:00 pm, Lind Hall
409 Prescribing thermal forcing for physical systems
Abstract:
I will describe the principles, particularly the
fluctuationdissipation theorem,
involved in adding the appropriate stochastic driving terms to
represent the effects of
finite temperature on a given physical system. The concepts
will be
described both for an elementary example as well as for the
more complicated immersed boundary method simulation scheme
for flexible structures coupled to an ambient fluid.
May 15, 2008, 2:00 pm, Lind Hall
409 Theoretical framework for microscopic osmotic
phenomena
Abstract:
My main intention in this seminar is to think through, in
simple physical terms,
how osmotic pressure (for a semipermeable membrane confining
a solute) manifests itself microscopically. That is, I will
approach the question
simply in terms of mechanical forces between the solute and
membrane, and
the pressure in the fluid. Somehow I am a little concerned
that I may be
naive about some aspects, and I would appreciate the current
IMA visitors
pointing out to me where my reasoning may be inadequate! The
reason
for this investigation was the recognition that the classical
statistical mechanical
formula for osmotic pressure (van't Hoff's law) requires
corrections when
some of the idealized assumptions (infinitesmal particles,
hardwall membrane)
break down. In the physical modeling and numerical simulation
of submicron
scale systems, these deviations from the idealized limits
appear to be relevant.
I'll explain the change to the classical formulas in terms of
simple examples;
in particular the osmotic pressure registered in the fluid must
be distinguished from
that exerted on the membrane.
This discussion will primarily involve elementary
statistical mechanics and fluid mechanics. Probability arises
only in the prescription of
the random configurations of the solute particles subject to
the confining potential of
the membrane.
June 5, 2008, 2:00 pm, Lind Hall
409 Stochastic mode reduction with metastability in
biomolecular modeling
Abstract: One approach to
accelerating biomolecular simulations is to simulate explicitly
only certain slow degrees of freedom of interest, incorporating
the effects of the remaining "fast" variables through effective
stochastic models. We illustrate a systematic multiscale
stochastic mode reduction procedure on a simple model problem
with metastability — a high potential energy barrier separating
different conformational states. Metastability is a prevalent
feature in biomolecular systems. We show in particular how the
metastability can lead to various effective stochastic
equations for the slow degrees of freedom depending on the
relations between the physical parameters and properties of the
potential energy landscape. This work is in collaboration with
Jessika Walter at Ecole Polytechnique Federale de Lausanne and
Christof Schuette at the Free University of Berlin. Time
permitting, I will also discuss some general observations
concerning the application of multiple scale asymptotics to
problems with three (or more) active time scales (joint work
with Adnan Khan (Lahore) and Robert E. Lee DeVille (University
of Illinois)).
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