12,196 research outputs found
The Schr\"odinger Equation in the Mean-Field and Semiclassical Regime
In this paper, we establish (1) the classical limit of the Hartree equation
leading to the Vlasov equation, (2) the classical limit of the -body linear
Schr\"{o}dinger equation uniformly in N leading to the N-body Liouville
equation of classical mechanics and (3) the simultaneous mean-field and
classical limit of the N-body linear Schr\"{o}dinger equation leading to the
Vlasov equation. In all these limits, we assume that the gradient of the
interaction potential is Lipschitz continuous. All our results are formulated
as estimates involving a quantum analogue of the Monge-Kantorovich distance of
exponent 2 adapted to the classical limit, reminiscent of, but different from
the one defined in [F. Golse, C. Mouhot, T. Paul, Commun. Math. Phys. 343
(2016), 165-205]. As a by-product, we also provide bounds on the quadratic
Monge-Kantorovich distances between the classical densities and the Husimi
functions of the quantum density matrices.Comment: 33 page
The case for absolute ligand discrimination : modeling information processing and decision by immune T cells
Some cells have to take decision based on the quality of surroundings
ligands, almost irrespective of their quantity, a problem we name "absolute
discrimination". An example of absolute discrimination is recognition of
not-self by immune T Cells. We show how the problem of absolute discrimination
can be solved by a process called "adaptive sorting". We review several
implementations of adaptive sorting, as well as its generic properties such as
antagonism. We show how kinetic proofreading with negative feedback implements
an approximate version of adaptive sorting in the immune context. Finally, we
revisit the decision problem at the cell population level, showing how
phenotypic variability and feedbacks between population and single cells are
crucial for proper decision
Quantitative games with interval objectives
Traditionally quantitative games such as mean-payoff games and discount sum
games have two players -- one trying to maximize the payoff, the other trying
to minimize it. The associated decision problem, "Can Eve (the maximizer)
achieve, for example, a positive payoff?" can be thought of as one player
trying to attain a payoff in the interval . In this paper we
consider the more general problem of determining if a player can attain a
payoff in a finite union of arbitrary intervals for various payoff functions
(liminf, mean-payoff, discount sum, total sum). In particular this includes the
interesting exact-value problem, "Can Eve achieve a payoff of exactly (e.g.)
0?"Comment: Full version of CONCUR submissio
Laser-induced rotation of a levitated sample in vacuum
A method of systematically controlling the rotational state of a sample levitated in a high vacuum using the photon pressure is described. A zirconium sphere was levitated in the high-temperature electrostatic levitator and it was rotated by irradiating it with a narrow beam of a high-power laser on a spot off the center of mass. While the laser beam heated the sample, it also rotated the sample with a torque that was proportional both to the laser power and the length of the torque arm. A simple theoretical basis was given and its validity was demonstrated using a solid zirconium sphere at ~2000 K. This method will be useful to systematically control the rotational state of a levitated sample for the containerless materials processing at high temperature
Dry microfoams: Formation and flow in a confined channel
We present an experimental investigation of the agglomeration of microbubbles
into a 2D microfoam and its flow in a rectangular microchannel. Using a
flow-focusing method, we produce the foam in situ on a microfluidic chip for a
large range of liquid fractions, down to a few percent in liquid. We can
monitor the transition from separated bubbles to the desired microfoam, in
which bubbles are closely packed and separated by thin films. We find that
bubble formation frequency is limited by the liquid flow rate, whatever the gas
pressure. The formation frequency creates a modulation of the foam flow,
rapidly damped along the channel. The average foam flow rate depends
non-linearly on the applied gas pressure, displaying a threshold pressure due
to capillarity. Strong discontinuities in the flow rate appear when the number
of bubbles in the channel width changes, reflecting the discrete nature of the
foam topology. We also produce an ultra flat foam, reducing the channel height
from 250 m to 8 m, resulting in a height to diameter ration of 0.02;
we notice a marked change in bubble shape during the flow.Comment: 7 pages; 7 figures; 1 tex file+ 22 eps-file
Reverse Mathematics and Algebraic Field Extensions
This paper analyzes theorems about algebraic field extensions using the
techniques of reverse mathematics. In section 2, we show that
is equivalent to the ability to extend -automorphisms of field extensions to
automorphisms of , the algebraic closure of . Section 3 explores
finitary conditions for embeddability. Normal and Galois extensions are
discussed in section 4, and the Galois correspondence theorems for infinite
field extensions are treated in section 5.Comment: 25 page
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