3,400 research outputs found
Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation
We calculate exactly both the microcanonical and canonical thermodynamic
functions (TDFs) for a one-dimensional model system with piecewise constant
Lennard-Jones type pair interactions. In the case of an isolated -particle
system, the microcanonical TDFs exhibit (N-1) singular (non-analytic)
microscopic phase transitions of the formal order N/2, separating N
energetically different evaporation (dissociation) states. In a suitably
designed evaporation experiment, these types of phase transitions should
manifest themselves in the form of pressure and temperature oscillations,
indicating cooling by evaporation. In the presence of a heat bath (thermostat),
such oscillations are absent, but the canonical heat capacity shows a
characteristic peak, indicating the temperature-induced dissociation of the
one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical
partition may be used to identify different degrees of dissociation in the
canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text,
references adde
Drying and cracking mechanisms in a starch slurry
Starch-water slurries are commonly used to study fracture dynamics. Drying
starch-cakes benefit from being simple, economical, and reproducible systems,
and have been used to model desiccation fracture in soils, thin film fracture
in paint, and columnar joints in lava. In this paper, the physical properties
of starch-water mixtures are studied, and used to interpret and develop a
multiphase transport model of drying. Starch-cakes are observed to have a
nonlinear elastic modulus, and a desiccation strain that is comparable to that
generated by their maximum achievable capillary pressure. It is shown that a
large material porosity is divided between pore spaces between starch grains,
and pores within starch grains. This division of pore space leads to two
distinct drying regimes, controlled by liquid and vapor transport of water,
respectively. The relatively unique ability for drying starch to generate
columnar fracture patterns is shown to be linked to the unusually strong
separation of these two transport mechanisms.Comment: 9 pages, 8 figures [revised in response to reviewer comments
Drying and cracking mechanisms in a starch slurry
Starch-water slurries are commonly used to study fracture dynamics. Drying
starch-cakes benefit from being simple, economical, and reproducible systems,
and have been used to model desiccation fracture in soils, thin film fracture
in paint, and columnar joints in lava. In this paper, the physical properties
of starch-water mixtures are studied, and used to interpret and develop a
multiphase transport model of drying. Starch-cakes are observed to have a
nonlinear elastic modulus, and a desiccation strain that is comparable to that
generated by their maximum achievable capillary pressure. It is shown that a
large material porosity is divided between pore spaces between starch grains,
and pores within starch grains. This division of pore space leads to two
distinct drying regimes, controlled by liquid and vapor transport of water,
respectively. The relatively unique ability for drying starch to generate
columnar fracture patterns is shown to be linked to the unusually strong
separation of these two transport mechanisms.Comment: 9 pages, 8 figures [revised in response to reviewer comments
Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery
The coefficient of normal restitution of colliding viscoelastic spheres is
computed as a function of the material properties and the impact velocity. From
simple arguments it becomes clear that in a collision of purely repulsively
interacting particles, the particles loose contact slightly before the distance
of the centers of the spheres reaches the sum of the radii, that is, the
particles recover their shape only after they lose contact with their collision
partner. This effect was neglected in earlier calculations which leads
erroneously to attractive forces and, thus, to an underestimation of the
coefficient of restitution. As a result we find a novel dependence of the
coefficient of restitution on the impact rate.Comment: 11 pages, 2 figure
Minimal Work Principle and its Limits for Classical Systems
The minimal work principle asserts that work done on a thermally isolated
equilibrium system, is minimal for the slowest (adiabatic) realization of a
given process. This principle, one of the formulations of the second law, is
operationally well-defined for any finite (few particle) Hamiltonian system.
Within classical Hamiltonian mechanics, we show that the principle is valid for
a system of which the observable of work is an ergodic function. For
non-ergodic systems the principle may or may not hold, depending on additional
conditions. Examples displaying the limits of the principle are presented and
their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte
On the work distribution for the adiabatic compression of a dilute classical gas
We consider the adiabatic and quasi-static compression of a dilute classical
gas, confined in a piston and initially equilibrated with a heat bath. We find
that the work performed during this process is described statistically by a
gamma distribution. We use this result to show that the model satisfies the
non-equilibrium work and fluctuation theorems, but not the
flucutation-dissipation relation. We discuss the rare but dominant realizations
that contribute most to the exponential average of the work, and relate our
results to potentially universal work distributions.Comment: 4 page
Analysis of ensemble learning using simple perceptrons based on online learning theory
Ensemble learning of nonlinear perceptrons, which determine their outputs
by sign functions, is discussed within the framework of online learning and
statistical mechanics. One purpose of statistical learning theory is to
theoretically obtain the generalization error. This paper shows that ensemble
generalization error can be calculated by using two order parameters, that is,
the similarity between a teacher and a student, and the similarity among
students. The differential equations that describe the dynamical behaviors of
these order parameters are derived in the case of general learning rules. The
concrete forms of these differential equations are derived analytically in the
cases of three well-known rules: Hebbian learning, perceptron learning and
AdaTron learning. Ensemble generalization errors of these three rules are
calculated by using the results determined by solving their differential
equations. As a result, these three rules show different characteristics in
their affinity for ensemble learning, that is ``maintaining variety among
students." Results show that AdaTron learning is superior to the other two
rules with respect to that affinity.Comment: 30 pages, 17 figure
On the Exponentials of Some Structured Matrices
In this note explicit algorithms for calculating the exponentials of
important structured 4 x 4 matrices are provided. These lead to closed form
formulae for these exponentials. The techniques rely on one particular Clifford
Algebra isomorphism and basic Lie theory. When used in conjunction with
structure preserving similarities, such as Givens rotations, these techniques
extend to dimensions bigger than four.Comment: 19 page
- …