3,832 research outputs found
Diffusion anomaly and dynamic transitions in the Bell-Lavis water model
In this paper we investigate the dynamic properties of the minimal Bell-Lavis
(BL) water model and their relation to the thermodynamic anomalies. The
Bell-Lavis model is defined on a triangular lattice in which water molecules
are represented by particles with three symmetric bonding arms interacting
through van der Waals and hydrogen bonds. We have studied the model diffusivity
in different regions of the phase diagram through Monte Carlo simulations. Our
results show that the model displays a region of anomalous diffusion which lies
inside the region of anomalous density, englobed by the line of temperatures of
maximum density (TMD). Further, we have found that the diffusivity undergoes a
dynamic transition which may be classified as fragile-to-strong transition at
the critical line only at low pressures. At higher densities, no dynamic
transition is seen on crossing the critical line. Thus evidence from this study
is that relation of dynamic transitions to criticality may be discarded
Limited-memory BFGS Systems with Diagonal Updates
In this paper, we investigate a formula to solve systems of the form (B +
{\sigma}I)x = y, where B is a limited-memory BFGS quasi-Newton matrix and
{\sigma} is a positive constant. These types of systems arise naturally in
large-scale optimization such as trust-region methods as well as
doubly-augmented Lagrangian methods. We show that provided a simple condition
holds on B_0 and \sigma, the system (B + \sigma I)x = y can be solved via a
recursion formula that requies only vector inner products. This formula has
complexity M^2n, where M is the number of L-BFGS updates and n >> M is the
dimension of x
Dynamic Transitions in a Two Dimensional Associating Lattice Gas Model
Using Monte Carlo simulations we investigate some new aspects of the phase
diagram and the behavior of the diffusion coefficient in an associating lattice
gas (ALG) model on different regions of the phase diagram. The ALG model
combines a two dimensional lattice gas where particles interact through a soft
core potential and orientational degrees of freedom. The competition between
soft core potential and directional attractive forces results in a high density
liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in
the behavior of the density with the temperature at constant pressure and of
the diffusion coefficient with density at constant temperature are also found.
The two liquid phases are separated by a coexistence line that ends in a
bicritical point. The low density liquid phase is separated from the gas phase
by a coexistence line that ends in tricritical point. The bicritical and
tricritical points are linked by a critical -line. The high density
liquid phase and the fluid phases are separated by a second critical
line. We then investigate how the diffusion coefficient behaves on different
regions of the chemical potential-temperature phase diagram. We find that
diffusivity undergoes two types of dynamic transitions: a fragile-to-strong
trans ition when the critical -line is crossed by decreasing the
temperature at a constant chemical potential; and a strong-to-strong transition
when the -critical line is crossed by decreasing the temperature at a
constant chemical potential.Comment: 22 page
Hydration and anomalous solubility of the Bell-Lavis model as solvent
We address the investigation of the solvation properties of the minimal
orientational model for water, originally proposed by Bell and Lavis. The model
presents two liquid phases separated by a critical line. The difference between
the two phases is the presence of structure in the liquid of lower density,
described through orientational order of particles. We have considered the
effect of small inert solute on the solvent thermodynamic phases. Solute
stabilizes the structure of solvent, by the organization of solvent particles
around solute particles, at low temperatures. Thus, even at very high
densities, the solution presents clusters of structured water particles
surrounding solute inert particles, in a region in which pure solvent would be
free of structure. Solute intercalates with solvent, a feature which has been
suggested by experimental and atomistic simulation data. Examination of solute
solubility has yielded a minimum in that property, which may be associated with
the minimum found for noble gases. We have obtained a line of minimum
solubility (TmS) across the phase diagram, accompanying the line of maximum in
density (TMD). This coincidence is easily explained for non-interacting solute
and it is in agreement with earlier results in the literature. We give a simple
argument which suggests that interacting solute would dislocate TmS to higher
temperatures
On Solving L-SR1 Trust-Region Subproblems
In this article, we consider solvers for large-scale trust-region subproblems
when the quadratic model is defined by a limited-memory symmetric rank-one
(L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact
representation of L-SR1 matrices. Our approach makes use of both an orthonormal
basis for the eigenspace of the L-SR1 matrix and the Sherman-Morrison-Woodbury
formula to compute global solutions to trust-region subproblems. To compute the
optimal Lagrange multiplier for the trust-region constraint, we use Newton's
method with a judicious initial guess that does not require safeguarding. A
crucial property of this solver is that it is able to compute high-accuracy
solutions even in the so-called hard case. Additionally, the optimal solution
is determined directly by formula, not iteratively. Numerical experiments
demonstrate the effectiveness of this solver.Comment: 2015-0
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