405,261 research outputs found
A note on modular forms and generalized anomaly cancellation formulas
By studying modular invariance properties of some characteristic forms, we
prove some new anomaly cancellation formulas which generalize the Han-Zhang and
Han-Liu-Zhang anomaly cancellation formula
On integrable natural Hamiltonian systems on the suspensions of toric automorphism
We point out a mistake in the main statement of \cite{liu} and suggest and
proof a correct statement.Comment: 5 pages, no figure
A Solution Set-Based Entropy Principle for Constitutive Modeling in Mechanics
Entropy principles based on thermodynamic consistency requirements are widely
used for constitutive modeling in continuum mechanics, providing physical
constraints on a priori unknown constitutive functions. The well-known
M\"uller-Liu procedure is based on Liu's lemma for linear systems. While the
M\"uller-Liu algorithm works well for basic models with simple constitutive
dependencies, it cannot take into account nonlinear relationships that exist
between higher derivatives of the fields in the cases of more complex
constitutive dependencies.
The current contribution presents a general solution set-based procedure,
which, for a model system of differential equations, respects the geometry of
the solution manifold, and yields a set of constraint equations on the unknown
constitutive functions, which are necessary and sufficient conditions for the
entropy production to stay nonnegative for any solution. Similarly to the
M\"uller-Liu procedure, the solution set approach is algorithmic, its output
being a set of constraint equations and a residual entropy inequality. The
solution set method is applicable to virtually any physical model, allows for
arbitrary initially postulated forms of the constitutive dependencies, and does
not use artificial constructs like Lagrange multipliers. A Maple implementation
makes the solution set method computationally straightforward and useful for
the constitutive modeling of complex systems.
Several computational examples are considered, in particular, models of gas,
anisotropic fluid, and granular flow dynamics. The resulting constitutive
function forms are analyzed, and comparisons are provided. It is shown how the
solution set entropy principle can yield classification problems, leading to
several complementary sets of admissible constitutive functions; such problems
have not previously appeared in the constitutive modeling literature
The nature of attraction between like charged rods
Comment on the paper of Ha and Liu (Phys. Rev. Lett. {\bf 79}, 1289 (1997))
regarding the nature of attraction between like charged rods. We demostrate
that their results do not produce the correct low temperature limit.Comment: Comment to appear in Phys. Rev. Let
A comparative study of some robust ridge and liu estimators
In multiple linear regression analysis, multicollinearity and outliers are two main problems. When multicollinearity exists, biased estimation techniques such as Ridge and Liu Estimators are preferable to Ordinary Least Square. On the other hand, when outliers exist in the data, robust estimators like M, MM, LTS and S Estimators, are preferred. To handle these two problems jointly, the study combines the Ridge and Liu Estimators with Robust Estimators to provide Robust Ridge and Robust Liu estimators respectively. The Mean Square Error (MSE) criterion was used to compare the performance of the estimators. Application to the proposed estimators to three (3) real life data set with multicollinearity and outliers problems reveals that the M-Liu and LTS-Liu Estimator are generally most efficient..Keywords: Ordinary Least Squares, Ridge Regression Estimator, Liu Estimator, Robust Estimator, Robust Ridge Regression Estimator, Robust Liu Estimato
Viscoelastic Multicomponent Fluids in confined Flow-Focusing Devices
The effects of elasticity on the break-up of liquid threads in microfluidic
cross-junctions is investigated using numerical simulations based on the
"lattice Boltzmann models" (LBM). Working at small Capillary numbers, we
investigate the effects of non-Newtonian phases in the transition from droplet
formation at the cross-junction (DCJ) and droplet formation downstream of the
cross-junction (DC) (Liu & Zhang, , 082101
(2011)). Viscoelasticity is found to influence the break-up point of the
threads, which moves closer to the cross-junction and stabilizes. This is
attributed to an increase of the polymer feedback stress forming in the corner
flows, where the side channels of the device meet the main channel.Comment: 4 pages, 2 figures, AIP Conference Proceedings, 201
Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D
In this paper we prove the existence of a trajectory attractor (in the sense
of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D
liquid crystal model accounting for stretching effects. The system couples a
nonlinear evolution equation for the director d (introduced in order to
describe the preferred orientation of the molecules) with an incompressible
Navier-Stokes equation for the evolution of the velocity field u. The technique
is based on the introduction of a suitable trajectory space and of a metric
accounting for the double-well type nonlinearity contained in the director
equation. Finally, a dissipative estimate is obtained by using a proper
integrated energy inequality. Both the cases of (homogeneous) Neumann and
(non-homogeneous) Dirichlet boundary conditions for d are considered.Comment: 32 page
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