11,118 research outputs found
Special values of shifted convolution Dirichlet series
In a recent important paper, Hoffstein and Hulse generalized the notion of
Rankin-Selberg convolution -functions by defining shifted convolution
-functions. We investigate symmetrized versions of their functions. Under
certain mild conditions, we prove that the generating functions of certain
special values are linear combinations of weakly holomorphic quasimodular forms
and "mixed mock modular" forms.Comment: 18 pages, corrected slight error in main theorem and made according
minor edits in Sections 3.4 and 3.
Novel structure formation of a phase separating colloidal fluid in a ratchet potential
Based on Dynamical Density Functional Theory (DDFT) we investigate a binary
mixture of interacting Brownian particles driven over a substrate via a
one-dimensional ratchet potential. The particles are modeled as soft spheres
where one component carries a classical Heisenberg spin. In the absence of a
substrate field, the system undergoes a first-order fluid-fluid demixing
transition driven by the spin-spin interaction. We demonstrate that the
interplay between the intrinsic spinodal decomposition and time-dependent
external forces leads to a novel dynamical instability where stripes against
the symmetry of the external potential form. This structural transition is
observed for a broad range of parameters related to the ratchet potential.
Moreover, we find intriguing effects for the particle transport.Comment: 6 pages, 4 figure
Eulerian method for multiphase interactions of soft solid bodies in fluids
We introduce an Eulerian approach for problems involving one or more soft
solids immersed in a fluid, which permits mechanical interactions between all
phases. The reference map variable is exploited to simulate finite-deformation
constitutive relations in the solid(s) on the same fixed grid as the fluid
phase, which greatly simplifies the coupling between phases. Our coupling
procedure, a key contribution in the current work, is shown to be
computationally faster and more stable than an earlier approach, and admits the
ability to simulate both fluid--solid and solid--solid interaction between
submerged bodies. The interface treatment is demonstrated with multiple
examples involving a weakly compressible Navier--Stokes fluid interacting with
a neo-Hookean solid, and we verify the method's convergence. The solid contact
method, which exploits distance-measures already existing on the grid, is
demonstrated with two examples. A new, general routine for cross-interface
extrapolation is introduced and used as part of the new interfacial treatment
A thermodynamical model for non-extremal black p-brane
We show that the correct entropy, temperature (and absorption probability) of
non-extremal black p-brane can be reproduced by a certain thermodynamical model
when maximizing its entropy. We show that the form of the model is related to
the geometrical similarity of non-extremal and near extremal black p-brane at
near horizon region, and argue about the appropriateness of the model.Comment: Almost the same version as the paper appeared in Physical Review
The IDEAL (Integrated Design and Engineering Analysis Languages) modeling methodology: Capabilities and Applications
The IDEAL (Integrated Design and Engineering Analysis Languages) modeling methodology has been formulated and applied over a five-year period. It has proven to be a unique, integrated approach utilizing a top-down, structured technique to define and document the system of interest; a knowledge engineering technique to collect and organize system descriptive information; a rapid prototyping technique to perform preliminary system performance analysis; and a sophisticated simulation technique to perform in-depth system performance analysis
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