34,333 research outputs found
Generic theory of active polar gels: a paradigm for cytoskeletal dynamics
We develop a general theory for active viscoelastic materials made of polar
filaments. This theory is motivated by the dynamics of the cytoskeleton. The
continuous consumption of a fuel generates a non equilibrium state
characterized by the generation of flows and stresses. Our theory can be
applied to experiments in which cytoskeletal patterns are set in motion by
active processes such as those which are at work in cells.Comment: 28 pages, 2 figure
The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes
This paper is dedicated to the question of surjectivity of the Cauchy-Riemann
operator on spaces of -smooth
vector-valued functions whose growth on strips along the real axis with holes
is induced by a family of continuous weights . Vector-valued
means that these functions have values in a locally convex Hausdorff space
over . We characterise the weights which give a
counterpart of the Grothendieck-K\"othe-Silva duality
with non-empty compact for weighted holomorphic functions.
We use this duality to prove that the kernel
of the Cauchy-Riemann operator
in
has the property
of Vogt. Then an application of the splitting theory of Vogt for
Fr\'{e}chet spaces and of Bonet and Doma\'nski for (PLS)-spaces in combination
with some previous results on the surjectivity of the Cauchy-Riemann operator
yields
the surjectivity of the Cauchy-Riemann operator on if
with some Fr\'{e}chet space satisfying the condition or
if is an ultrabornological (PLS)-space having the property . This
solves the smooth (holomorphic, distributional) parameter dependence problem
for the Cauchy-Riemann operator on
Surjectivity of the -operator between spaces of weighted smooth vector-valued functions
We derive sufficient conditions for the surjectivity of the Cauchy-Riemann
operator between spaces of weighted smooth
Fr\'echet-valued functions. This is done by establishing an analog of
H\"ormander's theorem on the solvability of the inhomogeneous Cauchy-Riemann
equation in a space of smooth -valued functions whose topologyis
given by a whole family of weights. Our proof relies on a weakened variant of
weak reducibility of the corresponding subspace of holomorphic functions in
combination with the Mittag-Leffler procedure. Using tensor products, we deduce
the corresponding result on the solvability of the inhomogeneous Cauchy-Riemann
equation for Fr\'echet-valued functions
Introducing Molly: Distributed Memory Parallelization with LLVM
Programming for distributed memory machines has always been a tedious task,
but necessary because compilers have not been sufficiently able to optimize for
such machines themselves. Molly is an extension to the LLVM compiler toolchain
that is able to distribute and reorganize workload and data if the program is
organized in statically determined loop control-flows. These are represented as
polyhedral integer-point sets that allow program transformations applied on
them. Memory distribution and layout can be declared by the programmer as
needed and the necessary asynchronous MPI communication is generated
automatically. The primary motivation is to run Lattice QCD simulations on IBM
Blue Gene/Q supercomputers, but since the implementation is not yet completed,
this paper shows the capabilities on Conway's Game of Life
Optimal Error Estimates of Galerkin Finite Element Methods for Stochastic Partial Differential Equations with Multiplicative Noise
We consider Galerkin finite element methods for semilinear stochastic partial
differential equations (SPDEs) with multiplicative noise and Lipschitz
continuous nonlinearities. We analyze the strong error of convergence for
spatially semidiscrete approximations as well as a spatio-temporal
discretization which is based on a linear implicit Euler-Maruyama method. In
both cases we obtain optimal error estimates.
The proofs are based on sharp integral versions of well-known error estimates
for the corresponding deterministic linear homogeneous equation together with
optimal regularity results for the mild solution of the SPDE. The results hold
for different Galerkin methods such as the standard finite element method or
spectral Galerkin approximations.Comment: 30 page
Extension of vector-valued functions and sequence space representation
We give a unified approach to handle the problem of extending functions with
values in a locally convex Hausdorff space over a field , which
have weak extensions in a space of
scalar-valued functions on a set , to functions in a vector-valued
counterpart of . The
results obtained base upon a representation of vector-valued functions as
linear continuous operators and extend results of Bonet, Frerick, Gramsch and
Jord\'{a}. In particular, we apply them to obtain a sequence space
representation of from a known representation of
.Comment: The former version arXiv:1808.05182v2 of this paper is split into two
parts. This is the first par
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