13,644 research outputs found
A nonequilibrium extension of the Clausius heat theorem
We generalize the Clausius (in)equality to overdamped mesoscopic and
macroscopic diffusions in the presence of nonconservative forces. In contrast
to previous frameworks, we use a decomposition scheme for heat which is based
on an exact variant of the Minimum Entropy Production Principle as obtained
from dynamical fluctuation theory. This new extended heat theorem holds true
for arbitrary driving and does not require assumptions of local or close to
equilibrium. The argument remains exactly intact for diffusing fields where the
fields correspond to macroscopic profiles of interacting particles under
hydrodynamic fluctuations. We also show that the change of Shannon entropy is
related to the antisymmetric part under a modified time-reversal of the
time-integrated entropy flux.Comment: 23 pages; v2: manuscript significantly extende
Neutralino Dark Matter in 2005
I summarize some recent work on supersymmetric neutralinos as candidates for
cold Dark Matter in the Universe. This includes a new scan of mSUGRA parameter
space, with special emphasis on neutralinos annihilating predominantly through
exchange of the light CP--even Higgs boson, and on bounds on sparticle masses.
Next, prospects of testing models with TeV higgsino--like Dark Matter at
colliders are discussed. Finally, I briefly comment on extensions of the mSUGRA
model, and on scenarios with non--standard cosmology.Comment: Plenary talk at PASCOS05, Gyeongju, Korea, June 2005; 14 pages, 3
figures (included
Spectral Theory of Time Dispersive and Dissipative Systems
We study linear time dispersive and dissipative systems. Very often such
systems are not conservative and the standard spectral theory can not be
applied. We develop a mathematically consistent framework allowing (i) to
constructively determine if a given time dispersive system can be extended to a
conservative one; (ii) to construct that very conservative system -- which we
show is essentially unique. We illustrate the method by applying it to the
spectral analysis of time dispersive dielectrics and the damped oscillator with
retarded friction. In particular, we obtain a conservative extension of the
Maxwell equations which is equivalent to the original Maxwell equations for a
dispersive and lossy dielectric medium.Comment: LaTeX, 57 Pages, incorporated revisions corresponding with published
versio
Covariant hamiltonian dynamics
We discuss the covariant formulation of the dynamics of particles with
abelian and non-abelian gauge charges in external fields. Using this
formulation we develop an algorithm for the construction of constants of
motion, which makes use of a generalization of the concept of Killing vectors
and tensors in differential geometry. We apply the formalism to the motion of
classical charges in abelian and non-abelian monopole fieldsComment: 15 pages, no figure
The modal logic of arithmetic potentialism and the universal algorithm
I investigate the modal commitments of various conceptions of the philosophy
of arithmetic potentialism. Specifically, I consider the natural potentialist
systems arising from the models of arithmetic under their natural extension
concepts, such as end-extensions, arbitrary extensions, conservative extensions
and more. In these potentialist systems, I show, the propositional modal
assertions that are valid with respect to all arithmetic assertions with
parameters are exactly the assertions of S4. With respect to sentences,
however, the validities of a model lie between S4 and S5, and these bounds are
sharp in that there are models realizing both endpoints. For a model of
arithmetic to validate S5 is precisely to fulfill the arithmetic maximality
principle, which asserts that every possibly necessary statement is already
true, and these models are equivalently characterized as those satisfying a
maximal theory. The main S4 analysis makes fundamental use of the
universal algorithm, of which this article provides a simplified,
self-contained account. The paper concludes with a discussion of how the
philosophical differences of several fundamentally different potentialist
attitudes---linear inevitability, convergent potentialism and radical branching
possibility---are expressed by their corresponding potentialist modal
validities.Comment: 38 pages. Inquiries and commentary can be made at
http://jdh.hamkins.org/arithmetic-potentialism-and-the-universal-algorithm.
Version v3 has further minor revisions, including additional reference
Identifying Quantum Structures in the Ellsberg Paradox
Empirical evidence has confirmed that quantum effects occur frequently also
outside the microscopic domain, while quantum structures satisfactorily model
various situations in several areas of science, including biological, cognitive
and social processes. In this paper, we elaborate a quantum mechanical model
which faithfully describes the 'Ellsberg paradox' in economics, showing that
the mathematical formalism of quantum mechanics is capable to represent the
'ambiguity' present in this kind of situations, because of the presence of
'contextuality'. Then, we analyze the data collected in a concrete experiment
we performed on the Ellsberg paradox and work out a complete representation of
them in complex Hilbert space. We prove that the presence of quantum structure
is genuine, that is, 'interference' and 'superposition' in a complex Hilbert
space are really necessary to describe the conceptual situation presented by
Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision
processes in economics and decision theory, and allows to deal with different
Ellsberg-type generalizations, e.g., the 'Machina paradox'.Comment: 16 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:1208.235
Models of nonlinear kinematic hardening based on different versions of rate-independent maxwell fluid
Different models of finite strain plasticity with a nonlinear kinematic hardening are analyzed in a systematic way. All the models are based on a certain formulation of a rate-independent Maxwell fluid, which is used to render the evolution of backstresses. The properties of each material model are determined by the underlying formulation of the Maxwell fluid. The analyzed approaches include the multiplicative hyperelastoplasticity, additive hypoelasto-plasticity and the use of generalized strain measures. The models are compared with respect to different classification criteria, such as the objectivity, thermodynamic consistency, pure volumetric-isochoric split, shear stress oscillation, exact integrability, and w-invariance
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