140 research outputs found
Dissipative systems: uncontrollability, observability and RLC realizability
The theory of dissipativity has been primarily developed for controllable
systems/behaviors. For various reasons, in the context of uncontrollable
systems/behaviors, a more appropriate definition of dissipativity is in terms
of the dissipation inequality, namely the {\em existence} of a storage
function. A storage function is a function such that along every system
trajectory, the rate of increase of the storage function is at most the power
supplied. While the power supplied is always expressed in terms of only the
external variables, whether or not the storage function should be allowed to
depend on unobservable/hidden variables also has various consequences on the
notion of dissipativity: this paper thoroughly investigates the key aspects of
both cases, and also proposes another intuitive definition of dissipativity.
We first assume that the storage function can be expressed in terms of the
external variables and their derivatives only and prove our first main result
that, assuming the uncontrollable poles are unmixed, i.e. no pair of
uncontrollable poles add to zero, and assuming a strictness of dissipativity at
the infinity frequency, the dissipativities of a system and its controllable
part are equivalent. We also show that the storage function in this case is a
static state function.
We then investigate the utility of unobservable/hidden variables in the
definition of storage function: we prove that lossless autonomous behaviors
require storage function to be unobservable from external variables. We next
propose another intuitive definition: a behavior is called dissipative if it
can be embedded in a controllable dissipative {\em super-behavior}. We show
that this definition imposes a constraint on the number of inputs and thus
explains unintuitive examples from the literature in the context of
lossless/orthogonal behaviors.Comment: 26 pages, one figure. Partial results appeared in an IFAC conference
(World Congress, Milan, Italy, 2011
Fundamental Aspects of the ISM Fractality
The ubiquitous clumpy state of the ISM raises a fundamental and open problem
of physics, which is the correct statistical treatment of systems dominated by
long range interactions. A simple solvable hierarchical model is presented
which explains why systems dominated by gravity prefer to adopt a fractal
dimension around 2 or less, like the cold ISM and large scale structures. This
has direct relation with the general transparency, or blackness, of the
Universe.Comment: 6 pages, LaTeX2e, crckapb macro, no figure, uuencoded compressed tar
file. To be published in the proceeedings of the "Dust-Morphology"
conference, Johannesburg, 22-26 January, 1996, D. Block (ed.), (Kluwer
Dordrecht
On the role of different Skyrme forces and surface corrections in exotic cluster-decay
We present cluster decay studies of Ni formed in heavy-ion
collisions using different Skyrme forces. Our study reveals that different
Skyrme forces do not alter the transfer structure of fractional yields
significantly. The cluster decay half-lives of different clusters lies within
\pm 10% for PCM and \pm 15% for UFM.Comment: 13 pages,6 figures and 1 table; in press Pramana Journal of Physics
(2010
Decision Making for Inconsistent Expert Judgments Using Negative Probabilities
In this paper we provide a simple random-variable example of inconsistent
information, and analyze it using three different approaches: Bayesian,
quantum-like, and negative probabilities. We then show that, at least for this
particular example, both the Bayesian and the quantum-like approaches have less
normative power than the negative probabilities one.Comment: 14 pages, revised version to appear in the Proceedings of the QI2013
(Quantum Interactions) conferenc
Epistemic and Ontic Quantum Realities
Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position
Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals
We employ a recently formulated dequantization procedure to obtain an exact
expression for the kinetic energy which is applicable to all kinetic-energy
functionals. We express the kinetic energy of an N-electron system as the sum
of an N-electron classical kinetic energy and an N-electron purely quantum
kinetic energy arising from the quantum fluctuations that turn the classical
momentum into the quantum momentum. This leads to an interesting analogy with
Nelson's stochastic approach to quantum mechanics, which we use to conceptually
clarify the physical nature of part of the kinetic-energy functional in terms
of statistical fluctuations and in direct correspondence with Fisher
Information Theory. We show that the N-electron purely quantum kinetic energy
can be written as the sum of the (one-electron) Weizsacker term and an
(N-1)-electron kinetic correlation term. We further show that the Weizsacker
term results from local fluctuations while the kinetic correlation term results
from the nonlocal fluctuations. For one-electron orbitals (where kinetic
correlation is neglected) we obtain an exact (albeit impractical) expression
for the noninteracting kinetic energy as the sum of the classical kinetic
energy and the Weizsacker term. The classical kinetic energy is seen to be
explicitly dependent on the electron phase and this has implications for the
development of accurate orbital-free kinetic-energy functionals. Also, there is
a direct connection between the classical kinetic energy and the angular
momentum and, across a row of the periodic table, the classical kinetic energy
component of the noninteracting kinetic energy generally increases as Z
increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac
Massive stars as thermonuclear reactors and their explosions following core collapse
Nuclear reactions transform atomic nuclei inside stars. This is the process
of stellar nucleosynthesis. The basic concepts of determining nuclear reaction
rates inside stars are reviewed. How stars manage to burn their fuel so slowly
most of the time are also considered. Stellar thermonuclear reactions involving
protons in hydrostatic burning are discussed first. Then I discuss triple alpha
reactions in the helium burning stage. Carbon and oxygen survive in red giant
stars because of the nuclear structure of oxygen and neon. Further nuclear
burning of carbon, neon, oxygen and silicon in quiescent conditions are
discussed next. In the subsequent core-collapse phase, neutronization due to
electron capture from the top of the Fermi sea in a degenerate core takes
place. The expected signal of neutrinos from a nearby supernova is calculated.
The supernova often explodes inside a dense circumstellar medium, which is
established due to the progenitor star losing its outermost envelope in a
stellar wind or mass transfer in a binary system. The nature of the
circumstellar medium and the ejecta of the supernova and their dynamics are
revealed by observations in the optical, IR, radio, and X-ray bands, and I
discuss some of these observations and their interpretations.Comment: To be published in " Principles and Perspectives in Cosmochemistry"
Lecture Notes on Kodai School on Synthesis of Elements in Stars; ed. by Aruna
Goswami & Eswar Reddy, Springer Verlag, 2009. Contains 21 figure
Random-phase approximation and its applications in computational chemistry and materials science
The random-phase approximation (RPA) as an approach for computing the
electronic correlation energy is reviewed. After a brief account of its basic
concept and historical development, the paper is devoted to the theoretical
formulations of RPA, and its applications to realistic systems. With several
illustrating applications, we discuss the implications of RPA for computational
chemistry and materials science. The computational cost of RPA is also
addressed which is critical for its widespread use in future applications. In
addition, current correction schemes going beyond RPA and directions of further
development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012
JOINT COMMITMENT, COERCION AND FREEDOM IN SCIENCE Conceptual Analysis and Case Studies
International audienceThis paper deals with the Ethics of group life in the sciences, if not directly with the policy of science that might evolve from it, and more precisely with the issue of democracy within scientific life
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