446 research outputs found
Utility, subjective probability, their interaction, and variance preferences
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66507/2/10.1177_002200276200600106.pd
Hamilton's principle: why is the integrated difference of kinetic and potential energy minimized?
I present an intuitive answer to an often asked question: why is the
integrated difference K-U between the kinetic and potential energy the quantity
to be minimized in Hamilton's principle?
Using elementary arguments, I map the problem of finding the path of a moving
particle connecting two points to that of finding the minimum potential energy
of a static string. The mapping implies that the configuration of a
non--stretchable string of variable tension corresponds to the spatial path
dictated by the Principle of Least Action; that of a stretchable string in
space-time is the one dictated by Hamilton's principle. This correspondence
provides the answer to the question above: while a downward force curves the
trajectory of a particle in the (x,t) plane downward, an upward force of the
same magnitude stretches the string to the same configuration x(t).Comment: 7 pages, 4 figures. Submitted to the American Journal of Physic
Thermotectonic evolution of an extensional dome: the Cenozoic Osogovo-Lisets core complex (Kraishte zone, western Bulgaria)
The Kraishte region of Bulgaria is located at the junction of the Balkanides and Hellenides-Dinarides tectonic belts. Fission-track analysis on both apatites and zircons documents the Cenozoic exhumation of a Precambrian basement bounded by low-angle detachments. Late Eocene-Oligocene extension began prior to 47Ma and was dominantly in a top-to-the-southwest direction, confirmed by the sense of younging of apatite and zircon ages. This crustal extension controlled the formation of half-graben sedimentary basins on the hanging walls of the detachments. Thermal modelling of these hanging wall units provides evidence for heat transfer across the detachments from a relatively warm rising footwall. From 32 to 29Ma, pervasive magmatic activity resulted in the emplacement of rhyolitic to dacitic subvolcanic bodies and dykes, along with intrusion of the Osogovo granite. The results give evidence for extension in the southern Balkan older than, and separated from, the Miocene to Quaternary Aegean extension. This might reflect transtension during northeastward extrusion and rotation of continental fragments around the western boundary of Moesia. Eocene-Oligocene extension seems to have been controlled by the distribution of earlier thickening all around the Carpatho-Balkanic orocline, which is reflected by the Cretaceous emplacement of the Morava Nappe in the Kraisht
Active Mass Under Pressure
After a historical introduction to Poisson's equation for Newtonian gravity,
its analog for static gravitational fields in Einstein's theory is reviewed. It
appears that the pressure contribution to the active mass density in Einstein's
theory might also be noticeable at the Newtonian level. A form of its
surprising appearance, first noticed by Richard Chase Tolman, was discussed
half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure
A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling
In this paper we propose a new nonparametric approach to interacting failing
systems (FS), that is systems whose probability of failure is not negligible in
a fixed time horizon, a typical example being firms and financial bonds. The
main purpose when studying a FS is to calculate the probability of default and
the distribution of the number of failures that may occur during the
observation period. A model used to study a failing system is defined default
model. In particular, we present a general recursive model constructed by the
means of inter- acting urns. After introducing the theoretical model and its
properties we show a first application to credit risk modeling, showing how to
assess the idiosyncratic probability of default of an obligor and the joint
probability of failure of a set of obligors in a portfolio of risks, that are
divided into reliability classes
Anomalous Behavior of the Contact Process with Aging
The effect of power-law aging on a contact process is studied by simulation
and using a mean-field approach. We find that the system may approach its
stationary state in a nontrivial, nonmonotonous way. For the particular value
of the aging exponent, , we observe a rich set of behaviors:
depending on the process parameters, the relaxation to the stationary state
proceeds as or via a power law with a nonuniversal exponent.
Simulation results suggest that for , the absorbing-state phase
transition is in the universality class of directed percolation.Comment: 4 pages revtex (twocolumn, psfig), 3 figure
Dynamics & Predictions in the Co-Event Interpretation
Sorkin has introduced a new, observer independent, interpretation of quantum
mechanics that can give a successful realist account of the 'quantum
microworld' as well as explaining how classicality emerges at the level of
observable events for a range of systems including single time 'Copenhagen
measurements'. This 'co-event interpretation' presents us with a new ontology,
in which a single 'co-event' is real. A new ontology necessitates a review of
the dynamical & predictive mechanism of a theory, and in this paper we begin
the process by exploring means of expressing the dynamical and predictive
content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein
Piecewise Linear Models for the Quasiperiodic Transition to Chaos
We formulate and study analytically and computationally two families of
piecewise linear degree one circle maps. These families offer the rare
advantage of being non-trivial but essentially solvable models for the
phenomenon of mode-locking and the quasi-periodic transition to chaos. For
instance, for these families, we obtain complete solutions to several questions
still largely unanswered for families of smooth circle maps. Our main results
describe (1) the sets of maps in these families having some prescribed rotation
interval; (2) the boundaries between zero and positive topological entropy and
between zero length and non-zero length rotation interval; and (3) the
structure and bifurcations of the attractors in one of these families. We
discuss the interpretation of these maps as low-order spline approximations to
the classic ``sine-circle'' map and examine more generally the implications of
our results for the case of smooth circle maps. We also mention a possible
connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request
Linear frictional forces cause orbits to neither circularize nor precess
For the undamped Kepler potential the lack of precession has historically
been understood in terms of the Runge-Lenz symmetry. For the damped Kepler
problem this result may be understood in terms of the generalization of Poisson
structure to damped systems suggested recently by Tarasov[1]. In this
generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a
constant in the linearly damped Kepler problem to leading order in the damping
coeComment: 16 pages. 1 figure, Rewrite for resubmissio
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
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