4,419 research outputs found
Tunneling behavior of Ising and Potts models in the low-temperature regime
We consider the ferromagnetic -state Potts model with zero external field
in a finite volume and assume that the stochastic evolution of this system is
described by a Glauber-type dynamics parametrized by the inverse temperature
. Our analysis concerns the low-temperature regime ,
in which this multi-spin system has stable equilibria, corresponding to the
configurations where all spins are equal. Focusing on grid graphs with various
boundary conditions, we study the tunneling phenomena of the -state Potts
model. More specifically, we describe the asymptotic behavior of the first
hitting times between stable equilibria as in probability,
in expectation, and in distribution and obtain tight bounds on the mixing time
as side-result. In the special case , our results characterize the
tunneling behavior of the Ising model on grid graphs.Comment: 13 figure
Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility
We study the hitting times of Markov processes to target set , starting
from a reference configuration or its basin of attraction. The
configuration can correspond to the bottom of a (meta)stable well, while
the target could be either a set of saddle (exit) points of the well, or a
set of further (meta)stable configurations. Three types of results are
reported: (1) A general theory is developed, based on the path-wise approach to
metastability, which has three important attributes. First, it is general in
that it does not assume reversibility of the process, does not focus only on
hitting times to rare events and does not assume a particular starting measure.
Second, it relies only on the natural hypothesis that the mean hitting time to
is asymptotically longer than the mean recurrence time to or .
Third, despite its mathematical simplicity, the approach yields precise and
explicit bounds on the corrections to exponentiality. (2) We compare and relate
different metastability conditions proposed in the literature so to eliminate
potential sources of confusion. This is specially relevant for evolutions of
infinite-volume systems, whose treatment depends on whether and how relevant
parameters (temperature, fields) are adjusted. (3) We introduce the notion of
early asymptotic exponential behavior to control time scales asymptotically
smaller than the mean-time scale. This control is particularly relevant for
systems with unbounded state space where nucleations leading to exit from
metastability can happen anywhere in the volume. We provide natural sufficient
conditions on recurrence times for this early exponentiality to hold and show
that it leads to estimations of probability density functions
A conversation with 590 nascent entrepreneurs
This paper summarizes interviews from 1998 with 590 individuals trying to create a business centered around five questions: “Who are you?”, “What are you trying to accomplish?”, “What have you and others put into the business?”, “What have you accomplished?”, “What remains to be done?” There is a great deal of heterogeneity across these Nascent entrepreneurs, but they tend to have more education than the general population. Growing up in a family in which one or both parents had a business does not seem to be an important determinant of entry into entrepreneurship for males, while it seems to be of some importance for females. Most of the nascent businesses are in retail and consumer services, and about 50 percent of nascent entrepreneurs expect to become employers within five years of the business’s birth. Most nascent entrepreneurs have already made personally-significant investments of time and money in their firms; and nearly all of them are saving for their firms out of non-business income. For about half of the sample, these investments have yielded a fully-specified product; and the remainder are still in the product development stage. Family and friends are an importance source of seed money for many Nascent Entrepreneurs. Formal credit markets have been requested for funds only by a minority of Nascent Entrepreneurs, and almost half of these applicants have been denied loans. About 40% of the Nascent Entrepreneurs believe that their businesses require significantly greater equity before they can attract external funds.Business ; Business enterprises
História da ciência x aprendizagem : algumas semalhanças detectadas a partir de um estudo psicogenético sobre las idéias que evoluem para a noção de campo de força
In this article, based upon a psychogenetic study on the ideas which evolve to the concept of field of force, we show some students' conceptions which seem to be similar to others found in the History of Science. We analyse aspects which could contribute to the construction of the teaching of this concept
Competitive nucleation in metastable systems
Metastability is observed when a physical system is close to a first order
phase transition. In this paper the metastable behavior of a two state
reversible probabilistic cellular automaton with self-interaction is discussed.
Depending on the self-interaction, competing metastable states arise and a
behavior very similar to that of the three state Blume-Capel spin model is
found
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