Mathematical Physics (MP)
http://hdl.handle.net/20.500.11824/16
2020-08-15T11:18:20ZA generalized Stefan model accounting for system memory and non-locality
http://hdl.handle.net/20.500.11824/1119
A generalized Stefan model accounting for system memory and non-locality
Garra R.; Falcini F.; Voller V.R.; Pagnini G.
The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the square root of time. When memory or non-locality are introduced into the system however, this classic signal may be anomalous; replaced by a power-law advance with a time exponent that differs from n = 1/2. Up to now memory treatments in Stefan problem models have only been able to reproduce sub-diffusive front movements with exponents n < 1/2 and non-local treatments have only been able to reproduce super-diffusive behavior n > 1/2. In the present paper, using a generalized Caputo fractional derivative operator, we introduce new memory and non-local treatment for Stefan problems. On considering a limit case Stefan problem, related to the melting problem, we are able to show that, this gen- eral treatment can not only produce arbitrary power-law in time predictions for the front movement but, in the case of memory treatments, can also produce non-power-law anomalous behaviors. Further, also in the context of the limit problem, we are able to establish an equivalence between non-locality and a space varying conductivity and memory and a time varying conductivity.
2020-05-01T00:00:00ZSome classes of homeomorphisms that preserve multiplicity and tangent cones
http://hdl.handle.net/20.500.11824/1114
Some classes of homeomorphisms that preserve multiplicity and tangent cones
Sampaio J. E.
In this paper we present some applications of A’Campo-Lˆe’s Theorem and we study some relations between Zariski’s Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant when we consider right equivalence and this class contains many known classes of homeomorphisms that preserve tangent cones. In particular, we present some effective approaches to Zariski’s Question A. We show a version of these results looking at infinity. Additionally, we present some results related with Nash modification and Lipschitz Geometry.
2020-01-01T00:00:00ZThe Nash Problem from Geometric and Topological Perspective
http://hdl.handle.net/20.500.11824/1113
The Nash Problem from Geometric and Topological Perspective
Fernández de Bobadilla J.; Pe Pereira M.
We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional statement and proof by de Fernex and Docampo. We end the paper by explaining later developments on generalized Nash problem and on Kollar and Nemethi holomorphic arcs.
2020-03-01T00:00:00ZA hypothesis about parallelism vs. seriality in dreams
http://hdl.handle.net/20.500.11824/1102
A hypothesis about parallelism vs. seriality in dreams
Barcaro U.; Paradisi P.; Sebastiani L.
The current article discusses the hypothesis about parallelism vs. Seriality in dreams. The process of dream building implies the construction of a complex network of closely interrelated sources. On the other hand, the dream experience develops as a succession of events. In this paper a hypothesis is advanced about how the psychophysiological system of dream building, which is distributed, acts to provide a serial output. This hypothesis is basically connected with the property, enjoyed by the dream experience, of simultaneously representing a plurality of meanings. Our point is that the serial output is created by the system in a conceptually simple way, i.e., by providing a dream plot able to simultaneously represent the overcoming of the present concerns, which are more than one because of the shift of the present concern. This property appears as a typical feature of the dreaming experience.
2019-10-10T00:00:00Z