scholarly journals Viscous Corrections of the Time Incremental Minimization Scheme and Visco-Energetic Solutions to Rate-Independent Evolution Problems

2017 ◽  
Vol 227 (2) ◽  
pp. 477-543 ◽  
Author(s):  
Luca Minotti ◽  
Giuseppe Savaré
Author(s):  
Alexander Mielke

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.


2021 ◽  
pp. 1-12
Author(s):  
Georg F. Striedter ◽  
R. Glenn Northcutt

Comparative neurobiologists have long wondered when and how the dorsal pallium (e.g., mammalian neocortex) evolved. For the last 50 years, the most widely accepted answer has been that this structure was already present in the earliest vertebrates and, therefore, homologous between the major vertebrate lineages. One challenge for this hypothesis is that the olfactory bulbs project throughout most of the pallium in the most basal vertebrate lineages (notably lampreys, hagfishes, and lungfishes) but do not project to the putative dorsal pallia in teleosts, cartilaginous fishes, and amniotes (i.e., reptiles, birds, and mammals). To make sense of these data, one may hypothesize that a dorsal pallium existed in the earliest vertebrates and received extensive olfactory input, which was subsequently lost in several lineages. However, the dorsal pallium is notoriously difficult to delineate in many vertebrates, and its homology between the various lineages is often based on little more than its topology. Therefore, we suspect that dorsal pallia evolved independently in teleosts, cartilaginous fishes, and amniotes. We further hypothesize that the emergence of these dorsal pallia was accompanied by the phylogenetic restriction of olfactory projections to the pallium and the expansion of inputs from other sensory modalities. We do not deny that the earliest vertebrates may have possessed nonolfactory sensory inputs to some parts of the pallium, but such projections alone do not define a dorsal pallium.


2021 ◽  
pp. 1-10
Author(s):  
Ishan Budhiraja ◽  
Neeraj Kumar ◽  
Sudhanshu Tyagi ◽  
Sudeep Tanwar

Author(s):  
Maria Michaela Porzio

AbstractIn this paper, we study the behavior in time of the solutions for a class of parabolic problems including the p-Laplacian equation and the heat equation. Either the case of singular or degenerate equations is considered. The initial datum $$u_0$$ u 0 is a summable function and a reaction term f is present in the problem. We prove that, despite the lack of regularity of $$u_0$$ u 0 , immediate regularization of the solutions appears for data f sufficiently regular and we derive estimates that for zero data f become the known decay estimates for these kinds of problems. Besides, even if f is not regular, we show that it is possible to describe the behavior in time of a suitable class of solutions. Finally, we establish some uniqueness results for the solutions of these evolution problems.


Animals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1429
Author(s):  
Yang Teng ◽  
Jing Yang ◽  
Guofen Zhu ◽  
Fuli Gao ◽  
Yingying Han ◽  
...  

Detailed molecular genetic research on amphibian populations has a significant role in understanding the genetic adaptability to local environments. The oriental fire-bellied toads (Bombina orientalis) were artificially introduced to Beijing from Shandong Province in 1927, and since then, this separated population went through an independent evolution. To explore the differentiation of the introduced population with its original population, this study analyzed the genetic structure of the oriental fire-bellied toad, based on the mitochondrial genome control region and six microsatellite sites. The results showed that the haplotype diversity and nucleotide diversity of the mitochondrial D-loop region partial sequences of the Beijing Botanical Garden population and the Baiwangshan population were lower than those of the Shangdong Kunyushan population. Microsatellite marker analysis also showed that the observed heterozygosity and expected heterozygosity of the Beijing populations were lower than those of the Kunyushan population. The phylogenetic trees and network diagrams of haplotypes indicated that the three populations were not genetically separated. However, the structure analysis showed a genetic differentiation and categorized the sampling individuals into Beijing and Shandong genetic clusters, which indicated a tendency for isolated evolution in the Beijing population. Although the Beijing populations showed a decline in genetic diversity, it was still at a moderate level, which could maintain the survival of the population. Thus, there is no need to reintroduce new individuals from the Kunyushan source population.


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