Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_

Crackling Noise

Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from earthquakes on faults to paper crumpling. Because these systems exhibit regular behavior over many decades of sizes, their behavior is likely independent of microscopic and macroscopic details, and progress can be made by the use of very simple models. The fact that simple models and real systems can share the same behavior on a wide range of scales is called universality. We illustrate these ideas using results for our model of crackling noise in magnets, explaining the use of the renormalization group and scaling collapses. This field is still developing: we describe a number of continuing challenges

Geometric methods on low-rank matrix and tensor manifolds

In this chapter we present numerical methods for low-rank matrix and tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus on two types of problems: The first are optimization problems, like matrix and tensor completion, solving linear systems and eigenvalue problems. Such problems can be solved by numerical optimization for manifolds, called Riemannian optimization methods. We will explain the basic elements of differential geometry in order to apply such methods efficiently to rank constrained matrix and tensor spaces. The second type of problem is ordinary differential equations, defined on matrix and tensor spaces. We show how their solution can be approximated by the dynamical low-rank principle, and discuss several numerical integrators that rely in an essential way on geometric properties that are characteristic to sets of low rank matrices and tensors

A common biological basis of obesity and nicotine addiction

J. Kaprio ja J. Tuomilehto työryhmien jäseniä (yht. 281).Peer reviewe

Temporal network analysis of literary texts

We study temporal networks of characters in literature focussing on Alice's Adventures in Wonderland (1865) by Lewis Carroll and the anonymous La Chanson de Roland (around 1100). The former, one of the most inuential pieces of nonsense literature ever written, describes the adventures of Alice in a fantasy world with logic plays interspersed along the narrative. The latter, a song of heroic deeds, depicts the Battle of Roncevaux in 778 A.D. during Charlemagne's campaign on the Iberian Peninsula. We apply methods recently developed by Taylor et al. [26] to find time-averaged eigenvector centralities, Freeman indices and vitalities of characters. We show that temporal networks are more appropriate than static ones for studying stories, as they capture features that the time-independent approaches fail to yield

Evaluation of skin sensitivity after shock wave treatment in horses

Objective: To evaluate the effects of shock wave treatment on cutaneous nerve function, compared with the effects of local nerve block and sedation. Animals: 18 clinically sound Swiss Warmbloods. Procedure: Horses were randomly allocated to 3 groups and received different amounts and types of shock waves (extracorporeal shock wave treatment [ESWT] or radial pressure wave treatment [RPWT]). Horses were sedated with xylazine and levomethadone. Shock waves were applied to the lateral palmar digital nerve at the level of the proximal sesamoid bones on 1 forelimb. Skin sensitivity was evaluated by means of an electrical stimulus at the coronary band before and 5 minutes after sedation and at 4, 24, and 48 hours after application of ESWT or RPWT. On the contralateral forelimb, skin sensitivity was tested before and 10 minutes after an abaxial sesamoid nerve block. Results: No significant changes in skin sensitivity were detected, regardless of the shock wave protocol applied. Mean reaction thresholds after sedation were more than twice the baseline thresholds. After the abaxial sesamoid block, no reaction was recorded in any of the horses. Conclusions and Clinical Relevance: Application of ESWT or RPWT to the palmar digital nerve had no effect on cutaneous sensation distal to the treated region for at least 2 days after application. The analgesic effect of sedation on reaction to electrical stimuli was distinct but varied among horses