A Monge–Kantorovich mass transport problem for a discrete distance

AbstractThis paper is concerned with a Monge–Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obtain, taking limits in the rescaled nonlocal formulation, the PDE formulation given by Evans–Gangbo for the classical problem

Study of two bovine bone blocks (sintered and non-sintered) used for bone grafts: physico-chemical characterization and in vitro bioactivity and cellular analysis

High-temperature compression and electron backscatter diffraction (EBSD) techniques were used in a systematic investigation of the dynamic recrystallization (DRX) behavior and texture evolution of the Inconel625 alloy. The true stress–true strain curves and the constitutive equation of Inconel625 were obtained at temperatures ranging from 900 to 1200 °C and strain rates of 10, 1, 0.1, and 0.01 s−1. The adiabatic heating effect was observed during the hot compression process. At a high strain rate, as the temperature increased, the grains initially refined and then grew, and the proportion of high-angle grain boundaries increased. The volume fraction of the dynamic recrystallization increased. Most of the grains were randomly distributed and the proportion of recrystallized texture components first increased and then decreased. Complete dynamic recrystallization occurred at 1100 °C, where the recrystallized volume fraction and the random distribution ratios of grains reached a maximum. This study indicated that the dynamic recrystallization mechanism of the Inconel625 alloy at a high strain rate included continuous dynamic recrystallization with subgrain merging and rotation, and discontinuous dynamic recrystallization with bulging grain boundary induced by twinning. The latter mechanism was less dominan

Biomechanical and histological analysis of titanium (machined and treated surface) versus zirconia implant materials: an in vivo animal study

This article belongs to the Special Issue Clinical Implants and the Biocompatibility of Biodegradable BiomaterialsObjectives: The aim of this study was to perform an in vivo histological comparative evaluation of bone formation around titanium (machined and treated surface) and zirconia implants. For the present study were used 50 commercially pure titanium implants grade IV, being that 25 implants with a machined surface (TiM group), 25 implants with a treated surface (TiT group) and, 25 implants were manufactured in pure zirconia (Zr group). The implants (n = 20 per group) were installed in the tibia of 10 rabbits. The implants distribution was randomized (n = 3 implants per tibia). Five implants of each group were analyzed by scanning electron microscopy and an optical laser profilometer for surface roughness characterization. Six weeks after the implantation, 10 implants for each group were removed in counter-torque for analysis of maximum torque value. The remaining samples were processed, included in historesin and cut to obtain non-decalcified slides for histomorphological analyses and histomorphometric measurement of the percentage of bone-implant contact (BIC%). Comparisons were made between the groups using a 5% level of significance (p < 0.05) to assess statistical differences. The results of removal torque values (mean ± standard deviation) showed for the TiM group 15.9 ± 4.18 N cm, for TiT group 27.9 ± 5.15 N cm and for Zr group 11.5 ± 2.92 N cm, with significant statistical difference between the groups (p < 0.0001). However, the BIC% presented similar values for all groups (35.4 ± 4.54 for TiM group, 37.8 ± 4.84 for TiT group and 34.0 ± 6.82 for Zr group), with no statistical differences (p = 0.2171). Within the limitations of the present study, the findings suggest that the quality of the new bone tissue formed around the titanium implants present a superior density (maturation) in comparison to the zirconia implants

On a nonlinear flux--limited equation arising in the transport of morphogens

Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion system. From a mathematical point of view the problem behaves more as an hyperbolic system that a parabolic one

A Fisher–Kolmogorov equation with finite speed of propagation

AbstractIn this paper we study a Fisher–Kolmogorov type equation with a flux limited diffusion term and we prove the existence and uniqueness of finite speed moving fronts and the existence of some explicit solutions in a particular regime of the equation

Jornada Ladyzhenskaya FME (Curs 2021-2022)

Benvinguda i presentació a càrrec de Jordi Guàrdia, degà de l'FME. El problema de la velocidad de propagación infinita en las ecuaciones de difusión. J.M. Mazón (Universidad de Valencia). Presenta: Albert Mas (Dept. Matemàtiques UPC). Lliurament premis als guanyadors del Concurs Ladyzhenskaya activitat conjunta de l’assignatura Història de la Matemàtica i la Biblioteca FME. Characterise and control turbulence in shear flows via nonlinear optimization. Stefania Cherubini (Polytechnical University of Bari). Presenta: Joan Sánchez (Dept. Física UPC). Hopf, Caccioppoli and Schauder, reloaded. Giuseppe Mingione (University of Parma) Presenta: Xaiver Cabré (Dept. Matemàtiques UPC)

A nonlocal p-Laplacian evolution equation with Neumann boundary conditions

In this paper we study the nonlocal p-Laplacian type diffusion equation,ut (t, x) = under(∫, Ω) J (x - y) | u (t, y) - u (t, x) |p - 2 (u (t, y) - u (t, x)) d y . If p &gt; 1, this is the nonlocal analogous problem to the well-known local p-Laplacian evolution equation ut = div (| ∇ u |p - 2 ∇ u) with homogeneous Neumann boundary conditions. We prove existence and uniqueness of a strong solution, and if the kernel J is rescaled in an appropriate way, we show that the solutions to the corresponding nonlocal problems converge strongly in L∞ (0, T ; Lp (Ω)) to the solution of the p-Laplacian with homogeneous Neumann boundary conditions. The extreme case p = 1, that is, the nonlocal analogous to the total variation flow, is also analyzed. Finally, we study the asymptotic behavior of the solutions as t goes to infinity, showing the convergence to the mean value of the initial condition. © 2008 Elsevier Masson SAS. All rights reserved.Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Polymer precursors of polyacetylene. Thermal degradation of poly(vinyl esters). Part II-Effect of the n-acyl chain length on the autocatalytic thermal degradation of a homologous series of poly(vinyl n-alkyl esters) (PV-n-AEs)

In order to determine the effect of the length of the n-acyl portion on the autocatalytic thermal elimination reaction, five of the shorter members of the homologous series of poly(vinyl n-alkyl esters) (PV-n-AEs) {A figure is presented} were studied under identical experimental conditions; namely, by a static procedure at several temperatures. The -R group was varied from one to five carbon atoms. All the PV-n-AEs were obtained by chemical modification of a unique sample of poly(vinyl alcohol) (PVA). Thus, by using a homologous series of PV-n-AEs with the same backbone molecular weight, any possible effect due to a change in molecular weight of the backbone and/or tacticity, structural chemical irregularities, etc., is eliminated. The shortest member of the series, i.e. poly(vinyl acetate) (PVAc) clearly degrades by an autocatalytic mechanism more readily than do longer ones. Thus, PVAc exhibits pure autocatalytic thermal degradation kinetics. On the contrary, the longest member of the series, poly(vinyl n-hexanoate ester) (PV-n-HE), degrades by very well defined first order kinetics. The other members of the series, poly(vinyl propionate) (PVPr), poly(vinyl butyrate) (PVBu) ≡ poly(vinyl n-butanoate ester) (PV-n-BE) and poly(vinyl valerate (PVVa) ≡ poly(vinyl n-pentanoate ester) (PV-n-PE) degrade by first order kinetics but with the participation, although to an insignificant extent, of the autocatalytic mechanism. For this and certain other reasons we have analyzed our experimental results by taking into account both types of mechanisms, separately. The three latter compounds followed first order rate kinetics quite well, the rate constants depending upon the n-alkyl chain length of the acyl portion. The energy of activation of the first order reaction decreases markedly as the length of the n-acyl portion increases. This decrease is neither constant nor regular as the acyl moeity increases in length but rather takes place in a quasi zig-zag fashion particularly with the longer members, suggesting an odd-even effect. On the basis of our experimental results we have arrived at the two following conclusions. Firstly, less stable poly(vinyl n-alkyl esters), i.e. poly(vinyl n-hexanoate ester) and, of course, higher members of the series which have not been investigated in the present work, would allow lower pyrolysis temperatures, thus increasing the synthetic applicability of this stripping reaction to the preparation of polyacetylene-like structures. Secondly, it was hoped that the kinetic study itself would shed more light on the mechanism of these decompositions in high molecular weight compounds. © 1989.Peer Reviewe

Some qualitative properties for the total variation flow

We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are nonzero solutions of an eigenvalue-type problem that seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p-Laplacian operator. Finally. the study of the radially symmetric case allows us to point out other qualitative properties that are peculiar of this special class of quasilinear equations