On distributional solutions of local and nonlocal problems of porous medium type

We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\partial_tu-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=g(x,t)\quad\quad\text{in}\quad\quad \mathbb{R}^N\times(0,T),$$ where $\varphi$ is merely continuous and nondecreasing and $\mathfrak{L}^{\sigma,\mu}$ is the generator of a general symmetric L\'evy process. This means that $\mathfrak{L}^{\sigma,\mu}$ can have both local and nonlocal parts like e.g. $\mathfrak{L}^{\sigma,\mu}=\Delta-(-\Delta)^{\frac12}$. New uniqueness results for bounded distributional solutions of this problem and the corresponding elliptic equation are presented and proven. A key role is played by a new Liouville type result for $\mathfrak{L}^{\sigma,\mu}$. Existence and a priori estimates are deduced from a numerical approximation, and energy type estimates are also obtained.Comment: 6 pages. Minor revision. Added details to Step 2 of the proof of Theorem 3.

Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type

We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ can be any nonlocal symmetric degenerate elliptic operator including the fractional Laplacian and numerical discretizations of this operator. The function $\varphi:\mathbb{R} \to \mathbb{R}$ is only assumed to be continuous and nondecreasing. The class of equations include nonlocal (generalized) porous medium equations, fast diffusion equations, and Stefan problems. In addition to very general uniqueness and existence results, we obtain $L^1$-contraction and a priori estimates. We also study local limits, continuous dependence, and properties and convergence of a numerical approximation of our equations.Comment: To appear in "Advances in Mathematics

Characteristics of stress-induced defects under positive bias in high-k/InGaAs stacks

The introduction of InGaAs as a channel material for complementary metal-oxide-semiconductor technology presents major challenges in terms of the characterization of the various defects that affect the performance and reliability. Understanding the generation of defects by constant voltage stresses is crucial in terms of their concentration profiles and energy levels. In particular, we want to understand the real nature of the defects responsible for the dispersion of C-V in strong accumulation. Here, we show that the degradation under positive bias of metal/Al2O3/n-InGaAs capacitors reveals two contributions depending on the temperature that affects the C-V curves in a different way. Based on features of stressed C-V curves, it is possible to estimate the onset point of the distribution of border traps near the midgap condition. The results suggest that these defects are strongly related to the characteristics of the InGaAs substrate.Fil: Palumbo, Félix Roberto Mario. Technion - Israel Institute of Technology; Israel. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Winter, R.. Technion - Israel Institute of Technology; IsraelFil: Krylov, I.. Technion - Israel Institute of Technology; IsraelFil: Eizenberg, M.. Technion - Israel Institute of Technology; Israe

Photon-Number-Splitting versus Cloning Attacks in Practical Implementations of the Bennett-Brassard 1984 protocol for Quantum Cryptography

In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs better than those described before. Using it, we confirm that, in the presence of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS. However, this improvement is very small for the implementations of the Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks is conceptually interesting but basically does not change the value of the security parameters of BB84. The main results are valid both for Poissonian and sub-Poissonian sources.Comment: 11 pages, 5 figures; "intuitive" formula (31) adde

Analysis of the quark sector in the 2HDM-III with a four-zero Yukawa texture using the most recent data on the CKM matrix

In this letter we analyse, in the context of the general 2-Higgs Doublet Model, the structure of the Yukawa matrices, $\widetilde{ \bf Y}_{ _{1,2} }^{q}$, by assuming a four-zero texture ansatz for their definition. In this framework, we obtain compact expressions for $\widetilde{ \bf Y}_{ _{1,2} }^{q}$, which are reduced to the Cheng and Sher ansatz with the difference that they are obtained naturally as a direct consequence of the invariants of the fermion mass matrices. Furthermore, in order to avoid large flavour violating effects coming from charged Higgs exchange, we consider the main flavour constraints on the off-diagonal terms of Yukawa texture {{$\left( \widetilde{\chi}_{j}^q \right)_{kl}$}} ($k\neq l$). We perform a $\chi^2$-fit based on current experimental data on the quark masses and the Cabibbo-Kobayashi-Maskawa mixing matrix ${ \bf V}_{\rm CKM }$. Hence, we obtain the allowed ranges for the parameters $\widetilde{ \bf Y}_{ _{1,2} }^{q}$ at 1$\sigma$ for several values of $\tan \beta$. The results are in complete agreement with the bounds obtained taking into account constraints on Flavour Changing Neutral Currents reported in the literature.Comment: 12 pages, 1 figure. Version accepted in Phys. Lett.

Pure spin current manipulation in antiferromagnetically exchange coupled heterostructures

We present a model to describe the spin currents generated by ferromagnet/spacer/ferromagnet exchange coupled trilayer systems and heavy metal layers with strong spin-orbit coupling. By exploiting the magnitude of the exchange coupling (oscillatory RKKY-like coupling) and the spin-flop transition in the magnetization process, it has been possible to produce spin currents polarized in arbitrary directions. The spin-flop transition of the trilayer system originates pure spin currents whose polarization vector depends on the exchange field and the magnetization equilibrium angles. We also discuss a protocol to control the polarization sign of the pure spin current injected into the metallic layer by changing the initial conditions of magnetization of the ferromagnetic layers previously to the spin pumping and inverse spin Hall effect experiments. The small differences in the ferromagnetic layers lead to a change in the magnetization vector rotation that permits the control of the sign of the induced voltage components due to the inverse spin Hall effect. Our results can lead to important advances in hybrid spintronic devices with new functionalities, particularly, the ability to control microscopic parameters such as the polarization direction and the sign of the pure spin current through the variation of macroscopic parameters, such as the external magnetic field or the thickness of the spacer in antiferromagnetic exchange coupled systems.Fil: Avilés Félix, L.. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Butera, Alejandro Ricardo. Comision Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones no Nucleares. Gerencia de Física (Centro Atómico Bariloche). División Resonancias Magnéticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: González Chávez, D. E.. Centro Brasileiro de Pesquisas Físicas; BrasilFil: Sommer, R. L.. Centro Brasileiro de Pesquisas Físicas; BrasilFil: Gomez, Javier Enrique. Comision Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones no Nucleares. Gerencia de Física (Centro Atómico Bariloche). División Resonancias Magnéticas; Argentin

On the Rational Type 0f Moment Angle Complexes

In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1)) which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the literature in the proof of Theorem 1.3. There is some text overlap with arXiv:1410.645

Teratogenic, oxidative stress and behavioural outcomes of three fungicides of natural origin (Equisetum arvense, mimosa tenuiflora, thymol) on zebrafish (danio rerio)

The improper use of synthetic fungicides has raised public concerns related to environmental pollution and animal health. Over the years, plant-derived antifungals have been investigated as safer alternatives, although little scientific evidence of its neurodevelopmental effects exist. The main objective of this study was to explore the effects of three alternative natural extracts (Equisetum arvense, Mimosa tenuiflora, Thymol) with antifungal properties during the early development of zebrafish by evaluating different teratogenic, oxidative stress and behavioural outcomes. Following the determination of the 96 h-LC50, exposure to sublethal concentrations showed the safety profile of both E. arvense and M. tenuiflora. However, following 96-h exposure to Thymol, increased lethality, pericardial oedema, yolk and eye deformations, and decreased body length were observed. The reduced and oxidized glutathione (GSH:GSSG) ratio was increased, and the glutathione-s-transferase activity in the group exposed to the highest Thymol concentration. Overall, these results support a more reducing environment associated with possible effects at the cellular proliferation level. In addition, the disruption of behavioural states (fear-and anxiety-like disorders) were noted, pointing to alterations in the c-Jun N-terminal kinase developmental signalling pathway, although further studies are required to explore this rationale. Notwithstanding, the results provide direct evidence of the teratogenic effects of Thymol, which might have consequences for non-target species.This research was funded by European Investment Funds by FEDER/COMPETE/POCI– Operational Competitiveness and Internationalization Programme, under the project POCI-01–0145-FEDER-006958 and National Funds by FCT—“Fundação para a Ciência e a Tecnologia”, under the project UIBD/04033/2020 and under the PhD grant number SFRH/BD/144904/2019