X-ray imaging of spin currents and magnetisation dynamics at the nanoscale

Understanding how spins move in time and space is the aim of both fundamental and applied research in modern magnetism. Over the past three decades, research in this field has led to technological advances that have had a major impact on our society, while improving the understanding of the fundamentals of spin physics. However, important questions still remain unanswered, because it is experimentally challenging to directly observe spins and their motion with a combined high spatial and temporal resolution. In this article, we present an overview of the recent advances in X-ray microscopy that allow researchers to directly watch spins move in time and space at the microscopically relevant scales. We discuss scanning X-ray transmission microscopy (STXM) at resonant soft X-ray edges, which is available at most modern synchrotron light sources. This technique measures magnetic contrast through the X-ray magnetic circular dichroism (XMCD) effect at the resonant absorption edges, while focusing the X-ray radiation at the nanometre scale, and using the intrinsic pulsed structure of synchrotron-generated X-rays to create time-resolved images of magnetism at the nanoscale. In particular, we discuss how the presence of spin currents can be detected by imaging spin accumulation, and how the magnetisation dynamics in thin ferromagnetic films can be directly imaged. We discuss how a direct look at the phenomena allows for a deeper understanding of the the physics at play, that is not accessible to other, more indirect techniques. Finally, we present an overview of the exciting opportunities that lie ahead to further understand the fundamentals of novel spin physics, opportunities offered by the appearance of diffraction limited storage rings and free electron lasers.Comment: 21 pages, 10 figure

A Dissipative Model for Hydrogen Storage: Existence and Regularity Results

We prove global existence of a solution to an initial and boundary value problem for a highly nonlinear PDE system. The problem arises from a thermomechanical dissipative model describing hydrogen storage by use of metal hydrides. In order to treat the model from an analytical point of view, we formulate it as a phase transition phenomenon thanks to the introduction of a suitable phase variable. Continuum mechanics laws lead to an evolutionary problem involving three state variables: the temperature, the phase parameter and the pressure. The problem thus consists of three coupled partial differential equations combined with initial and boundary conditions. Existence and regularity of the solutions are here investigated by means of a time discretization-a priori estimates-passage to the limit procedure joined with compactness and monotonicity arguments

The Relevance of the Policies of Development in the Agri-Food Sector of Emilia-Romagna Region

The aim of this paper is to analysis the impact of the policies of development and investments in the food industry at geographical and enterprises levels. We will analysis how the different geographical areas inside the Italian region Emilia-Romagna are sensitive to the development policies. A Principal Component Analysis and a Cluster Analysis will be applied to determine the most homogeneous geographical areas with respect to the considered variables. Then for evaluating the sensibility of these areas with respect to changes in investments and policies for food industry enterprise will be applied a Multicriterial Analysis and a Sensitivity Analysis.Agri-food sector, Development Policies, Food industry, Multicriterial Analysis, Region Emilia-Romagna, Sensitivity Analysis, Community/Rural/Urban Development,

Singular limit of an integrodifferential system related to the entropy balance

A thermodynamic model describing phase transitions with thermal memory, in terms of an entropy equation and a momentum balance for the microforces, is adressed. Convergence results and error estimates are proved for the related integrodifferential system of PDE as the sequence of memory kernels converges to a multiple of a Dirac delta, in a suitable sense.Comment: Key words: entropy equation, thermal memory, phase field model, nonlinear partial differential equations, asymptotics on the memory ter

Three-loop mixed QCD-electroweak corrections to Higgs boson gluon fusion

We compute the contribution of three-loop mixed QCD-electroweak corrections ($\alpha_S^2\alpha^2$) to the $gg \to H$ scattering amplitude. We employ the method of differential equations to compute the relevant integrals and express them in terms of Goncharov polylogarithms.Comment: 21 pages, associated ancillary files distributed with the paper or available from external repository. Correct typos and reference

The Eulerian numbers on restricted centrosymmetric permutations

We study the descent distribution over the set of centrosymmetric permutations that avoid the pattern of length 3. Our main tool in the most puzzling case, namely, $\tau=123$ and $n$ even, is a bijection that associates a Dyck prefix of length $2n$ to every centrosymmetric permutation in $S_{2n}$ that avoids 123.Comment: 17 pages, 6 figure