Magnetism at Finite Temperatures

Thermal properties of magnets are dominated by low-lying excitations, perused systematically. Magnon spectra of elementary metals and compounds are obtained theoretically and compared with experimental data. Spin fluctuations are discussed in mean-field theory to obtain ab initio estimates of ordering temperatures for a multitude of magnetic systems. The free energy is connected with dynamic susceptibility which supplies a solid basis for the magnetic phase of ferromagnetic compounds. Methods derived to obtain Heisenberg exchange constants from first-principle calculations are compared with experimental data. Magnetic skyrmions enrich the field of magnetism and are of possible use for data technology applications. Several cases are discussed and classified showing theoretical and experimental data. For high temperatures the disordered local moment picture supplies an alternative theory for magnetism where the coherent-potential approximation is used to solve the electronic-structure problem in an alloy analogy. The basic theory is presented and discussed together with experimental data.

On the VC-dimension of half-spaces with respect to convex sets

A family S of convex sets in the plane defines a hypergraph H = (S, E) as follows. Every subfamily S' of S defines a hyperedge of H if and only if there exists a halfspace h that fully contains S' , and no other set of S is fully contained in h. In this case, we say that h realizes S'. We say a set S is shattered, if all its subsets are realized. The VC-dimension of a hypergraph H is the size of the largest shattered set. We show that the VC-dimension for pairwise disjoint convex sets in the plane is bounded by 3, and this is tight. In contrast, we show the VC-dimension of convex sets in the plane (not necessarily disjoint) is unbounded. We provide a quadratic lower bound in the number of pairs of intersecting sets in a shattered family of convex sets in the plane. We also show that the VC-dimension is unbounded for pairwise disjoint convex sets in R^d , for d > 2. We focus on, possibly intersecting, segments in the plane and determine that the VC-dimension is always at most 5. And this is tight, as we construct a set of five segments that can be shattered. We give two exemplary applications. One for a geometric set cover problem and one for a range-query data structure problem, to motivate our findings.

The Prevalence Disability resulting from adult acquired Foot Flat Deformity among Middle aged population

Aim: To investigate about the prevalence of disability resulting from adult acquired foot flat deformity (AAFD) among middle aged population. Background: Adult acquired foot flat deformity (AAFD) which is also known as posterior tibialis tendon dysfunction (PTTD) is the condition which leads to pain due to the collapse of the longitudinal (length wise) arch of the foot. Its affects women more than non, peaking age of 55 years. The prevalence of flat foot is uncertain due to the lack of exact clinical or radiographic criteria. The foot structure problem which affects the functional activity in the adult population has been poorly studied. So the present study was undertaken about the prevalence of disability resulting from AAFD which may help to develop preventive approaches, as increased awareness serve to help the patient with earlier referral and treatment by limiting their disability. Methodology: 50 subjects who was diagnosed as AAFD was included in the study based on the inclusion and exclusion criteria. Foot function index score was calculated for the samples. Outcome Measure: Foot function index scale. Results: The total mean score is 112.75. The prevalence of disability resulting from adult acquired foot flat deformity which affects the quality of life for samples taken is 66%.

A Dependent Structure of Interdependence: Structure and Agency in Relational Perspective

In this article I argue for a relational approach to the agency–structure problem. Structure has three dimensions from this perspective but, at its most fundamental, it is a network comprising social actors (human and corporate) and the relations connecting them. Defined thus structure has measurable properties which generate both opportunities and constraints for actors and which shape processes, such as diffusion, which affect and implicate them. Agency is integral to this model. Actors are the nodes of the network and their relations are built, maintained, modified and broken by way of their interactions. However, I argue that the human organism only fully becomes a social actor by way of interaction. In effect, both agency and structure are emergent properties of social interactions/relations which act back upon and shape those interactions/relations. In addition to resolving theoretical problems this approach has the advantage of facilitating empirical analysis of structure.

Reduction of the molecular hamiltonian matrix using quantum community detection

Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

A simplified numerical and analytical study for assessing the seismic response of a gravity concrete lock

ABSTRACT: This work presents the dynamic response of a lock subjected to the horizontal S0E component of the El Centro earthquake for empty and completely filled water chamber cases, by coupled fluid-structure analysis. Initially, the lock was studied by approximation, considering it similar to the case of a double piston coupled to a two-dimensional acoustic cavity (tank), representing a simplified analytical model of the fluid-structure problem. This analytical formulation can be compared with numerical results, in order to qualify the responses of the ultimate problem to be investigated. In all the analyses performed, modeling and numerical simulations were done using the finite element method (FEM), supported by the commercial software ANSYS.

Benchmarking Adaptive Variational Quantum Eigensolvers

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

Freeze-in dark matter from secret neutrino interactions

We investigate a simplified freeze-in dark-matter model in which the dark matter only interacts with the standard-model neutrinos via a light scalar. The extremely small coupling for the freeze-in mechanism is naturally realized in several neutrino-portal scenarios with the secret neutrino interactions. We study possible evolution history of the hidden sector: the dark sector would undergo pure freeze-in production if the interactions between the dark-sector particles are negligible, while thermal equilibrium within the dark sector could occur if the reannihilation of the dark matter and the scalar mediator is rapid enough. We investigate the relic abundance in the freeze-in and dark freeze-out regimes, calculate evolution of the dark temperature, and study its phenomenological aspects on BBN and CMB constraints, the indirect-detection signature, as well as the potential to solve the small scale structure problem.