Fractal properties of quantum spacetime

We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of \k-Minkowski, the latter being relevant in the context of quantum gravity.Comment: 4 pages, 2 figures; some minor corrections; reference adde

Characterization of qubit chains by Feynman probes

We address the characterization of qubit chains and assess the performances of local measurements compared to those provided by Feynman probes, i.e. nonlocal measurements realized by coupling a single qubit regis- ter to the chain. We show that local measurements are suitable to estimate small values of the coupling and that a Bayesian strategy may be successfully exploited to achieve optimal precision. For larger values of the coupling Bayesian local strategies do not lead to a consistent estimate. In this regime, Feynman probes may be exploited to build a consistent Bayesian estimator that saturates the Cram\'er-Rao bound, thus providing an effective characterization of the chain. Finally, we show that ultimate bounds to precision, i.e. saturation of the quantum Cram\'er-Rao bound, may be achieved by a two-step scheme employing Feynman probes followed by local measurements.Comment: 8 pages, 5 figure

Dynamics of quantum correlations in colored environments

We address the dynamics of entanglement and quantum discord for two non interacting qubits initially prepared in a maximally entangled state and then subjected to a classical colored noise, i.e. coupled with an external environment characterized by a noise spectrum of the form $1/f^{\alpha}$. More specifically, we address systems where the Gaussian approximation fails, i.e. the sole knowledge of the spectrum is not enough to determine the dynamics of quantum correlations. We thus investigate the dynamics for two different configurations of the environment: in the first case the noise spectrum is due to the interaction of each qubit with a single bistable fluctuator with an undetermined switching rate, whereas in the second case we consider a collection of classical fluctuators with fixed switching rates. In both cases we found analytical expressions for the time dependence of entanglement and quantum discord, which may be also extended to a collection of flcutuators with random switching rates. The environmental noise is introduced by means of stochastic time-dependent terms in the Hamiltonian and this allows us to describe the effects of both separate and common environments. We show that the non-Gaussian character of the noise may lead to significant effects, e.g. environments with the same power spectrum, but different configurations, give raise to opposite behavior for the quantum correlations. In particular, depending on the characteristics of the environmental noise considered, both entanglement and discord display either a monotonic decay or the phenomena of sudden death and revivals. Our results show that the microscopic structure of environment, besides its noise spectrum, is relevant for the dynamics of quantum correlations, and may be a valid starting point for the engineering of non-Gaussian colored environments.Comment: 8 pages, 3 figure

Self-reported gait unsteadiness in mildly impaired neurological patients: an objective assessment through statistical gait analysis

Background Self-reported gait unsteadiness is often a problem in neurological patients without any clinical evidence of ataxia, because it leads to reduced activity and limitations in function. However, in the literature there are only a few papers that address this disorder. The aim of this study is to identify objectively subclinical abnormal gait strategies in these patients. Methods Eleven patients affected by self-reported unsteadiness during gait (4 TBI and 7 MS) and ten healthy subjects underwent gait analysis while walking back and forth on a 15-m long corridor. Time-distance parameters, ankle sagittal motion, and muscular activity during gait were acquired by a wearable gait analysis system (Step32, DemItalia, Italy) on a high number of successive strides in the same walk and statistically processed. Both self-selected gait speed and high speed were tested under relatively unconstrained conditions. Non-parametric statistical analysis (Mann-Whitney, Wilcoxon tests) was carried out on the means of the data of the two examined groups. Results The main findings, with data adjusted for velocity of progression, show that increased double support and reduced velocity of progression are the main parameters to discriminate patients with self-reported unsteadiness from healthy controls. Muscular intervals of activation showed a significant increase in the activity duration of the Rectus Femoris and Tibialis Anterior in patients with respect to the control group at high speed. Conclusions Patients with a subjective sensation of instability, not clinically documented, walk with altered strategies, especially at high gait speed. This is thought to depend on the mechanisms of postural control and coordination. The gait anomalies detected might explain the symptoms reported by the patients and allow for a more focused treatment design. The wearable gait analysis system used for long distance statistical walking assessment was able to detect subtle differences in functional performance monitoring, otherwise not detectable by common clinical examination

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

A three-dimensional boundary element model for the analysis of polycrystalline materials at the microscale

A three-dimensional multi-domain anisotropic boundary element formulation is presented for the analysis of polycrystalline microstructures. The formulation is naturally expressed in terms of intergranular displacements and tractions that play an important role in polycrystalline micromechanics, micro-damage and micro-cracking. The artificial morphology is generated by Hardcore Voronoi tessellation, which embodies the main statistical features of polycrystalline microstructures. Each crystal is modeled as an anisotropic elastic region and the integrity of the aggregate is restored by enforcing interface continuity and equilibrium between contiguous grains. The developed technique has been applied to the numerical homogenization of SiC and the obtained results agree very well with available data

Intergranular damage and fracture in polycrystalline materials. A novel 3D microstructural grain-boundary formulation

The design of advanced materials requires a deep understanding of degradation and failure pro- cesses. It is widely recognized that the macroscopic material properties depend on the features of the microstructure. The knowledge of this link, which is the main subject of Micromechanics [1], is of relevant technological interest, as it may enable the design of materials with specific requirements by means of suitable manipulations of the microstructure. Polycrystalline materials are used in many technological applications. Their microstructure is characterized by the grains morphology, size distribution, anisotropy, crystallographic orientation, stiffness and toughness mismatch and by the physical-chemical properties of the intergranular interfaces. These aspects have a direct influence on the initiation and evolution of micro-damage, which is also sensitive to the presence of micro-imperfections. Any theory trying to explain the failure mechanisms in these materials must then accommodate a relevant number of parameters. In this study, a novel 3D grain-boundary micro-mechanical model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The microstructure is generated by means of Voronoi tessellations, able to retain the main statistical features of polycrystals. The formulation is built on a boundary integral representation of the elastic problem for the crystals, that are modeled as 3D anisotropic elastic domains with arbitrary orientation [2]. This representa- tion involves only mechanical variables at the grains interfaces, i.e. displacement jumps and trac- tions, that play an important role in the micromechanics of polycrystals. The aggregate integrity is restored by enforcing suitable intergranular conditions. The onset and evolution of intergranular damage is modeled using an extrinsic irreversible cohesive law, able to address mixed-mode fail- ure conditions. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between the formed micro-crack surfaces. The incremental-iterative algorithm for tracking the micro-evolution is presented. Several numerical tests on pseudo and fully three-dimensional microstructures are discussed. The present formulation is a promising tool in the framework of multiscale analysis of degradation and failure in polycrystalline materials

Compressive strength of heterogeneous masonry walls containing blends of brick types

The study presents a systematic approach for the evaluation of the compression strength of masonry walls composed of heterogeneous mixes of different types of blocks. First of all, the mechanics of a compressed heterogeneous masonry stack is investigated through a series of experimental tests and Finite Element models, then it is reviewed and discussed. Then, the problem of deriving the necessary material parameters entering the Hilsdorf formula is addressed. Solutions for the correct evaluation of the lacking data are presented based on the existing literature data. Finally, the well-known Hilsdorf formula is extended to the field of block blends with different mechanical properties. A deep experimental investigation on stacks and wallets made with fired clay, limestone and sandstone blocks is introduced for the first time. The comparison of the experimental data with the proposed theory points out the very good predictive capability of the extended Hilsdorf formula derived herein

Statistical evaluation of the critical distance in the finite life fatigue regime

The procedure to evaluate the critical distance with an optimized V-notched specimen is initially reviewed in the paper. This procedure was devised by the authors, and another numerical methodology was recently proposed to evaluate the uncertainty of the critical distance assessment. The input of the analysis is the combination of the statistical distribution of the fatigue properties from which the critical distance is deduced. After assuming the specimen fatigue strengths as Gaussian (normal) distributions, the critical distance turns out to be well represented by a Skew-normal distribution. This statistical assessment is extended to the finite fatigue life, in the present paper, showing experimental results for the aluminium alloy 7075-T6 at two load ratios. The fatigue strength of other specimens are finally evaluated, reconsidering the critical distance deviation, thus providing a complete uncertainty analysis of the critical distance assessment, and a successful comparison with the experimental scatter is obtained