Lorentzian geometrical structures with global time, Gravity and Electrodynamics

We investigate Lorentzian structures in the four-dimensionalspace-time, supplemented either by a covector field of thetime-direction or by a scalar field of the global time. Furthermore,we propose a new metrizable model of the gravity. In contrast to theusual Theory of General Relativity where all ten components of thesymmetric pseudo-metrics are independent variables, the presentedhere model of the gravity essentially depend only on singlefour-covector field, restricted to have only three-independentcomponents. However, we prove that the Gravitational field, ruled bythe proposed model and generated by some massive body, resting andspherically symmetric in some coordinate system, is given by apseudo-metrics, which coincides with thewell known Schwarzschild metric from the General Relativity. TheMaxwell equations and Electrodynamics are also investigated in theframes of the proposed model. In particular, we derive the covariantformulation of Electrodynamics of moving dielectrics andpara/diamagnetic mediums.

High-throughput particle focusing and separation in split-recombination channel

Inertial microfluidic has been widely applied to manipulate particles or bio-sample based on the inertial lift force and Dean Vortices. This technology provides significant advantages over conventional technologies, including simple structure, high throughput and freedom from an external field. Among many inertial microfluidic systems, the straight microchannel is commonly used to produce inertial focusing, which is a phenomenon that particles or cells are aligned and separated based on their size under the influence of inertial lift force. Besides the inertial lift force, flow drag forces induced by the geometrical structures of microchannel can also affect particle focusing. Herein, a split-recombination microchannel, consisting of curved and straight channels, is proposed to focus and separate particles at high flow rate. As compared with the straight channel, the particle focusing in the split-recombination channel is greatly improved, which results from the combined effects of the inertial lift force, the curvature-induced Dean drag force and the structure of split and recombination. Moreover, the distribution of different-sized particles in designed microchannel is investigated. The results indicate that the proposed microchannel not only enhances the particle focusing but also enables the separation of different-sized particles with high throughput. Finally, it is discovered that the larger length of straight channel and curvature radius of curved channel can result in a more efficient particle separation. Another important feature of designed split-recombination microchannel is that it can be arranged in parallel to handle large-volume samples, holding great potential in lab-on-a-chip applications.

Pythagorean Nanogeneralized Closed Sets with Application in Decision-Making

Topology is studying the objects which are considered to be equal if they may also be continually deformed through other shapes as bending and twisting without tearing or glueing them. Topology is similar in geometrical structures and quantitatively equivalent. Nanotopology is the study of set. The main goal of this article is to propose the idea of generalized closed sets in Pythagorean nanotopological spaces. In addition, the concept of semigeneralized closed sets is also defined, and their properties are investigated. An application to MADM using Pythagorean nanotopology has been proposed and illustrated using a numerical example.

On Convex Functions Associated with Symmetric Cardioid Domain

The geometry of the image domain plays an important role in the characterization of analytic functions. Therefore, for a comprehensive and detailed study of these functions, a thorough analysis of the geometrical properties of their domains is of prime interest. In this regard, new geometrical structures are introduced and studied as an image domain and then their subsequent analytic functions are defined. Inspired and motivated by ongoing research, Malik et al. introduced a very innovative domain named the cardioid domain, which is symmetric about a real axis. Extending the same work on this symmetric cardioid domain, in this article, we provide a deeper analysis and define and study the convex functions associated with the symmetric cardioid domain, named cardio-convex functions.

Effect of geometrical structure on transport properties of silicene nanoconstrictions*

We study electrical modulation of transport properties of silicene nanoconstrictions with different geometrical structures. We investigate the effects of the position and width of the central scattering region on the conductance with increasing Fermi energy. It is found that the conductance significantly depends on the position and the width of the nanoconstriction. Interestingly, the symmetrical structure of the central constriction region can induce a resonance effect and significantly increase the systemʼs conductance. We also propose a novel two-channel structure with an excellent performance on the conductance compared to the one-channel structure with the same total width. Such geometrically-induced conductance modulation of silicene nanostructures can be achieved in practice via current nanofabrication technology.

Dynamic Behavior of Sandwich Structures with Magnetorheological Elastomer: A Review

Magnetorheological (MR) materials are classified as smart materials that can alter their rheological features once exposed to peripheral magnetic fields. MR materials have been a standard and one of the primary smart materials for the last few decades due to their outstanding vibration control performance in adaptive sandwich structures and systems. This paper reviews the vibration suppression investigations of flexible constructions using MR elastomers (MREs). In relations of field-dependent controllability, physical features such as stiffness and the damping of different geometrical structures integrated with the core layer of MREs are explored. The veracity of the knowledge is discussed in this article, whereby sandwich structures with different MR treatment configurations are analyzed for free and forced vibration, MRE sandwich structures are analyzed for stability under different working conditions, and the optimal positions of fully and partially treated MRE sandwich structures for improved vibration control are identified. MR materials′ field-dependent stiffness and damping characteristics are also discussed in this article. A few of the most noteworthy research articles over the last several years have been summarized.

Complex Dynamics of a Four-Dimensional Circuit System

Combining qualitative analysis and numerical technique, the present work revisits a four-dimensional circuit system in [Ma et al., 2016] and mainly reveals some of its rich dynamics not yet investigated: pitchfork bifurcation, Hopf bifurcation, singularly degenerate heteroclinic cycle, globally exponentially attractive set, invariant algebraic surface and heteroclinic orbit. The main contributions of the work are summarized as follows: Firstly, it is proved that there exists a globally exponentially attractive set with three different exponential rates by constructing a suitable Lyapunov function. Secondly, the existence of a pair of heteroclinic orbits is also proved by utilizing two different Lyapunov functions. Finally, numerical simulations not only are consistent with theoretical results, but also illustrate potential existence of hidden attractors in its Lorenz-type subsystem, singularly degenerate heteroclinic cycles with distinct geometrical structures and nearby hyperchaotic attractors in the case of small [Formula: see text], i.e. hyperchaotic attractors and nearby pseudo singularly degenerate heteroclinic cycles, i.e. a short-duration transient of singularly degenerate heteroclinic cycles approaching infinity, or the true ones consisting of normally hyperbolic saddle-foci (or saddle-nodes) and stable node-foci, giving some kind of forming mechanism of hyperchaos.

Monitoring the Recovery after 2016 Hurricane Matthew in Haiti via Markovian Multitemporal Region-Based Modeling

The aim of this paper is to address the monitoring of the recovery phase in the aftermath of Hurricane Matthew (28 September–10 October 2016) in the town of Jérémie, southwestern Haiti. This is accomplished via a novel change detection method that has been formulated, in a data fusion perspective, in terms of multitemporal supervised classification. The availability of very high resolution images provided by last-generation satellite synthetic aperture radar (SAR) and optical sensors makes this analysis promising from an application perspective and simultaneously challenging from a processing viewpoint. Indeed, pursuing such a goal requires the development of novel methodologies able to exploit the large amount of detailed information provided by this type of data. To take advantage of the temporal and spatial information associated with such images, the proposed method integrates multisensor, multisource, and contextual information. Markov random field modeling is adopted here to integrate the spatial context and the temporal correlation associated with images acquired at different dates. Moreover, the adoption of a region-based approach allows for the characterization of the geometrical structures in the images through multiple segmentation maps at different scales and times. The performances of the proposed approach are evaluated on multisensor pairs of COSMO-SkyMed SAR and Pléiades optical images acquired over Jérémie, in the aftermath of and during the three years after Hurricane Matthew. The effectiveness of the change detection results is analyzed both quantitatively, through the computation of accuracy measures on a test set, and qualitatively, by visual inspection of the classification maps. The robustness of the proposed method with respect to different algorithmic choices is also assessed, and the detected changes are discussed in relation to the recovery endeavors in the area and ground-truth data collected in the field in April 2019.

Experimental and Computational Investigation of Lattice Sandwich Structures Constructed by Additive Manufacturing Technologies

Additive Manufacturing (AM) technologies offer the ability to construct complex geometrical structures in short manufacturing lead time coupled with a relatively low production cost when compared to traditional manufacturing processes. The next trend in mechanical engineering design is the adaption of design strategies that build products with lightweight lattice geometries like sandwich structures. These structures possess low mass, large surface area to volume ratio, high porosity, and adequate mechanical behavior, which are properties of great importance in scientific fields such as bioengineering, automotive, and aerospace engineering. The present work is focused on producing sandwich structures with complex lattice patterns like the Triply Periodic Minimal Surface (TPMS) Schwarz diamond structure. The specimens were manufactured with two different Additive Manufacturing procedures employing various relative densities. More specifically, Material Jetting Printing (MJP) and Fused Filament Fabrication (FFF) processes were employed to investigate the performance of Acrylonitrile Butadiene Styrene (ABS) lightweight lattice structures. These structures were examined using digital microscopy in order to measure the dimensional accuracy and the surface characteristics of the utilized AM technologies. Furthermore, three-point bending tests and finite elements analyses have been applied to investigate the mechanical performance of the proposed technologies and designs as well as the influence of the relative density on the Schwarz diamond TPMS structure. The experimental results demonstrate that the investigated structure possesses a remarkable performance in respect to its weight due to the specific distribution of its material in space.