The virial theorem and ground state energy estimates of nonlinear Schrödinger equations in $$\mathbb {R}^2$$ with square root and saturable nonlinearities in nonlinear optics

The virial theorem is a nice property for the linear Schrödinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrödinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems to be no way of getting any eigenvalue estimates. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimates of nonlinear Schrödinger (NLS) equations in \({{\mathbb {R}}^{2}}\) with square-root and saturable nonlinearity, respectively. Furthermore, we show here that the eigenvalue estimates can be used to obtain the 2nd order term (which is of order \(\ln \Gamma \)) of the lower bound of the ground state energy as the coefficient \(\Gamma \) of the nonlinear term tends to infinity.     

On the exponential stabilization of the electromagneto‐elastic system with Wentzell conditions

We consider the stabilization of the electromagneto‐elastic system with Wentzell conditions in a bounded domain of . Using the multiplier method we prove an exponential stability result under some geometric condition. Previous results of this type have recently been obtained for the coupled Maxwell/wave system with Wentzell conditions by H. Kasri and A. Heminna (Evol Equ and Control Theo 5: 235‐250, 2016)     

Trifluoromethylated Flavonoid-Based Isoxazoles as Antidiabetic and Anti-Obesity Agents: Synthesis,In Vitro α-Amylase Inhibitory Activity,Molecular Docking and Structure–Activity Relationship Analysis

Diabetes mellitus is a major health problem globally. The management of carbohydrate digestion provides an alternative treatment. Flavonoids constitute the largest group of polyphenolic compounds, produced by plants widely consumed as food and/or used for therapeutic purposes. As such, isoxazoles have attracted the attention of medicinal chemists by dint of their considerable bioactivity. Thus, the main goal of this work was to discover new hybrid molecules with properties of both flavonoids and isoxazoles in order to control carbohydrate digestion. Moreover, the trifluoromethyl group is a key entity in drug development, due to its strong lipophilicity and metabolic stability. Therefore, the present work describes the condensation of a previously synthesized trifluoromethylated flavonol with different aryl nitrile oxides, affording 13 hybrid molecules indicated as trifluoromethylated flavonoid-based isoxazoles. The structures of the obtained compounds were deduced from by ¹H NMR, ¹³C NMR, and HRMS analysis. The 15 newly synthesized compounds inhibited the activity of α-amylase with an efficacy ranging from 64.5 ± 0.7% to 94.7 ± 1.2% at a concentration of 50 μM, and with IC₅₀ values of 12.6 ± 0.2 μM–27.6 ± 1.1 μM. The most effective compounds in terms of efficacy and potency were 3b, 3h, 3j, and 3m. Among the new trifluoromethylated flavonoid-based isoxazoles, the compound 3b was the most effective inhibitor of α-amylase activity (PI = 94.7 ± 1.2% at 50 μM), with a potency (IC₅₀ = 12.6 ± 0.2 μM) similar to that of the positive control acarbose (IC₅₀ = 12.4 ± 0.1 μM). The study of the structure–activity relationship based on the molecular docking analysis showed a low binding energy, a correct mode of interaction in the active pocket of the target enzyme, and an ability to interact with the key residues of glycosidic cleavage (GLU-230 and ASP-206), explaining the inhibitory effects of α-amylase established by several derivatives.     

Dittrichia graveolens (L.) Greuter,a Rapidly Spreading Invasive Plant: Chemistry and Bioactivity

Dittrichia graveolens L. Greuter belonging to the Asteraceae family, is an aromatic herbaceous plant native to the Mediterranean region. This plant species has been extensively studied for its biological activities, including antioxidant, antitumor, antimicrobial, antifungal, anti-inflammatory, anticholinesterase, and antityrosinase, and for its peculiar metabolic profile. In particular, bioactivities are related to terpenes and flavonoids metabolites, such as borneol (40), tomentosin (189), inuviscolide (204). However, D. graveolens is also well known for causing health problems both in animals and humans. Moreover, the species is currently undergoing a dramatic northward expansion of its native range related to climate change, now including North Europe, California, and Australia. This review represents an updated overview of the 52 literature papers published in Scopus and PubMed dealing with expansion, chemistry (262 different compounds), pharmacological effects, and toxicology of D. graveolens up to October 2021. The review is intended to boost further studies to determine the molecular pathways involved in the observed activities, bioavailability, and clinical studies to explore new potential applications.     

Measurement Uncertainty,Purity, and Entanglement Dynamics of Maximally Entangled Two Qubits Interacting Spatially with Isolated Cavities: Intrinsic Decoherence Effect

In a system of two charge-qubits that are initially prepared in a maximally entangled Bell’s state, the dynamics of quantum memory-assisted entropic uncertainty, purity, and negative entanglement are investigated. Isolated external cavity fields are considered in two different configurations: coherent-even coherent and even coherent cavity fields. For different initial cavity configurations, the temporal evolution of the final state of qubits and cavities is solved analytically. The effects of intrinsic decoherence and detuning strength on the dynamics of bipartite entropic uncertainty, purity and entanglement are explored. Depending on the field parameters, nonclassical correlations can be preserved. Nonclassical correlations and revival aspects appear to be significantly inhibited when intrinsic decoherence increases. Nonclassical correlations stay longer and have greater revivals due to the high detuning of the two qubits and the coherence strength of the initial cavity fields. Quantum memory-assisted entropic uncertainty and entropy have similar dynamics while the negativity presents fewer revivals in contrast.     

Entanglement Dynamics Induced by a Squeezed Coherent Cavity Coupled Nonlinearly with a Qubit and Filled with a Kerr-Like Medium

An analytical solution for a master equation describing the dynamics of a qubit interacting with a nonlinear Kerr-like cavity through intensity-dependent coupling is established. A superposition of squeezed coherent states is propped as the initial cavity field. The dynamics of the entangled qubit-cavity states are explored by negativity for different deformed function of the intensity-dependent coupling. We have examined the effects of the Kerr-like nonlinearity and the qubit-cavity detuning as well as the phase cavity damping on the generated entanglement. The intensity-dependent coupling increases the sensitivity of the generated entanglement to the phase-damping. The stability and the strength of the entanglement are controlled by the Kerr-like nonlinearity, the qubit-cavity detuning, and the initial cavity non-classicality. These physical parameters enhance the robustness of the qubit-cavity entanglement against the cavity phase-damping. The high initial cavity non-classicality enhances the robustness of the qubit-cavity entanglement against the phase-damping effect.     

Wavelength and beam launching effects on silica optical fiber in local area networks

In this paper, we report the modal dispersion of silica graded-index optical fibers as a function of the input mode parameters and lunching conditions in local area network (LAN) context. In that, we examine the mode-depending parameters, namely, modal delay, modal attenuation and mode-coupling effects as a function of wavelength. We show that the number of excited mode groups depends strongly on the spot beam radius when the fiber is excited with an axial Gaussian beam where we find an optimal axial diameter exciting only two mode groups. We present a comparison of the number of excited mode groups, the optimal spot radius beam, the signal penalty and the 3-dB baseband bandwidth enhancement for the optimal axial launching compared with full mode excitation, offset launching and mode-field matched axial launching.     

Surrogate Model via Artificial Intelligence Method for Accelerating Screening Materials and Performance Prediction

Predicting the performance of mechanical properties is an important and current issue in the field of engineering and materials science, but traditional experiments and modeling calculations often consume large amounts of time and resources. Therefore, it is imperative to use appropriate methods to accelerate the process of material selection and design. The artificial intelligence method, particularly deep learning models, has been verified as an effective and efficient method for handling computer vision and neural language problems. In this paper, a deep learning surrogate model (DLS) is proposed for predicting the mechanical performance of materials, that is, the maximum stress value under complex working conditions. The DLS can reproduce the finite element analysis model results with 98.79% accuracy. The results show that deep learning has great potential. This research also provides a new approach for material screening in practical engineering.     

Machine Learning Approaches for Thermoelectric Materials Research

Thermoelectric (TE) materials provide a solid‐state solution in waste heat recovery and refrigeration. During the past few decades, considerable effort has been devoted towards improving the performance of TE materials, which requires the optimization of multiple interrelated properties. A fundamental understanding of the interaction processes between the various energy carriers, such as electrons and phonons, is critical for advances in the development of TE materials. However, this understanding remains challenging primarily due to the inaccessibility of time scales using standard atomistic simulations. Machine learning methods, well known for their data‐analysis capability, have been successfully applied in research on TE materials in recent years. Here, an overview of the machine learning methods used in thermoelectric studies is provided, with the role that each machine learning method plays being systematically discussed. Furthermore, to date, the scale of thermoelectric‐related databases is much smaller than those in other fields, such as e‐commerce, image identification, and speech recognition. To overcome this limitation, possible strategies to utilize small databases in promoting materials science are also discussed. Finally, a brief conclusion and outlook are presented.