Phase Optimization for Multipoint Haptic Feedback Based on Ultrasound Array

Ultrasound based haptic feedback is a potential technology for human-computer interaction (HCI) with the advantages of low cost, low power consumption and controlled force. In this paper, the phase optimization for multipoint haptic feedback based on ultrasound array is investigated and the corresponding experimental verification is provided. A mathematical model of acoustic pressure is established for the ultrasound array and then a phase optimization model for an ultrasound transducer is constructed. We propose a pseudo-inverse (PINV) algorithm to accurately determine the phase contribution of each transducer in the ultrasound array. By controlling the phase difference of the ultrasound array, the multipoint focusing forces are formed leading to various shapes such as geometries and letters that can be visualized. Because the unconstrained PINV solution results in unequal amplitudes for each transducer, a weighted amplitude iterative optimization is deployed to further optimize the phase solution, by which the uniform amplitude distributions of each transducer are obtained. For the purpose of experimental verifications, a platform of ultrasound haptic feedback consisting of a Field Programmable Gate Array (FPGA), an electrical circuit and an ultrasound transducer array is prototyped. The haptic performances of single point, multiple points and dynamic trajectory were verified by controlling the ultrasound force exerted on the liquid surface. The experimental results demonstrate that the proposed phase optimization model and theoretical results are effective and feasible, and the acoustic pressure distribution is consistent with the simulation results.

Modeling the waves of Covid-19

Classical approaches to modeling the spread of epidemics are based on two assumptions: the exponential growth of the total number of infections and the saturation due to the herd immunity. With Covid-19, the growth is essentially power-type, especially during the middle stages, and the saturation is currently mostly due to the protective measures. Focusing on these features and the role of epidemic management, we obtain differential equations for the total number of detected cases of Covid-19, which describe the actual curves in many countries almost with the accuracy of physics laws. The two-phase solution we propose worked very well almost for the whole periods of the spread practically in all countries we analyzed that reached the saturation during the first waves. Bessel functions play the key role in our approach. Due to a very small number of parameters, namely, the initial transmission rate and the intensity of the hard and soft measures, we obtain a convincing explanation of the surprising uniformity of the curves of the total numbers of detected infections in many different areas. This theory can serve as a tool for forecasting the epidemic spread and evaluating the efficiency of the protective measures, which is very much needed for epidemics. For instance, the accuracy was very high for the early projection for the 3rd wave in the USA; projections for India, South Africa and UK are considered.

Actual Symmetry of Symmetric Molecular Adducts in the Gas Phase, Solution and in the Solid State

This review discusses molecular adducts, whose composition allows a symmetric structure. Such adducts are popular model systems, as they are useful for analyzing the effect of structure on the property selected for study since they allow one to reduce the number of parameters. The main objectives of this discussion are to evaluate the influence of the surroundings on the symmetry of these adducts, steric hindrances within the adducts, competition between different noncovalent interactions responsible for stabilizing the adducts, and experimental methods that can be used to study the symmetry at different time scales. This review considers the following central binding units: hydrogen (proton), halogen (anion), metal (cation), water (hydrogen peroxide).

Modeling the spread of Covid-19 under active management

Classical approaches to modeling the spread of epidemics are based on two assumptions: the exponential growth of the total number of infections and the saturation due to the herd immunity. With Covid-19, the growth is essentially power-type, especially during the middle stages, and the saturation is currently mostly due to the protective measures. Focusing on these features and the role of epidemic management, we obtain differential equations for the total number of detected cases of Covid-19, which describe the actual curves in many countries almost with the accuracy of physics laws. The two-phase solution we propose works very well almost for the whole periods of the spread practically in all countries we analyzed that reached the saturation during the first waves. Bessel functions play the key role in our approach. Due to a very small number of parameters, namely, the initial transmission rate and the intensity of the hard and soft measures, we obtain a convincing explanation of the surprising uniformity of the curves of the total numbers of detected infections in many different areas. This theory can serve as a tool for forecasting the epidemic spread and evaluating the efficiency of the protective measures, which is very much needed for epidemics. As its practical application, the computer programs aimed at providing projections for late stages of Covid-19 proved to be remarkably stable in many countries, including Western Europe, the USA and some in Asia. We provide a projection for the saturation of the 3rd wave in the USA: the corresponding number of total, detected or not, cases can presumably reach then the herd immunity levels (G-strains). This can be used to analyze the efficiency of the vaccinations.