Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the 1S0 neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

Study on Simulation Method of Virtual Material for Modal Characteristics of Steel-BFPC Joint Surface

Basalt fiber polymer concrete (BFPC) machine tool has the properties of lightweight and high damping, and the BFPC machine tool has excellent vibration damping and anti-vibration performance, which can improve the processing performance of the machine tool. There are many steel-BFPC jointsurfaces in the machine tool, and thesejoint surfaceshavea key influence on the dynamic performance such as the modal performance of the machine tool. In order to establish a virtual material simulation analysis method for modal characteristics of steel-BFPC joint surface, the detection principle of contact parameters of steel-BFPC joint surface was studied by using forced vibration theory, and the contact parameter detection experiment of steel-BFPC joint surface was designed. The virtual material model of BFPC joint surface was established, and the theoretical formulas of equivalent elastic modulus and equivalent shear modulus were derived based on the identified parameters of the BFPC joint surface. For the correctness of the analysis theory, a BFPC bed was taken as an example to study the modal performance of the BFPC bed by means of experiment and virtual material simulation analysis, respectively. The results of simulation analysis were compared with the experimental results. The results show that the maximum error of thenatural frequency is only 6.23%, and the modes of each order are consistent, which prove the effectiveness and accuracy of the virtual material simulation analysis method.

Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface

The continuous development of computer technology has made it applicable in many scientific fields, including research into a wide range of processes in agricultural machines. It allows the simulation of very complex physical phenomena, including grain motion. A recently discovered discrete element method (DEM) is used for this purpose. It involves direct integration of equations of grain system motion under the action of various forces, the most important of which are contact forces. The method’s accuracy depends mainly on precisely developed mathematical models of contacts. The creation of such models requires empirical validation, an experiment that investigates the course of contact forces at the moment of the impact of the grains. To achieve this, specialised test stations equipped with force and speed sensors were developed. The correct selection of testing equipment and interpretation of results play a decisive role in this type of research. This paper focuses on the evaluation of the force sensor dynamic properties’ influence on the measurement accuracy of the course of the plant grain impact forces against a stiff surface. The issue was examined using the computer simulation method. A proprietary computer software with the main calculation module and data input procedures, which presents results in a graphic form, was used for calculations. From the simulation, graphs of the contact force and force signal from the sensor were obtained. This helped to clearly indicate the essence of the correct selection of parameters used in the tests of sensors, which should be characterised by high resonance frequency.

Coupling fractal model for fretting wear on rough contact surfaces

In this paper, a fretting damage model based on fractal theory is proposed. The Weierstrass-Mandelbrot function of fractal theory is used to represent the rough contact surface, and a corresponding contact parameter analysis method is also established. Based on neural network algorithm, the values of fractal parameters are fitted, and the fitting accuracy has been greatly improved compared with traditional methods. According to the fractal parameters of the actual surface, the fretting wear process of the rough contact surface is analyzed based on theory of adhesive and three body abrasive wear. A generic program for the analysis of three-dimensional fretting wear problems is also proposed. Compared with material tests, the prediction error of fretting wear simulation model is 13.4% for wear depth and 16.7% and 3.9% for width and length of wear scar in stable wear stage. The prediction results show that the model can be applied to the prediction of the actual three-dimensional fretting wear model.

DYNAMICAL CONTACT PARAMETER IDENTIFICATION OF SPINDLE-HOLDER-TOOL ASSEMBLIES USING SOFT COMPUTING TECHNIQUES

In industry, the capability to predict the tool point frequency response function (FRF) is an essential matter in order to ensure the stability of cutting processes. Fast and accurate identification of contact parameters in spindle-holder-tool assemblies is very important issue in machining dynamics analysis. This work is an attempt to illustrate the utility of soft computing techniques in identification and prediction contact parameters of spindle-holder-tool assemblies. In this paper, three soft computing techniques, namely, genetic algorithm (GA), simulated annealing (SA), and particle swarm optimization (PSO) were used for identification of contact dynamics in spindle-holder-tool assemblies. In order to verify the proposed identification approaches, numerical and experimental analysis of the spindle-holder-tool assembly was carried out and the results are presented. Finally, a model based on the adaptive neural fuzzy inference system (ANFIS) was used to predict the dynamical contact parameters at the holder-tool interface of a spindle-holder-tool assembly. Accuracy and performance of the ANFIS model has been found to be satisfactory while validated with experimental results.

How can contemporary climate research help understand epidemic dynamics? Ensemble approach and snapshot attractors

Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed upon a monotonic decay needs a different description from that of the standard chaotic dynamics. The concept of snapshot attractors and their natural distribution has been adopted from the field of the latest climate change research. This shows the importance of the finite-time chaotic effect and ensemble interpretation while investigating the spread of a disease. By defining statistical measures over the ensemble, we can interpret the internal variability of the epidemic as the onset of complex dynamics—even for those values of contact parameters where originally regular behaviour is expected. We argue that anomalous outbreaks of the infectious class cannot die out until transient chaos is presented in the system. Nevertheless, this fact becomes apparent by using an ensemble approach rather than a single trajectory representation. These findings are applicable generally in explicitly time-dependent epidemic systems regardless of parameter values and time scales.

Modeling, analysis and simulations of MERS outbreak in Saudi Arabia

This work describes a continuous differential equations model for the dynamics of Middle Eastern Respiratory Syndrome (MERS) and provides its computer simulations. It is a continuation of our previous paper Al-Asuoad et al. (Biomath, 2016) and it extends the simulations results provided there, which were restricted to the city of Riyadh, to the whole of Saudi Arabia. In addition, it updates the results for the city of Riyadh itself. Using an optimization procedure, the system coefficients were obtained from published data, and the model allows for the prediction of possible scenarios for the transmission and spread of the disease in the near future. This, in turn, allows for the application of possible disease control measures. The model is found to be very sensitive to the daily effective contact parameter, and the presented simulations indicate that the system is very close to the bifurcation of the stability of the Disease Free Equilibrium (DFE) and appearance of the Endemic Equilibrium (EE), which indicates that the disease will not decay substantially in the near future. Finally, we establish the stability of the DFE using only the stability number $\mathcal{R}_c$, which simplifies and improves one of the main theoretical results in our previous paper.