Simple Approximate Solutions for Dynamic Response of Suspension System

An approximate simplified analytic solution is proposed for the one DOF (degree of freedom) static and dynamic displacements alongside the stiffness (dynamic and static) and damping coefficients (minimum and maximum/critical values) of a parallel spring-damper suspension system connected to a solid mass-body gaining its energy by falling from height h. The analytic solution for the prescribed system is based on energy conservation equilibrium, considering the impact by a special G parameter. The formulation is based on the works performed by Timoshenko (1928), Mindlin (1945), and the U. S. army-engineering handbook (1975, 1982). A comparison between the prescribed studies formulations and current development has led to qualitative agreement. Moreover, quantitative agreement was found between the current prescribed suspension properties approximate value - results and the traditionally time dependent (transient, frequency) parameter properties. Also, coupling models that concerns the linkage between different work and energy terms, e.g., the damping energy, friction work, spring potential energy and gravitational energy model was performed. Moreover, approximate analytic solution was proposed for both cases (friction and coupling case), whereas the uncoupling and the coupling cases were found to agree qualitatively with the literature studies. Both coupling and uncoupling solutions were found to complete each other, explaining different literature attitudes and assumptions. In addition, some design points were clarified about the wire mounting isolators stiffness properties dependent on their physical behavior (compression, shear tension), based on Cavoflex catalog. Finally, the current study aims to continue and contribute the suspension, package cushioning and containers studies by using an initial simple pre – design analytic evaluation of falling mass- body (like cushion, containers, etc.).

Mathematical Framework for Breathing Chimera States

About two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. Since then such patterns, called chimera states, have been the subject of intensive study but mostly in the stationary case when the coarse-grained system dynamics remains unchanged over time. Nonstationary coherence–incoherence patterns, in particular periodically breathing chimera states, were also reported, however not investigated systematically because of their complexity. In this paper we suggest a semi-analytic solution to the above problem providing a mathematical framework for the analysis of breathing chimera states in a ring of nonlocally coupled phase oscillators. Our approach relies on the consideration of an integro-differential equation describing the long-term coarse-grained dynamics of the oscillator system. For this equation we specify a class of solutions relevant to breathing chimera states. We derive a self-consistency equation for these solutions and carry out their stability analysis. We show that our approach correctly predicts macroscopic features of breathing chimera states. Moreover, we point out its potential application to other models which can be studied using the Ott–Antonsen reduction technique.

Inhomogeneous pion condensed phase hosting topologically stable baryons

We discuss the inhomogeneous pion condensed phase within the framework of chiral perturbation theory. We show how the general expression of the condensate can be obtained solving three coupled differential equations, expressing how the pion fields are modulated in space. Upon using some simplifying assumptions, we determine an analytic solution in (3+1)-dimensions. The obtained inhomogeneous condensate is characterized by a non-vanishing topological charge, which can be identified with the baryonic number. In this way, we obtain an inhomogeneous system of pions hosting an arbitrary number of baryons at fixed position in space.

Magnetized Einstein–Maxwell-dilaton model under an external electric field

We employ an analytic solution of a magnetized Einstein–Maxwell-dilaton gravity model whose parameters have been determined so that its holographic dual has the most similarity to the confining QCD-like theories. Analyzing the total potential of a quark–antiquark pair, we are able to investigate the effect of an electric field on different phases of the background which are the thermal AdS and black hole phases. This is helpful for better understanding of the confining character and the phases of the system. We find out that the field theory dual to the black hole solution is always deconfined, as expected. However, although the thermal AdS phase generally describes the confining phase, for quark pairs parallel to B (longitudinal case) with $$B>B_{\mathrm {critical}}$$ B > B critical the response of the system mimics the deconfinement, since there is no IR wall in the bulk and the critical field $$E_s=0$$ E s = 0 , as is the case for the deconfined phase. We moreover observe that in the black hole phase with sufficiently small values of $$\mu $$ μ and in the thermal AdS phase, for both longitudinal and transverse cases, the magnetic field enhances the Schwinger effect, which can be termed as the inverse magnetic catalysis (IMC). This is deduced both from the decrease of critical electric fields and decreasing the height and width of the total potential barrier the quarks are facing with. However, by increasing $$\mu $$ μ to higher values, IMC turns into magnetic catalysis, as also observed from the diagram of the Hawking–Page phase transition temperature versus B for the background geometry.

A Reliable Iterative Transform Method for Solving an Epidemic Model

The main purpose of the work is to apply a new method, so-called LTAM, which couples the Tamimi and Ansari iterative method (TAM) with the Laplace transform (LT). This method involves solving a problem of non-fatal disease spread in a society that is assumed to have a fixed size during the epidemic period. We apply the method to give an approximate analytic solution to the nonlinear system of the intended model. Moreover, the absolute error resulting from the numerical solutions and the ten iterations of LTAM approximations of the epidemic model, along with the maximum error remainder, were calculated by using MATHEMATICA® 11.3 program to illustrate the effectiveness of the method.

On Effects of a New Method for Fractional Initial Value Problems

The aim of this study is to analyze nonlinear Liouville-Caputo time-fractional problems by a new technique which is a combination of the iterative and ARA transform methods and is denoted by IAM. First, the ARA transform method and its inverse are utilized to get rid of time fractional derivative. Later, the iterative method is applied to establish the solution of the problem in infinite series form. The main advantages of this method are that it converges to analytic solution of the problem rapidly and implementation of method is easy. Finally, outcomes of the illustrative examples prove the efficiency and accuracy of the method.

Modeling the action of anaerobic biofilm

A mathematical problem of the action of a representative biofilm in the absence of oxygen is formulated. The anaerobic process of decomposition of a dissolved organic matter is considered as a two-stage process, proceeding due to the vital activity of two groups of microorganisms. An approximate analytic solution allowing one to calculate the concentration and consumption of primary and secondary organic substrates with minimal errors has been obtained. On test examples, their rates of transfer through the biofilm surface are determined, and the possibility of the movement of volatile fatty acids in both directions is discussed.