Radial Symmetry Research Articles

On the effect of remyelination in a mathematical model of multiple sclerosis

In the present work, we consider a mathematical model of multiple sclerosis, extending a model, known in the literature, so that it can account for the process of remyelination. Our model comprises of a reaction-diffusion-chemotaxis system of partial differential equations with a time delay. As a first approximation, we consider the model under the assumption of radial symmetry, which is consistent, e.g., with Baló's concentric disease. We conduct numerical experiments in order to study the effect of the remyelination strength on the disease progression. Furthermore, we show that the modified model has greatly enriched dynamics, which is capable of describing qualitatively different types of multiple sclerosis (according to classical classifications of the disease progression) as well as giving a better agreement with experimental data.

Model Problems on Oscillations of Mechanical and Biological Membranes

Various models of membrane oscillations emerging in the theory of elasticity of mechanical systems, biomechanics of the internal ear of vertebrata, and in the theory of electrical circuits are discussed in the article. The considered oscillations have different natures, but their mathematical models are described using similar initial boundary value problems for the second-order hyperbolic equation with the nontrivial boundary condition. The differential equations in these problems are the same. Thus, for example, the model of voltage distribution in the telegraph line emerges for the one-dimensional equation of oscillations. The model of oscillations of a circular homogeneous solid membrane, a membrane with a hole, and the model of gas oscillations in a sphere and spherical region emerge for the two-dimensional and three-dimensional operators, but take into account the radial symmetry of oscillations. The model problem on membrane oscillation can be considered as the problem on ear drum membrane oscillations. The unified approach to reducing the corresponding problems to the initial boundary value problem with zero boundary conditions is suggested. The technique of formulating the solution in the form of a Fourier series using eigenfunctions of the corresponding Sturm–Liouville problem is described.

Entanglement entropy in conformal quantum mechanics

We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory. Such states exhibit the structure of a thermofield double built on bipartite eigenstates of generators of non-global time evolution. In terms of the correspondence between radial conformal symmetries in Minkowski space-time and time evolution in conformal quantum mechanics proposed in [1, 2] these generators coincide with conformal Killing vectors tangent to worldlines of Milne and diamond observers at constant radius. The temperature of the thermofield double states in conformal quantum mechanics reproduces the temperatures perceived by such diamond and Milne observers. We calculate the entanglement entropy associated to the thermofield double states and obtain a UV divergent logarithmic behaviour analogous to known results in two-dimensional conformal field theory in which the entangling boundary is point-like.

On integral equations of Matukuma type

In this paper, we study the following integral equationu(x)=∫Rnup(y)(1+|y|α)|x−y|n−αdy,u>0inRn, where n≥3, α∈(0,n), and p>0. When α=2, the equation is associated with the classical Matukuma equation−Δu=up(x)1+|x|2,u>0inRn. We investigate qualitative properties of two kinds of positive solutions. One is the finite total mass solution, and the other is the finite energy solution. We investigate the qualitative properties of these solutions, including existence, radial symmetry, integrability and asymptotic behavior at infinity. Here we use the method of moving planes in integral forms introduced by Chen-Li-Ou to prove the radial symmetry, and develop a new comparing principle in integral forms to estimate the asymptotic rates. In addition, we consider the relation between finite total mass solutions and finite energy solutions, and in this process the Pohozaev identity in integral forms plays a key role.

Estimation of Two Component Activities of Binary Liquid Alloys by the Pair Potential Energy Containing a Polynomial of the Partial Radial Distribution Function

An investigation of partial radial distribution functions and atomic pair potentials within a system has established that the existing potential functions are rooted in the assumption of a static arrangement of atoms, overlooking their distribution and vibration. In this study, Hill’s proposed radial distribution function polynomials are applied for the pure gaseous state to a binary liquid alloy to derive the pair potential energy. The partial radial distribution functions of 36 binary liquid alloy from literatures were used to obtain the binary model parameters of four thermodynamic models for validation. Results show that the regular solution model (RSM) and molecular interaction volume model (MIVM) outperform other models when the asymmetric method calculates the partial radial distribution function. RSM demonstrates an average SD of 0.078 and an ARD of 32.2%. Similarly, MIVM exhibits an average SD of 0.095 and an average ARD of 32.2%. Wilson model yields an average SD of 0.124 and an average ARD of 226%. Nonrandom two-liquid (NRTL) model exhibits an average SD of 0.225 and an average ARD of 911%. On applying the partial radial distribution function symmetry method, MIVM and RSM outperform the other models, with an average SD of 0.143 and an average ARD of 165.9% for MIVM. RSM yields an average SD of 0.117 and an average ARD of 208.3%. Wilson model exhibits average values of 0.133 and 305.6% for SD and ARD, respectively. NRTL model shows an average SD of 0.200 and an average ARD of 771.8%. Based on this result, the influence of the symmetry degree on the thermodynamic model is explored by examining the symmetry degree as defined by the experimental activity curves of the two components.

Detection of inhomogeneous magnetic fields using magnetoelectric composites

Magnetoelectric (ME) composites have a wide range of possible applications, especially as room-temperature sensors of weak magnetic fields in magnetocardiography and magnetoencephalography medical diagnostic equipment. In most works on ME composites, structures are tested in uniform magnetic fields; however, for practical application, detailed knowledge of their behaviour in inhomogeneous magnetic fields (IMFs) is necessary. In this work, we measured IMFs with radial symmetry produced by alternate currents (AC) passing through an individual thin wire upon different placements of an ME sensor. An ME self-biased b-LN/Ni/Metglas structure with a sensitivity to the magnetic field of 120 V/T was created for IMF detection. The necessity of an external biasing magnetic field was avoided by the inclusion of a nickel layer having remanent magnetization. The ME composite shows a non-zero ME coefficient of 0.24 V/(cm · Oe) in the absence of an external DC magnetic field. It is shown that the output voltage amplitude from the ME composite, which is located in an AC IMF, is dependent on the relative position of the investigated sample and magnetic field lines. Maximum ME signal is obtained when the long side of the ME sample is perpendicular to the wire, and the symmetry plane which divides the long side into two similar pieces contains the wire axis. In the frequency range from 400 Hz to 1000 Hz in the absence of vibrational and other noises, the detection limit amounts to (2 ± 0.4) nT/Hz1/2.

Covariance models and Gaussian process regression for the wave equation. Application to related inverse problems

In this article, we consider the general task of performing Gaussian process regression (GPR) on pointwise observations of solutions of the 3 dimensional homogeneous free space wave equation. In a recent article, we obtained promising covariance expressions tailored to this equation: we now explore the potential applications of these formulas. We first study the particular cases of stationarity and radial symmetry, for which significant simplifications arise. We next show that the true-angle multilateration method for point source localization, as used in GPS systems, is naturally recovered by our GPR formulas in the limit of the small source radius. Additionally, we show that this GPR framework provides a new answer to the ill-posed inverse problem of reconstructing initial conditions for the wave equation from a limited number of sensors, and simultaneously enables the inference of physical parameters from these data. We finish by illustrating this “physics informed” GPR on a number of practical examples.

Generalised solution to a 2D parabolic-parabolic chemotaxis system for urban crime: Global existence and large-time behaviour

AbstractWe consider a parabolic-parabolic chemotaxis system with singular chemotactic sensitivity and source functions, which is originally introduced by Short et al to model the spatio-temporal behaviour of urban criminal activities with the particular value of the chemotactic sensitivity parameter $\chi =2$ . The available analytical findings for this urban crime model including $\chi =2$ are restricted either to one-dimensional setting, or to initial data and source functions with appropriate smallness, or to initial data and source functions with some radial symmetry. In the present work, our first result asserts that for any $\chi \gt 0$ the initial-boundary value problem of this urban crime model possesses a global generalised solution in the two-dimensional setting, without imposing any small or radial conditions on initial data and source functions. Our second result presents the asymptotic behaviour of such solution, under some additional assumptions on source functions.

Identification and characterization of CYC2-like genes related to floral symmetric development in Tagetes erecta (Asteraceae)

Marigold (Tagetes erecta) is an annual herbaceous flower belonging to Asteraceae, whose capitulum is composed of bilateral symmetry ray florets on the outer periphery and radial symmetry disk florets on the inside. The flower symmetry evolution from radial symmetry to bilateral symmetry has changed the morphology, inflorescence architecture and function of florets among several lineages in Asteraceae. Several studies have identified that CYC2 genes in TCP transcription factor family are the key genes regulating the flower morphogenesis, such as corolla symmetry and stamen development. Here, seven TeCYC2 genes were cloned and phylogenetically grouped into the CYC2 branch of TCP transcription family. TeCYC2c and TeCYC2d were found to be expressed specifically in ray florets, TeCYC2b was strongly expressed in both ray and disk florets, TeCYC2g was significantly higher expressed in ray florets than in disk florets, while TeCYC2a, TeCYC2e1 and TeCYC2e2 were significantly expressed in disk florets, according to an examination of the expression profile. Among the ectopic expression lines of seven TeCYC2 genes in Arabidopsis thaliana, the flower symmetry of all transgenic lines was changed from radial symmetry to bilateral symmetry, and only the reproductive growth of TeCYC2c lines was affected. In TeCYC2c transgenic Arabidopsis, the pollen sac was difficult to crack, and the filaments were shorter than the pistils, resulting in a significant decrease in the seed setting rate. All TeCYC2 proteins were localized in the nucleus. Eight pairs of interactions between TeCYC2 proteins were validated by Y2H and BiFC assays, indicating the possibility of TeCYC2 proteins forming homodimers or heterodimers to improve functional specificity. Our findings verified the main regulatory role of TeCYC2c on the development of corollas and stamen in marigold, and analyzed the interaction network of the formation mechanism of floral symmetry in two florets, which provided more insights into the expansion of CYC2 genes in the evolution of Asteraceae inflorescence and contributed to elucidate the complex regulatory network, as well as the molecular breeding concerning flower form diversity in marigold.

Radial Alignment of Carbon Nanotubes Via Dead-End Filtration

Dead-end filtration is a facile method to globally align single wall carbon nanotubes (SWCNTs) in large area films with a two-dimensional order parameter, , approaching unity. Uniaxial alignment has been achieved using pristine and hot-embossed membranes but more sophisticated geometries have yet to be investigated. In this work, we create three different patterns with radial symmetry and an area of 3.8 cm². Two of these patterns are replicated by the filtered SWCNTs and values of » 0.85 are obtained. Each of the radially aligned SWCNT films are characterized by scanning cross-polarized microscopy in reflectance and laser imaging in transmittance with linear, radial and azimuthal polarized light fields. The former is used to define a novel indicator akin to the two-dimensional order parameter using Malu’s law, yielding 0.82 for the respective film. The films are then transferred to a flexible printed circuit board and terminal two-probe electrical measurements are conducted to explore the potential of those new alignment geometries. Figure 1

Effect of electromagnetic stirring on the transient flow, solidification and inclusion movements in the continuous casting slab mold

PurposeThe purpose of this study is to explore how a time-varying electromagnetic stirring (EMS) affects the fluid flow and solidification behavior in a slab caster continuous casting mold. Further, the study of inclusion movements in the mold is carried out under the effect of a time-varying electromagnetic field.Design/methodology/approachA three-dimensional coupled numerical model of solidification and magnetohydrodynamics has been developed for slab caster mold to investigate the inclusions transport by discrete phase model with the use of user-defined functions. Enthalpy porosity and the Lagrangian approach are applied to analyze the behavior of solidification and inclusion.FindingsThe study shows that the magnetic field density distribution has a radial symmetry in relation to the stirrer’s center. As the EMS current intensity increases, the strength of the lower recirculation zone gradually decreases and nearly disappears at higher intensities. Additionally, the area of localized remelting zone expands in the solidification front with rising current intensity. The morphology of inclusions and EMS current intensity have a significant impact on the behavior and movement of inclusions within the molten steel.Practical implicationsBy using the model, one can optimize the EMS parameter to enhance the quality of steel casting through the elimination of impurities and by improving the microstructure of cast that mainly depend on solidification and flow patterns of molten steel.Originality/valueUntil now, the use of time-varying EMS in the slab caster mold to study solidification and inclusion behavior has not been explored.

Manipulating self-focusing beams induced by high-dimensional parabolic umbilic beams

The excellent property that the intensity of autofocusing beams in the focal plane increases exponentially, makes them especially beneficial for biomedical treatment. We experimentally generate tunable (2+1)-dimensional circular parabolic umbilic beams (CPUBs) for the first time based on the high-dimensional diffraction catastrophe integral, which is determined by the potential function. Such CPUBs have circular and symmetrical intensity distributions in space through radial symmetry transformation. Due to the flexibility of high dimensionality, these light beams have rich light field structures and self-focusing property. Where, the maximum intensity suddenly increases by orders of magnitude in the focal plane. Unlike the classical circular Airy beams, CPUBs exhibit multiple self-focusing points along the optical axis and a needle-like structure during propagation, which can be affected by manipulating the control parameters. The rich properties provide a new perspective for exploring the novel physical mechanisms and phenomena in autofocusing beams. The experimental results verify the correctness of the numerical simulations. CPUBs greatly enrich the autofocusing beam family and will be advantageous for medical treatments, optical micromanipulation, and microscopic imaging.

Comparative Analysis of T4SS Molecular Architectures.

The recently published high-resolution R388 T4SS structure provides exciting new details about the complete complex of T4SS, including the components making up the stalk and arches, numerous symmetry mismatches between regions of the complex, and an intriguing interpretation of the closed stalk and radial symmetry of the inner membrane complex, which is related to pilus biogenesis assembly. However, there are a few unidentified densities in the electron microscopy map and portions of the identified component sequences for which the structure is not yet known. It is also unclear how well this minimized DNA-transporting T4SS predicts the structure of other T4SSs, such as expanded systems and those that transport proteins rather than DNA. In this review, we evaluate what can be inferred from the recent high-resolution structure of the R388 T4SS with respect to the Cag and Dot/Icm systems. These systems were selected because, given what is currently known about these systems, we expect them to present most structural differences compared to the R388 T4SS structure. Furthermore, we discuss bacterial physiology and diversity, the T4SS structures and their variations between different bacterial species. These insights may prove beneficial for researchers who elucidate the structure and functions of T4SS in different bacterial species.

Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

We obtain an exact rotating BTZ-like black hole solution by solving the corresponding gravitational field equations and the bumblebee motion equations in Einstein-bumblebee gravity theory. Result is presented for the purely radial Lorentz symmetry violating and can only exist with a linear functional potential of the bumblebee field. This black hole has two horizons and an ergosphere which are dependent on the bumblebee coupling constant ell . The concepts of the area and volume of the horizon should be renewed in this LV spacetime due to the nontrivial contribution of coupling between the bumblebee field and the Ricci tensor. Only in this way, the entropy-area relation, first law of thermodynamics and the Smarr formula can still be constructed. We also study the AdS/CFT correspondence of this black hole, find that the entropy product of its inner and outer horizons is universal. So the central charges of the dual CFT on the boundary can be obtained via the thermodynamic method, and they can reappear black hole mass and angular momentum in the bulk.

Palynology of the genus Lagerstroemia (Lythraceae) in Thailand

Abstract. Saensouk S, Saensouk P. 2023. Palynology of the genus Lagerstroemia (Lythraceae) in Thailand. Biodiversitas 24: 3222-3229. Pollen morphology of Lagerstroemia (Lythraceae) from Thailand was poorly reported. This study aimed to study the pollen morphology of 17 species of the genus Lagerstroemia in Thailand by applying acetolysis under a light microscope and scanning electron microscope. Pollen of the genus Lagerstroemia in Thailand was described with the distinctive features of the pollen morphology, i.e., size, shape, exine sculpturing, the character of the aperture, polar, and symmetry. All pollen grains were monad with and polar view length of 43.83±2.84 µm, and equatorial view length of 26.33±2.05 µm. The shape of pollens was prolate spheroidal, subspheroidal, spheroidal, and subprolate. The pollens in this study were recognized as bilateral, radial, and sub-radial symmetries. All pollen grains were apolar and polar. The aperture of all pollen species in this study was reported with tricolpate and tricolporate. Exine sculpturing was exine sculpturing and scabrate-granulate. The pollen morphology of this study can be divided into groups based on shape, exine sculpturing, the character of the aperture, polarity, and symmetry. Pollen sizes of all species were medium size. The pollen ofall species from Thailand are reported as Lagerstroemia indica-type.The pollen morphology in this study cannot be used for species identification. Pollen of 16 Lagerstroemia species were studied here for the first time.

Ground state solutions for Choquard equations with Bessel potential

Firstly, we study the existence, regularity and decay of positive solutions for the elliptic system { − Δ u + u = vg ( u ) in R N , − Δv + v = G ( u ) in R N , where N ≥ 3 , g satisfies Berestycki-Lions type conditions. In Sobolev space, the system can be transformed into the Choquard equations with Bessel potential − Δ u + u = ( g 2 ⋆ G ( u ) ) g ( u ) in R N , where g 2 is the fundamental solution of the linear operator − Δ + I on R N . Moreover, by assuming that g is nondecreasing, we obtain the radial symmetry and monotonic property of positive solutions by moving plane method, and the existence of ground state solutions by non-Nehari manifold method.

Uniqueness, symmetry and convergence of positive ground state solutions of the Choquard type equation on a ball

This paper is concerned with the qualitative properties of the positive ground state solutions to the nonlocal Choquard type equation on a ball BR. First, we prove the radial symmetry of all the positive ground state solutions by using Talenti's inequality. Next we develop the Newton's Theorem and then resort to the contraction mapping principle to establish the uniqueness of the positive ground state solution. Finally, by constructing cut-off functions and applying energy comparison method, we show the convergence of the unique positive ground state solutions as the radius R→∞. Our results extend and complement the existing ones in the literature.

Free boundary value problem for a model of inviscid liquid‐gas two‐phase flow with radial symmetry

AbstractIn this paper, we are concerned with the free boundary value problem for a model of inviscid liquid‐gas two‐phase flow with radial symmetry. For simplicity, we assume that the gas velocity is always equal to the liquid one and the gas and liquid are both connected continuously to the outer vacuum through the same free boundary. First, we constructed two classes of global analytical solutions by using a self‐similar ansatz. Second, for the general free boundary value problem of this model, we show that the free boundary separating the two‐phase flow from vacuum will spread outward at least linearly in time, provided that the two‐phase fluids motion remains smooth and the initial flow moves outward on average to the vacuum. Third, we present a sufficient condition for the blowup of smooth solutions to the problem.

Protected spin-orbit induced absorption divergence in distorted Landau levels

The effect of spin-orbit (and Darwin) interaction on a 2D electron gas subject to a radial symmetric, inhomogeneous $1/r$-magnetic field is discussed analytically in a perturbative and non-perturbative manner. For this purpose, we investigate the radial Hall conductivity that emerges from an additional homogeneous electric field perturbation perpendicular to the 2D electron gas, which solely interacts via spin-orbit coupling. Numerical calculations of the absorptive spin-orbit spectra show for an ideal InSb electron gas a behaviour that is dominated by the localized (atomic) part of the distorted Landau levels. In contrast, however, we also find analytically that a (non-local) divergent static response emerges for Fermi energies close to the ionization energy in the thermodynamic limit. The divergent linear response implies that the external electric field is entirely absorbed outside the 2D electron gas by induced radial spin-orbit currents, as it would be the case inside a perfect conductor. This spin-orbit induced polarization mechanism depends on the effective $g^*$-factor of the material for which it shows a critical behaviour at $g^*_c=2$, where it abruptly switches direction. The diverging absorption relies on the presence of degenerate energies with allowed selection rules that are imposed by the radial symmetry of our inhomogeneous setup. We show analytically the presence of a discrete Rydberg-like band structure that obeys these symmetry properties. In a last step, we investigate the robustness of the spectra by solving analytically the Dirac equation expanded up to order $1/(mc)^2$. We find that the distorted Landau-levels, and thus the divergent spin-orbit polarization, remain protected with respect to slow changes of the applied $1/r$-magnetic field.

A Mathematical Study of Metal Biosorption on Algal–Bacterial Granular Biofilms

A multiscale mathematical model describing the metals biosorption on algal–bacterial photogranules within a sequencing batch reactor (SBR) is presented. The model is based on systems of partial differential equations (PDEs) derived from mass conservation principles on a spherical free boundary domain with radial symmetry. Hyperbolic PDEs account for the dynamics of sessile species and their free sorption sites, where metals are adsorbed. Parabolic PDEs govern the diffusion, conversion and adsorption of nutrients and metals. The dual effect of metals on photogranule ecology is also modelled: metal stimulates the production of EPS by sessile species and negatively affects the metabolic activities of microbial species. Accordingly, a stimulation term for EPS production and an inhibition term for metal are included in all microbial kinetics. The formation and evolution of the granule domain are governed by an ordinary differential equation with a vanishing initial value, accounting for microbial growth, attachment and detachment phenomena. The model is completed with systems of impulsive differential equations describing the evolution of dissolved substrates, metals, and planktonic and detached biomasses within the granular-based SBR. The model is integrated numerically to examine the role of the microbial species and EPS in the adsorption process, and the effect of metal concentration and adsorption properties of biofilm components on the metal removal. Numerical results show an accurate description of the photogranules evolution and ecology and confirm the applicability of algal–bacterial photogranule technology for metal-rich wastewater treatment.