Isotropic Sphere Research Articles

Anisotropic Hollow Structure with Chemotaxis Enabling Intratumoral Autonomic Therapy.

Effective intratumoral drug penetration is pivotal for successful cancer treatment. However, due to the disrupted capillary networks and poor perfusion in solid tumors, there exist challenges to realize autonomous directional drug penetration and controlled drug release within the tumor. Considering the specificity of glucose within tumor tissue, we draw inspiration from nature and engineer asymmetrical hollow structures exhibiting chemotaxis towards high glucose levels. By incorporating multiple shells into these structures, we enhance the local chemical concentration gradients, thereby improving cellular uptake and precise targeting. The advantages of anisotropic hollow multishell structure (a-HoMS) can be reflected from the diffusion coefficient and directivity, which increase by 73.4% and 265% respectively compared to conventional isotropic hollow spheres, achieving the most linear movement while ensuring the speed of movement. Furthermore, the multi-level porosity and temporal-spatial order of a-HoMS enable sequential drug delivery that inhibits angiogenesis with inducing cell apoptosis. After the eradication of localized tumor cells, the a-HoMS can automatically migrate to the alive tumor cells under the glucose gradient, inducing another cycle of drug delivery and chemotaxis, resulting in excellent antitumor efficacy. These anisotropic HoMS demonstrate intelligence, adaptability, and precision in tumor therapy, providing valuable insights for programmable treatment within tissues.

Anisotropic Hollow Structure with Chemotaxis Enabling Intratumoral Autonomic Therapy

Effective intratumoral drug penetration is pivotal for successful cancer treatment. However, due to the disrupted capillary networks and poor perfusion in solid tumors, there exist challenges to realize autonomous directional drug penetration and controlled drug release within the tumor. Considering the specificity of glucose within tumor tissue, we draw inspiration from nature and engineer asymmetrical hollow structures exhibiting chemotaxis towards high glucose levels. By incorporating multiple shells into these structures, we enhance the local chemical concentration gradients, thereby improving cellular uptake and precise targeting. The advantages of anisotropic hollow multishell structure (a‐HoMS) can be reflected from the diffusion coefficient and directivity, which increase by 73.4% and 265% respectively compared to conventional isotropic hollow spheres, achieving the most linear movement while ensuring the speed of movement. Furthermore, the multi‐level porosity and temporal‐spatial order of a‐HoMS enable sequential drug delivery that inhibits angiogenesis with inducing cell apoptosis. After the eradication of localized tumor cells, the a‐HoMS can automatically migrate to the alive tumor cells under the glucose gradient, inducing another cycle of drug delivery and chemotaxis, resulting in excellent antitumor efficacy. These anisotropic HoMS demonstrate intelligence, adaptability, and precision in tumor therapy, providing valuable insights for programmable treatment within tissues.

Scattering characteristics of dual counter-propagation high-order circularly symmetric Bessel beam by a multilayer chiral sphere

The interaction between dual counter-propagating high-order circularly symmetric Bessel beams (CSBBs) and multi-layered chiral particles is investigated. Within the framework of generalized Lorenz-Mie theory (GLMT), the distribution characteristics of the superposition of two beams are studied based on the vector superposition theorem. The near-field, internal field, and far-field radar cross section (RCS) of the dual-layered chiral sphere illuminated by dual CSBBs are obtained according to the boundary conditions. By comparing the results of RCS with those from the references for two cases: first, when CSBBs degenerate into plane waves incident on multi-layered chiral sphere, and second, when Bessel beams illuminate isotropic multi-layer sphere degenerated by chiral multi-layered sphere, the effectiveness of the principle and program exhibited here is confirmed. The impact of various parameters on the distribution of the superposed field, the near-field, internal field, and far-field RCS of the particles are analyzed in detail, such as the order, half-cone angle, incidence angle, and polarization angle. The research results in this paper provide theoretical assistance for understanding the interaction between dual CSBBs and non-uniform chiral multi-layered particles and have important value in realizing optical manipulation of complex chiral layered particles.

Role of Durgapal-Fuloria model on isotropic spheres in Rastall gravity

Role of Durgapal-Fuloria model on isotropic spheres in Rastall gravity

Anisotropic generalization of charged isotropic spheres with double equation of state

We propose a technique to generate a new class of solutions for an anisotropic charged matter distribution. We show its viability as a model to describe an ultra-compact static spherically symmetric star where anisotropy may be a dominant factor. The solution extends some previously reported stellar solutions with or without charge or anisotropy. The interior matter distribution satisfies a double equation of state with two parameters. The parameters affect the gravitational behaviour of the model and the physical features, such as stability.

Scattering properties of dual Bessel beams on chiral layered particle

The paper investigates the scattering analytical solution of arbitrary direction double zero-order Bessel beams (ZOBBs) incident on a non-uniform layered chiral sphere. Using the generalized Lorenz-Mie theory (GLMT), the electromagnetic field expansion expression of the double ZOBBs is obtained through the vector superposition of the spherical vector wave functions (SVWFs). Analytical solutions of the scattering on chiral layered particles by dual Bessel beams are derived based on the boundary condition. The iterative coefficient equations are constructed to obtain the expansion coefficients of the SVWFs in each region of the multi-layer chiral sphere. The variation of radar cross section (RCS) with angular distribution is numerically simulated, and the scattering results of layered chiral spheres degenerated into isotropic layered spheres are compared with the literature, which verifies the correctness of the theory and program. The effects of incident angle, polarization angle, cone angle and chiral parameters on the scattering characteristics of far region and internal field of the layered chiral particle are analyzed in detail. The theory and results can offer significant assistance in studying the optical properties of non-uniform chiral particles and complex biological cells irradiated by multiple beams and may also provide important practical value in the micromanipulation of multi-layered biological structures.

Efficient single-scattering lookup table for lidar and polarimeter phytoplankton studies.

Coupled atmosphere and ocean remote sensing retrievals of aerosol, cloud, and oceanic phytoplankton microphysical properties, such as those carried out by the NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, involve single-scattering calculations that are time consuming. Lookup tables (LUTs) exist to speed up these calculations for aerosol and water droplets in the atmosphere. In our new Lorenz-Mie lookup table, we tabulate single scattering by an ensemble of coated isotropic spheres representing oceanic phytoplankton at wavelengths from 0.355 µm. The lookup table covers phytoplankton particles with radii in the range of 0.15-100 µm at an increase of up to 104 in computational speed compared to single-scattering calculations. The allowed complex refractive indices range from 1.05 to 1.24 for the shell's real part, from 10-7 to 0.3 for the shell's imaginary part, from 0 to 0.001 for the core's imaginary part, and equal to 1.02 for the core's real part. We show that we precisely compute inherent optical properties for the phytoplankton size distributions ranging up to 5 µm for the effective radius and up to 0.6 for the effective variance. We test wavelengths from 0.355 to 1.065 µm and find that all the inherent optical properties of interest agree with the single-scattering calculations to within 1% for 99.9% of cases. We also provide an example of using the lookup table to reproduce the phytoplankton optical datasets listed in the PANGAEA database for synthetic hyperspectral algorithm development. The table together with C++, Fortran, MATLAB, and Python codes to apply different complex refractive indices and phytoplankton size distributions is freely available online.

Construction of exact and asymptotic solutions for the problem of torsional vibrations of a radially inhomogeneous sphere

In this paper, the torsional vibrations of a radially inhomogeneous isotropic open sphere containing no 0 and π poles are studied. It is considered that the elastic moduli and density of the material are linear functions of the radius of the sphere. Cases are considered when the lateral surface of the sphere is stress-free and fixed, and arbitrary boundary conditions are specified on conic sections. The formulated boundary value problems are reduced to spectral problems. After fulfilling boundary conditions specified on the lateral surfaces of the sphere, a dispersion equation is obtained. Exact solutions to the problem are constructed. Next, we analyzed the roots of the dispersion equation for a relatively small parameter characterizing the thickness of the sphere, depending on the oscillation frequency. For a sphere of small thickness, asymptotic zeros are constructed, and their characteristics are studied.

Optical pulling force on a uniaxial anisotropic sphere by a high-order Bessel (vortex) beam.

Based on the generalized Lorenz-Mie theory (GLMT) and the scattering theory of uniaxial spheres, a theoretical approach is introduced to study the axial radiation force (AOF) exerted on a uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel (vortex) beams (HOBVBs). Applying Maxwell's stress tensor, an analytical expression of the AOF on a uniaxial anisotropic sphere by the on-axis HOBVB is derived. The correctness of the theoretical and numerical results is verified by comparing the AOF on an isotropic sphere by a zero-order Bessel beam (ZOBB) with those results by a plane wave, Gaussian beam, and ZOBB. The focus of this study is to determine some conditions of the tractor beam, so as to realize the inverse motion of an anisotropic sphere through a Bessel beam. The range of optical pulling force (OPF) that can pull particles in reverse motion generated by zero-order and first-order Bessel beams is extended from isotropic spherical particles to anisotropic spherical particles. The effects of the sphere radius, conical angle, and especially electromagnetic anisotropy parameters on the OPF in water or a vacuum environment are discussed in detail. Moreover, the OPF exerted on the uniaxial anisotropic sphere illuminated by a HOBVB with l=2, 3, and 4 is also exhibited. It indicates that the HOBVB with l=2, 3 is also a good tractor beam for the uniaxial anisotropic sphere. The OPF generated by Bessel beams on uniaxial anisotropic spherical particles is not only affected by the conical angle and radius but is also significantly influenced by anisotropic parameters and topological charges. These properties of the OPF are different from those on an isotropic sphere. The theory and results are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by optical tractor (vortex) beams.

Linking sand permeability anisotropy to fabric anisotropy via numerical simulation

Characterisation of the permeability of soils is of practical importance and, for cohesionless or granular soils, it can be predicted from the void ratio and the particle size distribution (PSD). However, the effect of fabric anisotropy on the permeability is rarely discussed. Restricting consideration to granular (cohesionless) soil, this study combines a variety of numerical methods to investigate (1) how the anisotropy of the permeability evolves as the soil fabric anisotropy evolves in triaxial deformation and (2) establish a link between the anisotropy of the permeability and the fabric anisotropy. The Discrete Element Method (DEM) was employed to create linearly graded virtual samples of spheres (Cu of 1 to 2). Initially isotropic sphere packings were subjected to triaxial compression or triaxial extension up to 30% of absolute axial strain to induce an anisotropic fabric. Pore Network Models (PNMs) present a computationally efficient option for simulation of flow through the pore space. A PNM models fluid flow between pores (nodes) connected by pipes (edges) whose geometry is defined by the topology of the connected pores and the mass balance equation is solved at each pore. After demonstrating the accuracy of the PNM framework adopted here, this contribution presents data from PNM simulations that used the positions of individual particles in the sheared spherical packings as input data. The fabric and permeability anisotropies during triaxial shear deformation were compared at axial strain intervals of 1%. Detailed microscale analyses suggest that the anisotropy in the permeability can be attributed to an increase in the local conductance of fluid pipes in the direction of the major principal stress, which is related to the evolution of the pore topologies during the shear deformation.

Optomechanical effects caused by non-zero field quantities in multiple evanescent waves.

Evanescent waves, with their high energy density, intricate local momentum, and spatial distribution of spins, have been the subject of extensive recent study. These waves offer promising applications in near-field particle manipulation. Consequently, it becomes imperative to gain a deeper understanding of the impacts of scattering and gradient forces on particles in evanescent waves to enhance and refine the manipulation capabilities. In this study, we employ the multipole expansion theory to present analytical expressions for the scattering and gradient forces exerted on an isotropic sphere of any size and composition in multiple evanescent waves. The investigation of these forces reveals several unusual optomechanical phenomena. It is well known that the scattering force does not exist in counter-propagating homogeneous plane waves. Surprisingly, in multiple pairs of counter-propagating evanescent waves, the scattering force can arise due to the nonzero orbital momentum (OM) density and/or the curl part of the imaginary Poynting momentum (IPM) density. More importantly, it is found that the optical scattering force can be switched on and off by simply tuning the polarization. Furthermore, optical forces typically vary with spatial position in an interference field. However, in the interference field generated by evanescent waves, the gradient force becomes a spatial constant in the propagating plane as the particle's radius increases. This is attributed to the decisive role of the non-interference term of the electromagnetic energy density gradient. Our study establishes a comprehensive and rigorous theoretical foundation, propelling the advancement and optimization of optical manipulation techniques harnessed through multiple evanescent waves. Specifically, these insights hold promise in elevating trapping efficiency through precise control and manipulation of optical scattering and gradient forces, stimulating further explorations.

Phase separation of a magnetic fluid: Asymptotic states and nonequilibrium kinetics.

We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model, which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the nonequilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms-a diffusive growth law ℓ(t)∼t^{1/3} in the nucleation regime and hydrodynamics-driven inertial growth law ℓ(t)∼t^{2/3} in the spinodal regimes. [ℓ(t) is the average size of the condensate at time t after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected nonconserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile, and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a Janus particle to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.

Resolving an inverse problem through a momentum flow within the framework of electromagnetic scattering.

Although there have been many approaches to inverse problem in the classic theory of potential scattering, they are implicitly confined to the analysis of the scattered electric field, and thus the magnetic counterpart of the scattered wave is ignored, which limits the further application of those approaches to some extent. Here, we propose a new, to the best of our knowledge, technique for an inverse problem within the framework of electromagnetic scattering. This technique aims at reconstructing the correlation function of the scattering potential of a random medium through measuring the electromagnetic momentum flow of the scattered field in the far zone. As illustrative examples, we use the technique to determine the correlation functions of the scattering potentials of homogeneous, isotropic, and Gaussian-correlated spheres. Our new inversion approach works both microscopically and macroscopically.

One Definition to Join Them All: The N-Spherical Solution for the EEG Lead Field.

Albeit its simplicity, the concentric spheres head model is widely used in EEG. The reason behind this is its simple mathematical definition, which allows for the calculation of lead fields with negligible computational cost, for example, for iterative approaches. Nevertheless, the literature shows contradictory formulations for the electrical solution of this head model. In this work, we study several different definitions for the electrical lead field of a four concentric spheres conduction model, finding that their results are contradictory. A thorough exploration of the mathematics used to build these formulations, provided in the original works, allowed for the identification of errors in some of the formulae, which proved to be the reason for the discrepancies. Moreover, this mathematical review revealed the iterative nature of some of these formulations, which allowed us to develop a formulation to solve the lead field in a head model built from an arbitrary number of concentric, homogeneous, and isotropic spheres.

Isotropic Durgapal IV fluid sphere in bigravity

We analyze an isotropic uncharged fluid sphere model within bigravity considering the Durgapal IV metric (M.C. Durgapal, J. Phys. A: Math. Gen. 15, 2637 (1982)). In this work, we investigate the effects of the scale parameter k on the local matter distribution. Here, we have chosen the compact star candidate SMC X-1 with observed values of mass = (1.29 ± 0.05) M⊙ and radius [Formula: see text] km, respectively, to analyze our results analytically as well as graphically. For smaller values of k, we get the stiff (or hard) equation of state (EoS). Here, we solve the modified Einstein field equations in the presence of the background metric γμν. Due to this constant curvature background, the density and pressure terms are modified by adding an extra term, which affects the EoS. For r ≪ k, the background de Sitter space–time reduces into Minkowski form, and the coupling vanishes. We discuss certain physical quantities of our obtained solution, such as density, isotropic pressure, sound speed, pressure-density gradients, compactness, and surface redshift, to claim the physical viability of our model. It is found that our model clearly satisfies all the energy conditions, the causality condition, and the dynamical equilibrium via a modified Tolman–Oppenheimer–Volkov equation. Finally, we can conclude that our proposed model is physically realistic and well behaved.

Colloidal tubular microrobots for cargo transport and compression

Microrobot swarms have seen increased interest in recent years due to their potentials for in vivo delivery and imaging with cooperative propulsion modes and enhanced imaging signals. Yet most swarms developed so far are limited to dense particle aggregates, far simpler than complicated three-dimensional assemblies of anisotropic particles. Here, we show via assembly path design that complex hollow tubular structures can be assembled from simple isotropic colloidal spheres and those complicated, metastable, microtubes can be formed from simple, energetically favorable colloidal membranes. The assembled microtubes can remain intact and roll under a precessing magnetic field, with propulsion directions and velocities precisely controlled by field components. The hollow spaces inside enable these tubular microrobots to grab, transport, and release cargos on command. We also demonstrate unique compressing and uncompressing capabilities with our tubular microrobots, making them effective microtweezers. Our work shows that complicated microrobots can be transformed from simple assemblies, providing an insight on building micromachines.

Nanoscale Porosity in Microellipsoids Cloaks Interparticle Capillary Attraction at Fluid Interfaces.

Anisotropic particles pinned at fluid interfaces tend toward disordered multiparticle configurations due to large, orientationally dependent, capillary forces, which is a significant barrier to exploiting these particles to create functional self-assembled materials. Therefore, current interfacial assembly methods typically focus on isotropic spheres, which have minimal capillary attraction and no dependence on orientation in the plane of the interface. In order to create long-range ordered structures with complex configurations via interfacially trapped anisotropic particles, control over the interparticle interaction energy via external fields and/or particle engineering is necessary. Here, we synthesize colloidal ellipsoids with nanoscale porosity and show that their interparticle capillary attraction at a water-air interface is reduced by an order of magnitude compared to their smooth counterparts. This is accomplished by comparing the behavior of smooth, rough, and porous ellipsoids at a water-air interface. By monitoring the dynamics of two particles approaching one another, we show that the porous particles exhibit a much shorter-range capillary interaction potential, with scaling intriguingly different than theory describing the behavior of smooth ellipsoids. Further, interferometry measurements of the fluid deformation surrounding a single particle shows that the interface around porous ellipsoids does not possess the characteristic quadrupolar symmetry of smooth ellipsoids, and quantitatively confirms the decrease in capillary interaction energy. By engineering nanostructured surface features in this fashion, the interfacial capillary interactions between particles may be controlled, informing an approach for the self-assembly of complex two-dimensional microstructures composed of anisotropic particles.

Generalized Thermoelastic Heat Conduction Model Involving Three Different Fractional Operators

Abstract The purpose of this paper is to introduce a new time-fractional heat conduction model with three-phase-lags and three distinct fractional-order derivatives. We investigate the introduced model in the situation of an isotropic and homogeneous solid sphere. The exterior of the sphere is exposed to a thermal shock and a decaying heat generation rate. We recuperate some earlier thermoelasticity models as particular cases from the proposed model. Moreover, the effects of different fractional thermoelastic models and the effect of instant time on the physical variables of the medium are studied. We obtain the numerical solutions for the various physical fields using a numerical Laplace inversion technique. We represent the obtained results graphically and discuss them. Physical views presented in this article may be useful for the design of new materials, bio-heat transfer mechanisms between tissues and other scientific domains.

A Simulation of Artificial Neutral Gas‐Dust Plasma in the Ionosphere

AbstractDusty plasma is generally defined as a plasma system containing a large number of nano‐ or micron‐sized dust particles. Its plasma properties and propagation properties of wave travel through it is of great scientific significance to the understanding of many fundamental problems in space physics and astrophysics. Based on previous studies on rocket exhaust and Polar Mesosphere Summer Echoes, fluid mechanics and dust microphysics are combined to simulate the ionospheric plasma structure generated by neutral gases and charged aerosols using fluid theory and kinetic theory. The Total Electron Content of the in‐situ detection beacon is simulated and compared with the experimental phenomenon given in Charged Aerosol Release Experiment by Bernhardt et al. The ray tracing algorithm is used to simulate the path deflection of the radio wave when it passes through the artificial disturbance area generated by the gas‐solid mixture, and the simulation results of ionosonde and analysis are given. Since the neutral gas expands substantially isotropically after being released, the resulting depleted structure is an approximately isotropic sphere, or an acorn‐like structure. The solid particles are constrained by the nozzle, and particles will distribute within a spray angle, and the depletion structure will appear as a “broom‐like” or “cone‐like” structure. If the size of dust particles is small enough, the particle movement will be restricted by the geomagnetic field, resulting in a “squid‐like” ionospheric structure. Because of the fishtail‐like sharp boundary, radio waves passing through it are deflected in a specific path, which is markedly different from the effect of pure neutral gas injected into the ionosphere.

Tailoring of functionally graded spheres using a uniform stress condition

Homogeneous and isotropic thick spheres loaded with constant internal and/or external pressures can not be economically designed because the maximum equivalent stress is a local value. It was analytically demonstrated that, by neglecting the body loads, a functionally graded material (FGM) may be characterized in linear static analyses by two material constants: Young's modulus E(r) and Poisson's ratio ν(r). If these two functions are both known, the solution of the problem, displacement and stress distributions may be relatively easy obtained. For the inverse problem, in which a desired stress combination distribution is imposed, finding of E(r) and ν(r) is more difficult, if such a solution exists. More than that, if the solution exists, it is not unique, because two unknown functions are involved. For ν(r) = const., analytical solutions are available for E(r), but only for two particular stress conditions. In this paper, the inverse problem is solved iteratively using a finite element model and an algorithm of stress uniformization developed by the authors of this paper is proposed. In this original approach, the existing solutions were reproduced as a verification and afterwards new solutions were obtained for the remaining classical theories of resistance. The new obtained solutions were also verified by using the analytical solutions of the direct problem.