49 research outputs found
Universal Expressions for the Polarization and the Depolarization Factor in Homogeneous Dielectric and Magnetic Spheres Subjected to an External Field of Any Form
No full textSpherical structures of dielectric and magnetic materials are studied intensively in basic research and employed widely in applications. The polarization, (Figure presented.) (P for dielectric and M for magnetic materials), is the parent physical vector of all relevant entities (e.g., moment, (Figure presented.), and force, F), which determine the signals recorded by an experimental setup or diagnostic equipment and configure the motion in real space. Here, we use classical electromagnetism to study the polarization, (Figure presented.), of spherical structures of linear and isotropic—however, not necessarily homogeneous—materials subjected to an external vector field, (Figure presented.) (Eext for dielectric and Hext for magnetic materials), dc (static), or even ac of low frequency (quasistatic limit). We tackle an integro-differential equation on the polarization, (Figure presented.), able to provide closed-form solutions, determined solely from (Figure presented.), on the basis of spherical harmonics, (Formula presented.). These generic equations can be used to calculate analytically the polarization, (Figure presented.), directly from an external field, (Figure presented.), of any form. The proof of concept is studied in homogeneous dielectric and magnetic spheres. Indeed, the polarization, (Figure presented.), can be obtained by universal expressions, directly applicable for any form of the external field, (Figure presented.). Notably, we obtain the relation between the extrinsic, (Figure presented.), and intrinsic, (Figure presented.), susceptibilities ((Formula presented.) and (Formula presented.) for dielectric and (Formula presented.) and (Formula presented.) for magnetic materials) and clarify the nature of the depolarization factor, (Figure presented.), which depends on the degree l—however, not on the order m of the mode (Formula presented.) of the applied (Figure presented.). Our universal approach can be useful to understand the physics and to facilitate applications of such spherical structures. © 2025 by the author
Multipole Expansion of the Scalar Potential on the Basis of Spherical Harmonics: Bridging the Gap Between the Inside and Outside Spaces via Solution of the Poisson Equation
No full textThe multipole expansion on the basis of Spherical Harmonics is a multifaceted mathematical tool utilized in many disciplines of science and engineering. Regarding physics, in electromagnetism, the multipole expansion is exclusively focused on the scalar potential, Ur, defined only in the so-called inside, Uinr, and outside, Uoutr, spaces, separated by the middle space wherein the source resides, for both dielectric and magnetic materials. Intriguingly, though the middle space probably encloses more physics than the inside and outside spaces, it is never assessed in the literature, probably due to the rather complicated mathematics. Here, we investigate the middle space and introduce the multipole expansion of the scalar potential, Umidr, in this, until now, unsurveyed area. This is achieved through the complementary superposition of the solutions of the inside, Uinr, and outside, Uoutr, spaces when carefully adjusted at the interface of two appropriately defined subspaces of the middle space. Importantly, while the multipole expansion of Uinr and Uoutr satisfies the Laplace equation, the expression of the middle space, Umidr, introduced here satisfies the Poisson equation, as it should. Interestingly, this is mathematically proved by using the method of variation of parameters, which allows us to switch between the solution of the homogeneous Laplace equation to that of the nonhomogeneous Poisson one, thus completely bypassing the standard method in which the multipole expansion of |r−r′|−1 is used in the generalized law of Coulomb. Due to this characteristic, the notion of Umidr introduced here can be utilized on a general basis for the effective calculation of the scalar potential in spaces wherein sources reside. The proof of concept is documented for representative cases found in the literature. Though here we deal with the static and quasi-static limit of low frequencies, our concept can be easily developed to the fully dynamic case. At all instances, the exact mathematical modeling of Umidr introduced here can be very useful in applications of both homogeneous and nonhomogeneous, dielectric and magnetic materials
Electrostatics in Materials Revisited: The Case of Free Charges Combined with Linear, Homogeneous, and Isotropic Dielectrics
No full textHere we revisit the electrostatics of material systems comprising of free charges and linear, homogeneous, and isotropic (LHI) dielectrics. We focus on D(r) suggesting that this is the primary vector field of electrostatics. We show that D(r) is sufficient to conceptually describe all underlying physics and to mathematically accomplish all necessary calculations, beforehand, independently of the secondary vector fields P(r) and E(r) that, if needed, can be easily calculated from D(r). To this effect, we introduce a P-D electric susceptibility, χε, with −1≤χε≤0, that couples linearly P(r) with D(r) (instead of the standard P-E electric susceptibility, χe, with 0≤χe<∞, that couples linearly P(r) with E(r)). This concept restores the somehow misleading causality/feedback between P(r) and E(r) of the standard formulation, captures efficiently the underlying physics, enables electrostatics to obtain a form analogous to that of magnetostatics, and facilitates analytical/computational calculations in relevant systems. To document these claims, we provide technical means, among others, the free scalar potential, Ufr, and clarify the conditions that enable the calculation of D(r) on a standalone basis, directly from the free charge density, ρf, and the electric susceptibility, χε, of the LHI dielectrics. Our concept sets interesting perspectives for the treatment of all dielectrics
Electromagnetism in Linear, Homogeneous and Isotropic Materials: The Analogy Between Electricity and Magnetism in the Susceptibility and Polarization
No full textThrough the years, the asymmetry in the constitutive relations that define the electric and magnetic polarization, P and M, respectively, by the relevant vector field, E and H, has been imprinted, rather arbitrarily, in Maxwell’s equations. Accordingly, in linear, homogeneous, and isotropic (LHI) materials, the electric and magnetic polarization are defined via P = χeε0E (‘P-E, χe’ formulation; 0 ≤ χe < ∞) and M = χmH (‘M-H, χm’ formulation; −1 ≤ χm < ∞), respectively. Recently, the constitutive relation of the polarization was revisited in LHI dielectrics by introducing an electric susceptibility, χε, which couples linearly the reverse polarization, P~ = −P, with the electric displacement D through P~ = χεD (‘P-D, χε’ formulation; −1 ≤ χε ≤ 0). Here, the ‘P-D, χε’ formulation is generalized for the time-dependent case. It is documented that the susceptibility and polarization of LHI dielectric and magnetic materials can be described by the ‘P-D, χε’ and ‘M-H, χm’ formulation, respectively, on a common basis. To this end, the depolarizing effect is taken into account, which unavoidably emerges in realistic specimens of limited size, by introducing a series scheme to describe the evolution of polarization and calculate the extrinsic susceptibility. The engagement of the depolarizing factor N (0 ≤ N≤ 1) with the accompanying convergence conditions dictates that the intrinsic susceptibility of LHI materials, whether electric or magnetic, should range within [−1, 1]. The ‘P-D, χε’ and ‘M-H, χm’ formulations conform with this expectation, while the ‘P-E, χe’ does not. Remarkably, Maxwell’s equations are unaltered by the ‘P-D, χε’ formulation. Thus, all time-dependent processes of electromagnetism described by the standard ‘P-E, χe’ approach, are reproduced equivalently, or even advantageously, by the alternative ‘P-D, χε’ formulation
Does the extracorporeal circulation worsen anemia in hemodialysis patients? Investigation with advanced microscopes of red blood cells drawn at the beginning and end of dialysis
No full textDimosthenis Stamopoulos,1 Nerantzoula Bakirtzi,2,3 Efthymios Manios,1 Eirini Grapsa41Institute of Advanced Materials, Physicochemical Processes, Nanotechnology and Microsystems, National Center for Scientific Research 'Demokritos,' Athens, Greece; 2Department of Nephrology, Hospital 'G. Gennimatas,' Athens, Greece; 3Renal Unit, Hospital 'Alexandra,' Athens, Greece; 4Renal Unit, Hospital 'Aretaieion,' Athens, GreeceBackground: In hemodialysis (HD) patients, anemia relates to three main factors: insufficient production of erythropoietin; impaired management of iron; and decreased lifespan of red blood cells (RBCs). The third factor can relate to structural deterioration of RBCs due to extrinsic (extracorporeal circuit; biochemical activation and/or mechanical stress during dialysis) and intrinsic (uremic milieu; biochemical interference of the RBC membrane constituents with toxins) mechanisms. Herein, we evaluate information accessed with advanced imaging techniques at the cellular level.Methods: Atomic force and scanning electron microscopes were employed to survey intact RBCs (iRBCs) of seven HD patients in comparison to seven healthy donors. The extrinsic factor was investigated by contrasting pre- and post-HD samples. The intrinsic environment was investigated by comparing the microscopy data with the clinical ones.Results: The iRBC membranes of the enrolled HD patients were overpopulated with orifice-like (high incidence; typical size within 100–1,000 nm) and crevice-like (low incidence; typical size within 500–4,000 nm) defects that exhibited a statistically significant (P < 0.05) relative increase (+55% and +350%, respectively) in respect to healthy donors. The relative variation of the orifice and crevice indices (mean population of orifices and crevices per top membrane surface) between pre- and post-HD was not statistically significant (−3.3% and +4.5%, respectively). The orifice index correlates with the concentrations of urea, calcium, and phosphorus, but not, however, with that of creatinine.Conclusion: Extracorporeal circulation is not detrimental to the structural integrity of RBC membranes. Uremic milieu is a candidate cause of RBC membrane deterioration, which possibly worsens anemia.Keywords: hemodialysis, anemia, red blood cells, atomic force microscopy, scanning electron microscop
Magnetism and superconductivity in low-dimensional systems: utilization in future applications
No full textAssemblies of Coaxial Pick-Up Coils as Generic Inductive Sensors of Magnetic Flux: Mathematical Modeling of Zero, First and Second Derivative Configurations
No full textCoils are one of the basic elements employed in devices. They are versatile, in terms of both design and manufacturing, according to the desired inductive specifications. An important characteristic of coils is their bidirectional action; they can both produce and sense magnetic fields. Referring to sensing, coils have the unique property to inductively translate the temporal variation of magnetic flux into an AC voltage signal. Due to this property, they are massively used in many areas of science and engineering; among other disciplines, coils are employed in physics/materials science, geophysics, industry, aerospace and healthcare. Here, we present detailed and exact mathematical modeling of the sensing ability of the three most basic scalar assemblies of coaxial pick-up coils (PUCs): in the so-called zero derivative configuration (ZDC), having a single PUC; the first derivative configuration (FDC), having two PUCs; and second derivative configuration (SDC), having four PUCs. These three basic assemblies are mathematically modeled for a reference case of physics; we tackle the AC voltage signal, VAC (t), induced at the output of the PUCs by the temporal variation of the magnetic flux, Φ(t), originating from the time-varying moment, m(t), of an ideal magnetic dipole. Detailed and exact mathematical modeling, with only minor assumptions/approximations, enabled us to obtain the so-called sensing function, FSF, for all three cases: ZDC, FDC and SDC. By definition, the sensing function, FSF, quantifies the ability of an assembly of PUCs to translate the time-varying moment, m(t), into an AC signal, VAC (t). Importantly, the FSF is obtained in a closed-form expression for all three cases, ZDC, FDC and SDC, that depends on the realistic, macroscopic characteristics of each PUC (i.e., number of turns, length, inner and outer radius) and of the entire assembly in general (i.e., relative position of PUCs). The mathematical methodology presented here is complete and flexible so that it can be easily utilized in many disciplines of science and engineering
Phase diagram of vortex matter and hysteresis mechanisms in single crystals of HgBa_2CuO_4+δ and YBa_2Cu_3O_7-δ superconductors
No full textAC Magnetic Susceptibility: Mathematical Modeling and Experimental Realization on Poly-Crystalline and Single-Crystalline High-Tc Superconductors YBa2Cu3O7−δ and Bi2−xPbxSr2Ca2Cu3O10+y
No full textThe multifaceted inductive technique of AC magnetic susceptibility (ACMS) provides versatile and reliable means for the investigation of the respective properties of magnetic and superconducting materials. Here, we explore, both mathematically and experimentally, the ACMS set-up, based on four coaxial pick-up coils assembled in the second-derivative configuration, when employed in the investigation of differently shaped superconducting specimens of poly-crystalline YBa2Cu3O7−δ and Bi2−xPbxSr2Ca2Cu3O10+y and single-crystalline YBa2Cu3O7−δ. Through the mathematical modeling of both the ACMS set-up and of linearly responding superconducting specimens, we obtain a closed-form relation for the DC voltage output signal. The latter is translated directly to the so-called extrinsic ACMS of the studied specimen. By taking into account the specific characteristics of the studied high-Tc specimens (such as the shape and dimensions for the demagnetizing effect, porosity for the estimation of the superconducting volume fraction, etc.), we eventually draw the truly intrinsic ACMS of the parent material. Importantly, this is carried out without the need for any calibration specimen. The comparison of the mathematical modeling with the experimental data of the aforementioned superconducting specimens evidences fair agreement
Ferroelectric/Piezoelectric Materials in Energy Harvesting: Physical Properties and Current Status of Applications
No full textThe inevitable feedback between the environmental and energy crisis within the next decades can probably trigger and/or promote a global imbalance in both financial and public health terms. To handle this difficult situation, in the last decades, many different classes of materials have been recruited to assist in the management, production, and storage of so-called clean energy. Probably, ferromagnets, superconductors and ferroelectric/piezoelectric materials stand at the frontline of applications that relate to clean energy. For instance, ferromagnets are usually employed in wind turbines, superconductors are commonly used in storage facilities and ferroelectric/piezoelectric materials are employed for the harvesting of stray energy from the ambient environment. In this work, we focus on the wide family of ferroelectric/piezoelectric materials, reviewing their physical properties in close connection to their application in the field of clean energy. Among other compounds, we focus on the archetypal compound Pb(Zr,Ti)O3 (or PZT), which is well studied and thus preferred for its reliable performance in applications. Also, we pay special attention to the advanced ferroelectric relaxor compound (1−x)Pb(Mg1/3Nb2/3)O3−xPbTiO3 (or PMN-xPT) due to its superior performance. The inhomogeneous composition that many kinds of such materials exhibit at the so-called morphotropic phase boundary is reviewed in connection to possible advantages that it may bring when applications are considered
