Infinite Charge Research Articles

Novel multi-modular power conditioning system and decoupling control strategy for SMES with coupled superconducting coil

The high-temperature superconducting magnetic energy storage system (HTS-SMES) utilizes a superconducting coil (SC) to store electric energy in a magnetic field. It has several advantages such as high efficiency, fast response, and infinite charge–discharge cycles. Coupling two SCs made of different HTS materials, known as coupled SC (CSC), can enhance the utilization rate of HTS tapes, reduce manufacturing costs, increase the energy storage density of the SC, and lower magnetic leakage. However, the presence of a coupled magnetic field in CSC makes precise power and current regulation of the individual SC challenging. Additionally, the self-inductances of the individual SCs, composed of different materials, typically differ from each other. Consequently, the current variation induces electromotive force in each SC that differs from the others, necessitating the design of power converters with different voltage ratings connected to each SC. To address the difficulties associated with SMES implementation using CSC, this paper proposes novel modular power conditioning system (MPCS) and decoupling control strategy for SMES. The MPCS enables the flexible design of individual SC power ratings by selecting the appropriate number of power modules. The decoupling control ensures precise current control of each individual SC, which significantly reduces the current ripple of the SCs. Moreover, by employing carrier phase shift modulation, the total harmonic distortion (THD) of the PCS output current is as low as 0.79%. Furthermore, the feedforward power control is proposed to reduce the power control overshoot, and the current sharing control is presented to ensure precise current sharing between each SC. Simulation results verify the efficacy of the proposed approaches.

Analysis of infinite plane assumption and point charge assumption in the particle–plane electrostatic interaction model by re-expansion method and image multipole method

The solutions for the electrostatic interacting force between a particle and a plane typically assume that the plane is infinite and the particle can be approximated as a point charge. Nevertheless, the prerequisites of underlying assumptions of these calculations remain unspecified, resulting in the inability to assess the reliability of the results and constraining the practical applicability of analytical models. In this paper, the authors introduce the particle–coated plane electrostatic interaction model by employing the re-expansion method. Additionally, the multipole–coated plane electrostatic interaction model is presented using the image multipole method. An analysis of the assumptions’ prerequisites is conducted, considering a relative error of less than 2 % as the approximate standard. The findings indicate that, irrespective of the material properties of the particle and plane, the radius of the planar plate must exceed three times the distance between the particle’s center and the plane to satisfy the infinite plane assumption. When the distance between the particle’s center and the plane surpasses three times the radius, it is permissible to approximate the charged particle as a point charge. The study presented in this paper establishes a standard for prior estimation of the departure range in existing analytical models related to particle–plane electrostatic interaction. This work also serves as a theoretical basis for the practical application of these models in engineering.

Development of a MATLAB‐based graphical user interface to illustrate Coulomb's law and Gauss's law

AbstractCoulomb's law and Gauss's law are two fundamental laws in electrostatics that involve electric charges and electric fields. These concepts that are not visible physically in real life can be challenging for students to understand, especially when it involves complex charge distributions. This paper presents a MATLAB‐based graphical user interface (GUI) to visualise the concept of Coulomb's law and Gauss's law as well as a serious snake game to reinforce users' knowledge. This MATLAB GUI features a diverse range of 3‐dimensional (3D) visualisations illustrating electric field attributes such as electric force, charge distribution and electric flux. These visualisations dynamically adapt to user‐defined parameters, offering a rich and varied exploration of the electric field's characteristics without confining the scope to a specific count of models. In Coulomb's law section, the GUI plots the electric forces in 3‐D for dipole, three‐point charges, and unlimited charge. The Gauss's law section consists of windows for illustration of the fundamentals of Gauss's law for the electric field, and the illustration for the application of Gauss's law in finding the electric field for a point charge, infinite line charge and infinite plane charge. The serious snake game developed in this work allows students to engage in quizzes related to Coulomb's law and Gauss's law to serve as a tool for reinforcing their learning outcomes. The MATLAB‐based GUI was chosen as the platform due to its excellent visualisation capabilities, ease of programming and capability to act as a powerful tool to enhance the learning of Coulomb's law and Gauss's law for students.

Generation of orbital angular momentum hologram using a modified U-net

Orbital angular momentum (OAM) holography has become a promising technique in information encryption, data storage and opto-electronic computing, owing to the infinite topological charge of one single OAM mode and the orthogonality of different OAM modes. In this paper, we propose a novel OAM hologram generation method based on a densely connected U-net (DCU), where the densely connected convolution blocks (DCB) replace the convolution blocks of the U-net. Importantly, the reconstruction process of the OAM hologram is integrated into DCU as its output layer, so as to eliminate the requirement to prepare training data for the OAM hologram, which is required by conventional neural networks through an iterative algorithm. The experimental and simulation results show that the OAM hologram can rapidly be generated with the well-trained DCU, and the reconstructed image’s quality from the generated OAM hologram is significantly improved in comparison with those from the Gerchberg–Saxton generation method, the Gerchberg–Saxton based generation method and the U-net method. In addition, a 10-bit OAM multiplexing hologram scheme is numerically demonstrated to have a high capacity with OAM hologram.

Celestial Supersymmetry

We discuss supersymmetric Yang-Mills theory coupled to dilatons in the framework of celestial holography. We show that in the presence of point-like dilaton sources, the CCFT operators associated with the gauge supermultiplet acquire a simple, factorized form. They factorize into the holomorphic (super)current part and the exponential “light” operators of Liouville theory, in the infinite central charge limit. The current sector exhibits (1,0) supersymmetry, thus implementing spacetime supersymmetry in CCFT.

3D Asymmetric Bilayer Garnet-Hybridized High-Energy-Density Lithium–Sulfur Batteries

Lithium garnet Li7La3Zr2O12 (LLZO), with high ionic conductivity and chemical stability against a Li metal anode, is considered one of the most promising solid electrolytes for lithium-sulfur batteries. However, an infinite charge time resulting in low capacity has been observed in Li-S cells using Ta-doped LLZO (Ta-LLZO) as a solid electrolyte. It was observed that this cell failure is correlated with lanthanum segregation to the surface of Ta-LLZO that reacts with a sulfur cathode. We demonstrated this correlation by using lanthanum excess and lanthanum deficient Ta-LLZO as the solid electrolyte in Li-S cells. To resolve this challenge, we physically separated the sulfur cathode and LLZO using a poly(ethylene oxide) (PEO)-based buffer interlayer. With a thin bilayer of LLZO and the stabilized sulfur cathode/LLZO interface, the hybridized Li-S batteries achieved a high initial discharge capacity of 1307 mA h/g corresponding to an energy density of 639 W h/L and 134 W h/kg under a high current density of 0.2 mA/cm2 at room temperature without any indication of a polysulfide shuttle. By simply reducing the LLZO dense layer thickness to 10 μm as we have demonstrated before, a significantly higher energy density of 1308 W h/L and 257 W h/kg is achievable. X-ray diffraction and X-ray photoelectron spectroscopy indicate that the PEO-based interlayer, which physically separates the sulfur cathode and LLZO, is both chemically and electrochemically stable with LLZO. In addition, the PEO-based interlayer can adapt to the stress/strain associated with sulfur volume expansion during lithiation.

Celestial Liouville theory for Yang-Mills amplitudes

We consider Yang-Mills theory with the coupling constant and theta angle determined by the vacuum expectation values of a dynamical (complex, zero mass) dilaton field. We discuss the tree-level N-gluon MHV scattering amplitudes in the presence of a nontrivial background dilaton field and construct the corresponding celestial amplitudes by taking Mellin transforms with respect to the light cone frame energies. In this way, we obtain two-dimensional CFT correlators of primary fields on the celestial sphere. We show that the celestial Yang-Mills amplitudes evaluated in the presence of a spherical dilaton shockwave are given by the correlation functions of primary field operators factorized into the holomorphic current operators times the “light” Liouville operators. They are evaluated in the semiclassical limit of Liouville theory (the limit of infinite central charge) and are determined by the classical Liouville field describing metrics on the celestial sphere.

Celestial Yang-Mills amplitudes and D = 4 conformal blocks

We discuss the properties of recently constructed “single-valued” celestial four-gluon amplitudes. We show that the amplitude factorizes into the “current” part and the “scalar” part. The current factor is given by the group-dependent part of the Wess-Zumino-Witten correlator of four holomorphic currents with a non-vanishing level of Kač-Moody algebra. The scalar factor can be expressed in terms of a complex integral of the Koba-Nielsen form, similar to the integrals describing four-point correlators in Coulomb gas models and, more generally, in the infinite central charge limit of Liouville theory. The scalar part can be also obtained by a dimensional reduction of a single D = 4 conformal block and the shadow block from Minkowski space to the celestial sphere.

Multichannel Generations of Orbital Angular Momentum Modes with On‐Demand Characteristics on a Chip

AbstractThe orthogonality among optical beams with different orbital angular momentum (OAM) modes presents a new perspective as independent data‐carrying channels for multiplexing and demultiplexing. In particular, the theoretically infinite topological charge of OAM beam promises the unbounded capacity in communication systems. As a key part for the advancement of OAM technologies, OAM source has attracted considerable interest and experienced a rapid development. Nevertheless, conventional approaches to create OAM modes mainly rely on the use of bulky optical devices and external laser source, preventing their implementation into a miniaturized system. As a contrast, on‐chip generation of OAM beams with a built‐in source stands out with several advantages, including small footprint, compactness, portability, and high‐power efficiency. In this work, a versatile approach to directly produce OAM modes with on‐demand characteristics on a chip is demonstrated. Featuring the judicious combination of the emerging dielectric metasurface with the standard vertical cavity surface‐emitting laser (VCSEL) platform, the approach represents a feasible solution to the wide implementation of wafer‐level OAM emitters for optoelectronic integrations. Prototype laser chips for the generation of both individual OAM beam and OAM array with novel functionalites, such as controllable directionality and spatially varying topological charge and distribution, are systematically presented.

Optical vortices with an infinite number of screw dislocations

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

Optical vortices with an infinite number of screw dislocations

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

Propagation-invariant laser beams with an array of phase singularities

In this work, we investigate multivortex beams with an infinite topological charge. Such optical vortices contain an array of an infinite, but countable, number of phase singularities (isolated intensity nulls), which typically have the unitary topological charge and are located either uniformly (or not uniformly) on a straight line (or on several crossing straight lines) in the beam transverse cross section. Such optical vortices are form invariant and their transverse intensity distribution is conserved on propagation, changing only in scale and rotation. The orbital angular momentum of such optical vortices is finite, since only a finite number of screw dislocations is located within the area of the notable intensity of the Gaussian beam, while the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to a parabolic growth of the orbital angular momentum of such beams.

On the non-dominance of counterions in the 1:z planar electrical double layer of point-ions

According to the dominance prescription of point-ions in the non-linear Poisson-Boltzmann theory, proposed by Valleau and Torrie almost 40 years ago, the microscopic and thermodynamic properties of an asymmetric binary electrolyte converge asymptotically to those of a completely symmetric electrolyte, in the limit of an infinite surface charge density of a planar electrode, if the properties of the counterions are the same in both instances. By using the Grahame equation and the non-linear Poisson-Boltzmann theory, we show here that this prescription is certainly exact for the mean electrostatic potential at the electrode's surface and for the capacitive compactness. Contrastingly, analytical and numerical solutions of the non-linear Poisson-Boltzmann equation show that, in the limit of an infinite surface charge density of the planar electrode, it is possible to observe finite differences between the local mean electrostatic potentials and electric fields associated to a 1:1 and a 1:z electrolyte at places near the electrode's surface. Thus, we prove here that even in the absence of ion correlations and ionic excluded volume effects, the counterions do not fully dominate the structural properties in the entire electrical double layer in the non-linear Poisson-Boltzmann picture, which is confirmed through comparisons with new Monte Carlo simulations.

Optical vortex beams with the infinite topological charge

Up to now, Gaussian optical vortices (OVs) were investigated with the finite topological charge (TC). Here, we study an OV with the infinite TC. Such OVs have a countable number of phase singularities (isolated intensity nulls), which typically have the unitary TC and are located either equidistantly or not equidistantly on a straight line in the beam transverse cross section. Such OVs are structurally stable (form-invariant) and their transverse intensity is conserved on propagation, changing only in scale and rotation. Orbital angular momentum (OAM) of such OVs is finite, since only a finite number of screw dislocations are within the Gaussian beam in the area of notable intensity, whereas the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to the parabolic growth of the OAM of such beams. A unique feature of these beams is that their normalized OAM can be adjusted (both increased and decreased) by simple change of the waist radius of the Gaussian beam. In addition to the two form-invariant beams, we studied a Gaussian beam with a countable number of edge dislocations (zero-intensity lines), which is not form-invariant, but, after an astigmatic transform by a cylindrical lens, also becomes an infinite-topological-charge beam.

On classical solutions of the two-species Vlasov–Poisson system in R3 with infinite charge

We are concerned with the initial value problem for the two-species Vlasov–Poisson system in the plasma physics case in R3. It is assumed that initially the phase-space densities of ions and electrons decay only polynomially with respect to the velocities, but the net charge density vanishes at infinity with a polynomial rate, which allows for defining the electrostatic field. This situation falls into the so-called infinite charge problem, and there is no rigorous result as far as we know. Local existence, uniqueness, and continuation criteria of the classical solution are established in this paper. Moreover, this article also shows the existence of a global solution in the case of radial symmetry.

The Swampland Distance Conjecture for K\xe4hler moduli

The Swampland Distance Conjecture suggests that an infinite tower of modes becomes exponentially light when approaching a point that is at infinite proper distance in field space. In this paper we investigate this conjecture in the Kähler moduli spaces of Calabi-Yau threefold compactifications and further elucidate the proposal that the infinite tower of states is generated by the discrete symmetries associated to infinite distance points. In the large volume regime the infinite tower of states is generated by the action of the local monodromy matrices and encoded by an orbit of D-brane charges. We express these monodromy matrices in terms of the triple intersection numbers to classify the infinite distance points and construct the associated infinite charge orbits that become massless. We then turn to a detailed study of charge orbits in elliptically fibered Calabi-Yau threefolds. We argue that for these geometries the modular symmetry in the moduli space can be used to transfer the large volume orbits to the small elliptic fiber regime. The resulting orbits can be used in compactifications of M-theory that are dual to F-theory compactifications including an additional circle. In particular, we show that there are always charge orbits satisfying the distance conjecture that correspond to Kaluza-Klein towers along that circle. Integrating out the KK towers yields an infinite distance in the moduli space thereby supporting the idea of emergence in that context.

Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit

We discuss partition function of 2d CFTs decorated by higher qKdV charges in the thermodynamic limit when the size of the spatial circle goes to infinity. In this limit the saddle point approximation is exact and at infinite central charge generalized partition function can be calculated explicitly. We show that leading 1/c corrections to free energy can be reformulated as a sum over Young tableaux which we calculate for the first two qKdV charges. Next, we compare generalized ensemble with the “eigenstate ensemble” that consists of a single primary state. At infinite central charge the ensembles match at the level of expectation values of local operators for any values of qKdV fugacities. When the central charge is large but finite, for any values of the fugacities the aforementioned ensembles are distinguishable.

The leading correction to the Thomas–Fermi model at finite temperature

The semi-classical approach leading to the Thomas–Fermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of Z→∞, i.e., infinite nuclear charge, at finite density and temperature. Motivated by the zero-temperature case, we show in the current paper that the correction to TF due to quantum treatment of the strongly bound inner-most electrons, for which the semi-classical approximation breaks, scales as Z−1∕3, with respect to the TF solution. As such, it is more dominant than the quantum corrections to the kinetic energy, as well as exchange and correlation, which are known to be suppressed by Z−2∕3. We conjecture that this is the leading correction for this model. In addition, we present a different free energy functional for the TF model, and a successive functional that includes the strongly bound electrons correction. We use this corrected functional to derive a self-consistent potential and the electron density in the atom, and to calculate the corrected energy. At this stage, our model has a built-in validity limit, breaking as the L shell ionizes.

The Vlasov–Poisson equation in ℝ3 with infinite charge and velocities

We consider the Vlasov–Poisson equation in [Formula: see text] with initial data which are not [Formula: see text] in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we prove the existence and uniqueness of the solution, thus generalizing the analogous result by the same authors for data compactly supported in the velocities.

A Material Perspective of Rechargeable Metallic Lithium Anodes

AbstractRechargeable lithium‐based batteries are long considered as the most promising candidates for application in various electronic devices, electric vehicles, and even electrical grids owing to their ultrahigh energy densities. However, to date, metallic lithium‐based batteries are still far from practical applications due to the low Coulombic efficiency and fast capacity decay of lithium anodes. The poor electrochemical performances of metallic lithium anodes are inherently related to random growth of lithium dendrites and infinite volume charge of lithium anodes. In this review, the failure mechanisms of metallic lithium anodes are summarized and ascribed to the unstable and inhomogeneous solid electrolyte interphase, uneven distributions of electric field, and lithium‐ion flux during the lithium plating processes. Correspondingly, efficient strategies for mitigating these problems, including surficial engineering, electric field, and lithium‐ion flux regulation are discussed from the perspective of anode materials. Finally, an outlook is proposed for the design and fabrication of next‐generation rechargeable metallic lithium anodes that aims to address the intrinsic problems of metallic lithium anodes.