Point-like Research Articles

Probing massive gravitons in f(R) with lensed gravitational waves

We investigate the novel features of gravitational wave solutions in f(R) gravity under proper gauge considerations in the shifted Ricci scalar background curvature (R1+ϵ). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on ϵ. Our analysis yields new insights as we scrutinize these dispersion effects on the polarization (modified Newman-Penrose content) and lensing properties of gravitational waves. It is discovered that the existing longitudinal scalar mode, and transverse breathing scalar mode are both independent of the mass parameter for ϵ<<1. Further, by analysing the lensing amplification factor for the point mass lens model, we show that lensing of gravitational wave is highly sensitive to these dispersion effects in the milli-Hertz frequency (wave optics regime). It is expected that ultra-light modes, having mass about O(10−15) eV for ϵ<<1(≈10−7) lensed by (103≤MLens≤106)M⊙ compact objects are likely to be detected by the advanced gravitational wave space-borne detectors, particularly within LISA's (The Laser Interferometer Space Antenna) sensitivity band.

Pressure Change in a Duct with a Flow of a Homogeneous Gaseous Substance in the Presence of a Point Mass and Momentum Sink of Gas

The flow characteristics of homogeneous gases in complex systems are an important issue in many areas, including underground mines. The flow in mine excavations and ventilation systems is described by known mathematical relationships that could be applied to various cases. In this paper, a flow in a duct with a local sink of mass and momentum for multiple variants of cooperation of a mechanical fan was analyzed. The relationships for the total and static pressure of air in the duct were derived. In the next stage, a calculation example of how the mass flow rate of air, and the total and static pressure of the flowing air will change in the tested sections for the duct with and without a sink, is presented. The derived formulas and calculated values for the considered calculation case allow the verification of the obtained relationships at the measurement station. Analyzing the results of the examples presented in the article, it can be concluded that the total and static pressure at the sink point differ depending on the equation of motion used. In the case of the classic equation, the value of total pressure is lower than the value calculated from the new equation of motion, and the difference between them is about 20 Pa. In the case of static pressure, this difference is about 46 Pa. Qualitative differences in the static pressure distribution at the release location were also demonstrated. Depending on the applied approach, positive or negative changes in the static pressure are noticed. The presented form of the equation of motion made it possible to determine the flow characteristics in the duct with a point mass and momentum sink in the case of the operation with and without a fan.

Dissociation Energies via Embedding Techniques.

Due to the large number of interactions, evaluating interaction energies for large or periodic systems results in time-consuming calculations. Prime examples are liquids, adsorbates, and molecular crystals. Thus, there is a high demand for a cheap but still accurate method to determine interaction energies and gradients. One approach to counteract the computational cost is to fragment a large cluster into smaller subsystems, sometimes called many-body expansion, with the fragments being molecules or parts thereof. These subsystems can then be embedded into larger entities, representing the bigger system. In this work, we test several subsystem approaches and explore their limits and behaviors, determined by calculations of trimer interaction energies. The methods presented here encompass mechanical embedding, point charges, polarizable embedding, polarizable density embedding, and density embedding. We evaluate nonembedded fragmentation, QM/MM (quantum mechanics/molecular mechanics), and QM/QM (quantum mechanics/quantum mechanics) embedding theories. Finally, we make use of symmetry-adapted perturbation theory utilizing density functional theory for the monomers to interpret the results. Depending on the strength of the interaction, different embedding methods and schemes prove favorable to accurately describe a system. The embedding approaches presented here are able to decrease the interaction energy errors with respect to full system calculations by a factor of up to 20 in comparison to simple/unembedded approaches, leading to errors below 0.1 kJ/mol.

The Lavrentiev Phenomenon

The basic problem of the calculus of variations consists of finding a function that minimizes an energy, like finding the fastest trajectory between two points for a point mass in a gravity field or finding the best shape of a wing. The existence of a solution may be established in quite abstract spaces, much larger than the space of smooth functions. An important practical problem is that of being able to approach the value of the infimum of the energy. However, numerical methods work with very “concrete” functions and sometimes they are unable to approximate the infimum: this is the surprising Lavrentiev phenomenon. The papers that ensure the nonoccurrence of the phenomenon form a recent saga, and the most general result formulated in the early ’90s was actually fully proved just recently, more than 30 years later. Our aim here is to introduce the reader to the calculus of variations, to illustrate the Lavrentiev phenomenon with the simplest known example, and to give an elementary proof of the nonoccurrence of the phenomenon.

Protoporphyrin IX iron(II) revisited. An overview of the Mössbauer spectroscopic parameters of low-spin porphyrin iron(II) complexes.

Mössbauer parameters of low-spin six-coordinate [Fe(II)(Por)L2] complexes (where Por is a synthetic porphyrin; L is a nitrogenous aliphatic, an aromatic base or a heterocyclic ligand, a P-bonding ligand, CO or CN) and low-spin [Fe(Por)LX] complexes (where L and X are different ligands) are reported. A known point charge calculation approach was extended to investigate how the axial ligands and the four porphyrinato-N atoms generate the observed quadrupole splittings (ΔEQ) for the complexes. Partial quadrupole splitting (p.q.s.) and partial chemical shifts (p.c.s.) values were derived for all the axial ligands, and porphyrins reported in the literature. The values for each porphyrin are different emphasising the importance/uniqueness of the [Fe(PPIX)] moiety, (which is ubiquitous in nature). This new analysis enabled the construction of figures relating p.c.s and p.q.s values. The relationships presented in the figures indicates that strong field ligands such as CO can, and do change the sign of the electric field gradient in the [Fe(II)(Por)L2] complexes. The limiting p.q.s. value a ligand can have and still form a six-coordinate low-spin [Fe(II)(Por)L2] complex is established. It is shown that the control the porphyrin ligands exert on the low-spin Fe(II) atom limits its bonding to a defined range of axial ligands; outside this range the spin state of the iron is unstable and five-coordinate high-spin complexes are favoured. Amongst many conclusions, it was found that oxygen cannot form a stable low-spin [Fe(II)(Por)L(O2)] complex and that oxy-haemoglobin is best described as an [Fe(III)(Por)L(O2-)] complex, the iron is ferric bound to the superoxide molecule.

"Blade of Polarized Water Molecule" Is the Key to Hydrolase Catalysis Regulation.

Hydrolysis catalyzed by aspartic proteases is a crucial reaction in many biological processes. However, anchoring water molecules and unifying multiple catalytic pathways remain significant challenges. Consequently, molecular design often compromises by focusing on enhancing substrate specificity. Using our self-developed polarizable point charge (PPC) force field, we determined the significant role of polarization in the hydrolase of pepsin for the first time. To be stably anchored in the active site, the water should be intensely polarized with a charge higher than -0.94e. Induced by this polarization, the pepsin was shown to support three general base/general acid pathways, with a preference for the gemdiol-intermediate-based pathway. Consequently, we proposed the "Blade of Polarized Water Molecule" model for rational enzyme design, highlighting that the polarization of both the attacking water and the attacked carbonyl is crucial for enhancing hydrolysis. Mutants D290Q and S172P showed activity enhancements of 191.23% and 324.70%, respectively. The improved polarization of water, carbonyl, and relevant nucleophilic attack distances in the mutants reaffirmed the crucial role of polarization in improving hydrolysis. This study provides a new perspective on hydrolase analysis and modification.

Acoustic radiation characteristics of shark skin inspired surface modified plates

This paper aims to evaluate the acoustic radiation characteristics of thin plates featuring a layer of small-scale biomimetic shark skin type additive surface treatment. The shark skin dermal denticles are modelled as point masses arranged in a bi-directional pattern on both the upper and lower surfaces of the plate. The governing equations are obtained through a variational approach, incorporating the Dirac Delta function in the derivation of the proposed semi-analytical model for the shark skin layer. A semi-analytical method based on the Rayleigh–Ritz formulation is utilized to analyze the vibrations of these plates with surface modification. The sound radiation characteristics are then derived from the solution of the Rayleigh integral. A comprehensive investigation is performed on the influence of surface modification on different vibro-acoustic characteristics, using a continuous structural mode and power transfer matrix-based approach. Notable observations include a reduction in peak vibro-acoustic responses with dense denticle arrangements, especially at resonance, demonstrating a direct relationship with mass ratios, i.e., the ratio of denticle mass to plate mass. The study further reveals a shift of vibro-acoustic responses towards low frequencies with an increase in mass ratios. A thorough comparative study indicates that while additive surface modifications inspired by shark skin may weaken sound radiation characteristics at resonance frequencies, a reverse effect can be observed at intermittent operational frequencies.

Optical induction of monopoles, knots, and skyrmions in quantum gases

Single topological defects and related structures have been experimentally created inside clouds of Bose-Einstein condensates. However, a practical protocol for creating multiple defects inside a single cloud—a prerequisite for studying defect interactions—has been lacking. Here we propose, and theoretically analyze, a practical protocol for the creation of configurations of topological monopoles, quantum knots, and skyrmions in Bose-Einstein condensates by employing fictitious magnetic fields induced by the interaction of the atomic cloud with coherent light fields. It is observed that a single coherent field is not enough for this purpose, but instead we find incoherent superpositions of several coherent fields that introduce topological point charges. We numerically estimate the experimentally achievable strengths and gradients of the induced fictitious magnetic fields and find them to be adjustable at will to several orders of magnitude greater than those of the physical magnetic fields employed in previous experimental studies. This property together with ultrafast control of the optical fields paves the way for advanced engineering of topological defects in quantum gases. Published by the American Physical Society 2024

Finite Nuclear Size Effect on the Relativistic Hyperfine Splittings of 2s and 2p Excited States of Hydrogen-like Atoms

Hyperfine splittings play an important role in quantum information and spintronics applications. They allow for the readout of the spin qubits, while at the same time providing the dominant mechanism for the detrimental spin decoherence. Their exact knowledge is thus of prior relevance. In this work, we analytically investigate the relativistic effects on the hyperfine splittings of hydrogen-like atoms, including finite-size effects of the nucleis’ structure. We start from exact solutions of Dirac’s equation using different nuclear models, where the nucleus is approximated by (i) a point charge (Coulomb potential), (ii) a homogeneously charged full sphere, and (iii) a homogeneously charged spherical shell. Equivalent modelling has been done for the distribution of the nuclear magnetic moment. For the 1s ground state and 2s excited state of the one-electron systems H1, H2, H3, and He+3, the calculated finite-size related hyperfine shifts are quite similar for the different structure models and in excellent agreement with those estimated by comparing QED and experiment. This holds also in a simplified approach where relativistic wave functions from a Coulomb potential combined with spherical-shell distributed nuclear magnetic moments promises an improved treatment without the need for an explicit solution of Dirac’s equation within the nuclear core. Larger differences between different nuclear structure models are found in the case of the anisotropic 2p3/2 orbitals of hydrogen, rendering these excited states as promising reference systems for exploring the proton structure.

Trajectory analysis and flight modeling of combat aircrafts ejection seats

In this study, it is aimed to develop a generic model which calculates the trajectory of the ejection seat from the jet aircraft, by taking into account the parameters that will affect the seat movement such as the seat’s launch speed, ejection direction, ejection angle, altitude of the aircraft, distance/height from the aircraft rudder and canopy, pilot and ejection seat weight. With the model algorithm proposed, the ejection seat trajectory model was developed on MATLAB. The ejection seat trajectory model is based on point mass trajectory mathematical model. In this study, an analytical study of the problem has been made for modeling the flight trajectory of the ejection seat after it has been ejected. Past studies were used as a basis for validation and simulation. By writing a generic MATLAB code, a user interface was developed and presented to the user as a module. This generic code that has been developed could be used for simulations by users in the future by revising it in accordance with their own job descriptions.

Quantum Chemical Approaches for Manipulation and Evaluation of Intracage Microelectric Field Strength of Molecular Containers in Y@C64 and Y@C64X4 (X = Cl, F, and H, Y = NH4Cl, H3O-Cl, and 2H2O).

The effect of an oriented external electric field (EEF) on materials has led to the ongoing development, which stimulates us to consider whether intracage microelectric fields (IMEFs) can be used to substitute for the EEF. Focusing on the manipulation and evaluation of the IMEF of asymmetric molecular containers, the host-guest compounds of interesting pineapple-shaped Y@C64X4 (X = vacant, Cl, F, and H; Y = NH4Cl, H3O-Cl, and 2H2O) are theoretically constructed and the strength of the IMEF was evaluated by the intrapotential energy surface analysis by using the point charge (q = +1) scanning method. Interestingly, the left and right halves of each cage are like two IMEFs connected in reverse series. Both the addition of four X atoms and the orientation of the guest can sensitively influence the IMEF's strengths and directions of both half cages and further determine the entire cage's IMEF. Subsequently, the IMEF can sensitively change the binding characteristics and properties of the guest species. Therefore, the manipulation and evaluation of the IMEF can be achievable. This work may provide support for an asymmetric molecular container with an IMEF to manipulate the novel structural and chemical bond characteristics of the guest species.

Smart home power management algorithm using real-time model predictive control for a stand-alone PV system with battery energy storage

A smart home power management system is critical for stand-alone home-photovoltaic (HPV) with battery energy storage. Existing approaches often focus on maximizing power extraction from PV systems without considering real-time power adjustments or battery state of charge (SoC), which can lead to over-current or over-voltage issues that damage the battery. To address these limitations, this paper proposes a home power management algorithm that dynamically adjusts the power flow between the PV system, home loads, and the battery based on real-time system power measurements and battery SoC. This dynamic adjustment ensures an uninterrupted power supply to the home loads while maintaining battery safety. The proposed home manager algorithm features multiple operating modes: Maximum power point (MPP) charging, partial charging, fast charging, float charging, and partial discharging. Each mode is integrated with its dedicated model predictive controller (MPC) to achieve its specific control objective. Finally, through a semi-experimental simulation using a process-in-the-loop (PIL) test approach with the embedded board eZdsp TMS320F28335, testing under various irradiance levels shows that the home manager achieves significant improvement over conventional approaches. For instance, over the MPP mode it achieve a power efficiency of 99.36% with a 2.05% SoC increase, while fast charging mode resulted in 87.44% efficiency with an 11.2% SoC increase. However, float charging mode maintained an 87.27% efficiency with a 2.6% SoC increase, and partial discharging led to a 1.3% SoC decrease. The overall battery efficiency reached 96.45%, demonstrating the algorithm’s ability to optimize power flow, ensure a reliable energy supply, and maintain battery safety under varying weather conditions.

Circular motion of a charged particle on the inner surface of a frictionless cone under the influence of an electric field due to an electric dipole

A common problem provided in elementary physics textbooks is the analysis of the circular motion of a point-like particle affected by a gravitational field on the frictionless inner surface of an inverted cone. In this research, we study the motion of a charged particle on the same surface subject to an electric field generated by an electric dipole placed at the bottom of the cone. We study negatively and positively charged particles and analyse the dynamics of both. We calculate the physical quantities such as speed, angular velocity, angular momentum, and mechanical energy. Furthermore, we determine all possible distances travelled by the particles measured from the dipole. We also discuss the stability of the circular orbit using the effective potential. Finally, we consider the particle’s motion on a generic surface formed by the revolution of the curve ρz around the vertical axis. We determine the differential equation of ρz , in which the kinematic variables including speed v, angular velocity ω, and angular momentum L are constant.

Theory of Classical Electrodynamics with Topologically Quantized Singularities as Electric Charges

AbstractA theory of classical electrodynamics, where the only admissible electric charges are topological singularities in the electromagnetic field, is formulated. Charge quantization is accounted by the Chern theorem, such that Dirac magnetic monopoles are not needed. The theory allows positive and negative charges of equal magnitude, where the sign of the charge corresponds to the chirality of the topological singularity. Given the trajectory of the singularity, one can calculate electric and magnetic fields identical to those produced by Maxwell's equations for a moving point charge, apart from a multiplicative constant factor related to electron charge and vacuum permittivity. The theory is based on the relativistic Weyl equation in frequency‐wavevector space, with eigenstates comprising the position, velocity, and acceleration of the singularity, and eigenvalues defining the retarded position of the charge. From the eigenstates, one calculates the Berry connection and the Berry curvatures, and identifies the curvatures as electric and magnetic fields.

Summing gravitational effects from loops of inflationary scalars

Abstract We develop a procedure for re-summing the large logarithms induced&amp;#xD;in gravity by loops of inflationary scalars. We first show how the&amp;#xD;scalar can be integrated out of the field equations in the presence&amp;#xD;of constant graviton field. We then extend this result to a fully&amp;#xD;conserved form which explains the need for a finite renormalization&amp;#xD;of the cosmological constant which was previously inferred from &amp;#xD;explicit computation. A variant of the renormalization group turns&amp;#xD;out to explain the large logarithmic corrections revealed by &amp;#xD;explicit computation in the electric field strength of gravitational &amp;#xD;radiation and in the potentials which characterize the response to&amp;#xD;a point mass. The implications for graviton loops are discussed.

Sustainable Heat Generation in Flow from a Molecular Solar Thermal Energy Storage System

As the global deployment of renewable technologies accelerate, finding efficient ways to store energy will aid in responding to shifting energy demands. A prospective option not only in harvesting solar energy but also in emission‐free heating is MOlecular Solar Thermal (MOST) energy storage. A central part of MOST applications is to develop methods to release the stored energy. Herein, the Quadricyclane (QC)‐to‐Norbornadiene catalyzed back reaction is explored in a specially designed packed‐bed reactor. Four distinctly sized and purposely synthesized platinum on activated carbon catalysts are studied to trigger the heat release from the energy‐dense QC isomer. The catalysts are fully characterized using a variety of structural, surface, and spectroscopic techniques. Parameters to optimize catalytic conversion and heat release in flow conditions are explored including particle size and packing behavior, flow rates, and molecular residence times. Moreover, using CO pulse chemisorption technique, site time yield values and a turnover number are reported. Complementary to the flow reactions, computational fluid dynamic simulations applying lattice Boltzmann methods to two catalytic packed beds of different size ranges are done to evaluate fluid‐dynamic behavior within the reactor bed to ascertain the ideal particle size and packing density for catalysis in MOST applications.

On Positive Inflated Geometric Distribution: Properties and Applications

One-inflation in zero-truncated count data has recently found considerable attention. In this regard, zero-truncated Geometric distribution and distribution to a point mass at one are used to create a one-inflated model, namely, one-inflated zero-truncated Geometric distribution. Its reliability characteristics, generating functions, and distributional properties are investigated in detail, which includes survival function, hazard rate function, reverse hazard rate function, probability generating function, characteristic function, variance, skewness, and kurtosis. Monte Carlo simulation have been undertaken to evaluate the effectiveness of the maximum likelihood estimators. To test the compatibility of our proposed model, the baseline model and the proposed model are distinguished by using the two different test procedures. The adaptability of the suggested model is demonstrated using two real-life datasets from separate domains by taking various performance measures into consideration.

The phase transformation of the electron forms an atomic capacitor

Reinterpretation of existing experimental results suggests that the electron goes through a phase transformation in the vicinity of the nucleus and forms a nonrevolving surface charge electron shell from point charge and vice versa. Experimental results also strongly suggest that the laws of classical physics are valid at the atomic scale. The static, nonrevolving surface charge electron shell around the nucleus is a capacitor. Following a classical physics approach, the energy stored in this atomic capacitor is calculated for the hydrogen atom. The stored energy in the formed atomic capacitor agrees reasonably well with the rest energy of the electron. This agreement is in line with the predicted phase transformation of the electron and shows that the transformation from point to surface charge and vice versa is energetically feasible.

Kernel-Based Minimal Distributed Charges: A Conformationally Dependent ESP-Model for Molecular Simulations.

A kernel-based method (kernelized minimal distributed charge model (kMDCM)) to represent the molecular electrostatic potential (ESP) in terms of off-center point charges is introduced. The positions of the charges adapt to the molecular geometry and allow the description of intramolecular charge flow. Using Gaussian kernels and atom-atom distances as the features, the ESPs for water and methanol are shown to improve by at least a factor of 2 compared with point charge models fit to an ensemble of structures. The conformationally fluctuating molecular dipole moment of water is reproduced almost twice as accurately using kMDCM compared with static PCs, despite not fitting to the dipole directly. The role of hyperparameters in the kernelization is investigated and their implication on model performance and simulation stability is discussed. Combining kMDCM for the electrostatics and reproducing kernels for the bonded terms allows energy-conserving simulations of 2000 water molecules with periodic boundary conditions on the nanosecond time scale. These MD simulations sample geometries outside the training set but remain stable, which demonstrates the robustness of the model and its implementation.

Design of Point Charge Models for Divalent Metal Cations Targeting Quantum Mechanical Ion–Water Dimer Interactions

Divalent metal cations are of vital importance in biochemistry and materials science, and their structural and thermodynamic properties in aqueous solution have often been used as targets for the development of ion models. This study presented a strategy for designing nonbonded point charge models of divalent metal cations (Mg2+ and Ca2+) and Cl− by targeting quantum mechanics (QM)-based ion–water dimer interactions. The designed models offered an accurate representation of ion–water interactions in the gas phase and showed reasonable performance for non-targeted properties in aqueous solutions, such as the ion–water oxygen distance (IOD), coordination number (CN), and density and viscosity of MgCl2 and CaCl2 solutions at low concentrations. Our metal cation models yielded considerable overestimates of the hydration free energies (HFEs) of the ions, whereas the Cl− model displayed good performance. Together with the overestimated density and viscosity of the salt solutions, these results indicated the necessity of re-optimizing ion–ion interactions and/or including polarization effects in the design of ion models. The designed Mg2+ model was capable of maintaining the crystal metal-binding networks during MD simulation of a metalloprotein, indicating great potential for biomolecular simulations. This work highlighted the potential of QM-based ion models to advance the study of metal ion interactions in biological and material systems.