Point-like Research Articles

Fluids with power-law repulsion: Hyperuniformity and energy fluctuations.

We revisit the equilibrium statistical mechanics of a classical fluid of point-like particles with repulsive power-law pair interactions, focusing on density and energy fluctuations at finite temperature. Such long-range interactions, decaying with inter-particle distance $r$ as $1/r^s$ in $d$ dimensions, are known to fall into two qualitatively different categories. For $s<d$ (``strongly" long-range interactions) there are screening of correlations and suppression of large-wavelength density fluctuations (hyperuniformity). These effects eliminate density modes with arbitrarily large energy. For $s>d$ (``weakly" long-range interactions) screening and hyperuniformity do not occur. Using scaling arguments, variational analysis, and Monte Carlo simulations, we find another qualitative distinction. For $s\geq d/2$ the strong repulsion at short distances leads to enhanced small-wavelength density fluctuations, decorrelating particle positions. This prevents indefinitely negative entropy and large energy fluctuations. The distinct behaviors for $s\geq d/2$ and $s<d/2$ give rise to qualitatively different dependencies of the entropy, heat capacity, and energy fluctuations on temperature and density. We investigate the effect of introducing an upper cutoff distance in the pair-potential. The effect of the cutoff on energy fluctuations is strong for $s<d/2$ and negligible for $s \geq d/2$.

Low Computational Cost for Multiple Waypoints Trajectory Planning: A Time‐Optimal‐Based Approach

In the field of mobile robots, achieving minimum time in executing trajectories is crucial for applications like delivery, inspection, and search and rescue. In this article, a novel time‐optimal planner based on optimization methods is introduced. Despite the high computational cost associated with such methods, the solution calculates time‐optimal multi‐waypoint trajectories, achieving results in the order of milliseconds. The proposed method formulates a time‐optimal trajectory using the Pontryagin's maximum principle as a policy. By utilizing a point mass model, the planner generates trajectories that are adaptable to different robot models. The approach incorporates a definition of a search space to guarantee convergence while considering the system limits. Simulation and real‐world experiments are performed to validate the feasibility of our method with different configurations. Simulation results compared to a benchmark method demonstrate our approach's superior performance in terms of computational time, achieving near‐optimal solutions. In addition, in the real‐world experiments, the integration of the method into practical applications is validated.

High-performance copper terephthalic acid metal-organic framework/gum Arabic/carrageenan composite beads for efficient lead(II) removal from aqueous solutions

Lead (Pb(II)) contamination poses a significant threat to human health and the environment. This study investigates a new approach for Pb(II) removal from polluted water using copper terephthalic acid metal-organic framework/gum Arabic/potassium carrageenan (MGC) composite beads. We synthesized copper terephthalic acid MOF, potassium carrageenan beads, and MGC composite beads to evaluate their adsorption potential. Characterization of the synthesized adsorbents was performed using TGA, nitrogen adsorption/desorption, ATR-FTIR, zeta potential, SEM, and TEM analyses, revealing that MOF > MGC > KG in thermal stability. The MGC composite exhibited a high specific surface area (398.03 m2/g) with mesopores and diverse functional groups, alongside a pH of zero point charge (pHpzc) of 6.8 and a small particle size (20 nm). The maximum Langmuir adsorption capacity for Pb(II) removal by MGC reached 374.7 mg/g under optimized conditions (20 °C, pH 5, 60 min shaking time, 3.0 g/L adsorbent dosage). The adsorption data fit well with the Pseudo-First-Order kinetic model and Langmuir and Dubinin-Radushkevich isotherm models. The adsorption process was physical, favorable, and endothermic. EDTA was used as a desorption agent, showing that the composite beads retained 97 % efficiency after ten cycles, highlighting MGC's potential as a sustainable strategy for Pb(II) remediation.

A new multiple-arc model of the resonant Kuiper belt objects – plutinos

Abstract To incorporate the gravitational influence of Kuiper belt objects (KBOs) in planetary ephemerides, uniform-ring models are commonly employed. In this paper, for representing the KBO population residing in Neptune’s 2:3 mean motion resonance (MMR), known as the Plutinos, we introduce a three-arc model by considering their resonant characteristics. Each ‘arc’ refers to a segment of the uniform ring and comprises an appropriate number of point masses. Then the total perturbation of Plutinos is numerically measured by the change in the Sun-Neptune distance (ΔdSN). We conduct a comprehensive investigation to take into account various azimuthal and radial distributions associated with the resonant amplitudes (A) and eccentricities (e) of Plutinos, respectively. The results show that over a 100-year period: (1) at the smallest e = 0.05, the Sun-Neptune distance change ΔdSN caused by Plutinos decreases significantly as A reduces. It can deviate from the value of ΔdSN obtained in the ring model by approximately 100 km; (2) as e increases in the medium range of 0.1-0.2, the difference in ΔdSN between the arc and ring models becomes increasingly significant; (3) at the largest e ≳ 0.25, ΔdSN can approach zero regardless of A, and the arc and ring models exhibit a substantial difference in ΔdSN, reaching up to 170 km. Then the applicability of our three-arc model is further verified by comparing it to the perturbations induced by observed Plutinos on the positions of both Neptune and Saturn. Moreover, the concept of the multiple-arc model, designed for Plutinos, can be easily extended to other MMRs densely populated by small bodies.

The Geometric Scale of an Urban Space—Neuro-perceptual Limitations for Face-to-Face Driver Behavior

For the last century, the roadway design paradigm has been grounded in the physics of point masses, adjusted for human limitations. However, this is inadequate to assure pedestrian safety in complete streets where vehicle kinematics no longer control. Instead, social and psychological factors manage behavior. Unfortunately, the appropriate design critical psychological principles have yet to be elucidated. We posit that interpersonal perception governs drivers’ behavior, attentiveness and speed in streets. This is bounded by previously delineated human neurological and perceptual propensities. Using these perceptual limitations as postulates in a geometric style proof, we derive the person perception panorama (PPP): a window of interactivity around the moving driver that is continuously monitored for human presence, roughly 60 to 90 feet wide. In this area interpersonal interaction is implicit, functional, and has an impact on driver behavior. Validating evidence, additional governing principles, and an initial speed prediction formula are also included.

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.

Coconut shells based MrGO@CMC adsorbent for the chromium (VI) ion removal from contaminated water through batch adsorption method

The chromium (III) ion is necessary for biological function and the chromium (VI) ion (Cr (VI)) induces toxicity to humans and animals. From the sources of industries, the contaminated Cr (VI) is an important issue to remove from the solution. Here, we synthesized magnetic reduced graphene oxide @ carboxymethyl cellulose (MrGO@CMC) adsorbent for the removal of Cr (VI) from aqueous solution. The fabricated adsorbent was characterized through XRD, FT-IR, SEM, EDX, BET, VSM, and TGA. Adsorption studies were conducted various parameters and the optimized contact time, dosage and concentration was fixed such 60 min and 10 mg L−1 respectively. By the MrGO@CMC adsorbent almost 93% efficiency Cr (VI) was removed from the aqueous solution at 40 min, 25 mg, 10 mg L−1, and neutral pH. The zero point charge (pHzpc) of the adsorbent was observed at pH-6.3. The MrGO@CMC adsorbent followed Langmuir isotherm model at achieving a maximum adsorption capacity of 625.8 mg g−1 and it indicates chemisorption dominated monolayer adsorption and the system follows pseudo-second-order kinetics model indicating a bimolecular system. Thermodynamic analysis revealed that the adsorption process was endothermic and spontaneous reaction. The adsorbent regeneration and reusability studies demonstrated that MrGO@CMC retained over 70.90% efficiency in removing Cr (VI) ions even after five recovery cycles compare with other graphene oxide-based adsorbent, the current adsorbent have potential removal efficiency, since the proposed adsorbent shows excellent adsorbent for Cr (VI) ions from industrial wastewater.

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.