General Expression Research Articles

Research on propagation characteristics of an electromagnetic wave in magnetized fully ionized dusty plasma

When some spacecraft fly at high speed in near-earth space, the dusty plasma is attached to the surface of the spacecraft due to the intense friction between the spacecraft and the space. The dusty plasma attached to the aircraft hinders the propagation of electromagnetic (EM) waves and affects the flight safety of the pilot. In this paper, we replace the collision term of the general Boltzmann equation with the Fokker-Planck-Landau collision term and obtain the general correlation expression of the electron distribution function in the fully ionized dusty plasma. The dielectric relation of EM waves in magnetized fully ionized dusty plasma is calculated considering the impact effect and charging effect of dust particles in the case of an external magnetic field. The reflection coefficient (R) and transmission coefficient (T) of the EM wave in magnetized fully ionized dusty plasma are calculated by a scattering matrix method. The effects of applied magnetic field intensity and dust particle parameters on the propagation characteristics of EM waves in magnetized fully ionized dusty plasma are discussed by simulation. In addition, the propagation characteristics of EM waves in ordinary plasma and magnetized fully ionized dusty plasma are compared. The results show that with the increase in the additional magnetic field, the reflection of the EM wave in the fully ionized dusty plasma decreases and the transmission increases. In the 0–100 GHz band, dust particles block EM waves from penetrating fully ionized dusty plasma. Other dusty plasma parameters also affect the propagation characteristics of EM waves to varying degrees. These results provide a theoretical reference for solving the communication related problems of high-speed aircraft.

Energetics of particle-size segregation

We introduce a continuum framework for the energetics of particle-size segregation in bidisperse granular flows. Building on continuum segregation equations and a recent segregation flux model, the proposed framework offers general analytical expressions to study the physics of granular flows from a mechanical energy perspective. We demonstrate the framework's applicability by examining the energetics of shear-driven granular flows. Numerical experiments with varying frictional coefficients and particle-size ratios reveal two distinct phases in the energetics, marked by the separate onset of particle segregation and diffusive remixing. Furthermore, our numerical simulations alongside previous experimental results show that the bulk Richardson number $Ri$ , defined as the potential energy to kinetic energy ratio at steady state, follows the scaling relationship $Ri\equiv \hat {E}^{(s)}_{gp} / \hat {E}^{(s)}_{k} \propto Pe^{-1/2}_{sr}$ for $0.1 \leq Ri\leq ~10^{3}$ and $10^{-4} \leq Pe_{sr} \leq ~300$ , the segregation–rheology Péclet number. Finally, we present a Péclet-number-dependent theoretical expression for the degree of mixing (or segregation), validated by the compiled numerical and experimental dataset. Our findings hint that the bulk segregation–mixing state can be predicted and controlled using the segregation Péclet number $Pe$ and $Pe_{sr}$ , both determined from known system parameters, providing an instrumental tool for engineering and geophysical applications.

Genuine N-partite entanglement in Schwarzschild-de Sitter black hole spacetime

Complex quantum information tasks in a gravitational background require multipartite entanglement for effective processing. Therefore, it is necessary to investigate the properties of multipartite entanglement in a relativistic setting. In this paper, we study genuine N-partite entanglement of massless Dirac fields in the Schwarzschild-de Sitter (SdS) spacetime, characterized by the presence of a black hole event horizon (BEH) and a cosmological event horizon (CEH). We obtain the general analytical expression of genuine N-partite entanglement shared by n observers near BEH and m (n+m=N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n+m=N$$\\end{document}) observers near CEH. It is shown that genuine N-partite entanglement monotonically decreases with the decrease of the mass of the black hole, suggesting that the Hawking effect of the black hole destroys quantum entanglement. It is interesting to note that genuine N-partite entanglement is a non-monotonic function of the cosmological constant, meaning that the Hawking effect of the expanding universe can enhance quantum entanglement. This result contrasts with multipartite entanglement in single-event horizon spacetime, offering a new perspective on the Hawking effect in multi-event horizon spacetime.

Comparative study of methodologies for SOH diagnosis and forecast of LFP and NMC lithium batteries used in electric vehicles

The exponential growth of electric mobility requires alternatives to extend the life of batteries in new applications and reduce the environmental impact of retired lithium batteries. The second life is an economic and environment-friendly alternative for battery management. The development of fast, low-cost, and reliable diagnostic methodologies makes it possible to increase the economic benefits and reduce the remanufacturing time of second-life batteries (SLBs). In the present work, battery state of health (SOH) distribution analysis, incremental capacity (IC), internal resistance (IR), and electrochemical impedance spectroscopy (EIS) were applied as diagnostic methodologies for two different chemistries of lithium-ion batteries previously used in electric vehicles (EV). In addition, module equalization in batteries was done in order to assess whether the state of module charge (SOC) variation affects the SOH. The results demonstrate that the diagnosis methodology depends on the chemistry of the battery, and that there is no single reliable diagnostic procedure that can be applied to all types of lithium-ion batteries. It was determined that the most adequate diagnostic method for LFP batteries (LiFePO4 cathode) is the IC method, while for NMC batteries (LiNi0.33Mn0.33Co0.33O2 cathode) the IR and EIS diagnostic methods are the most appropriate. Similarly, the present work proposed a simple methodology for IC capacity diagnosis and a general expression for SOH determination by IC and incremental voltage diagnosis of LFP batteries. Higher stability of LFP respect to NMC modules was observed during the SLBs performance, retaining >99 % after 500 cycles for LFP, compared with 90.2 % for NMC. The remaining useful life (RUL) shows that there are kinetics and lithium inventory changes in the batteries temperature-dependent.

Quantum dissipative effects for a real scalar field coupled to a time-dependent Dirichlet surface in d+1 dimensions

We study the dynamical Casimir effect for a real scalar field φ in d+1 dimensions, in the presence of a mirror that imposes Dirichlet boundary conditions and undergoes time-dependent motion or deformation. Using a perturbative approach, we expand in powers of the deviation of the mirror’s surface Σ from a hyperplane, up to fourth order. General expressions for the probability of pair creation induced by motion are derived, and we analyze the impact of space-time dimensionality as well as of the nonlinear effects introduced by the fourth-order terms. Published by the American Physical Society 2024

Kant on Pure Apperception and Indeterminate Empirical Inner Intuition

It is well known that Kant distinguishes between two kinds of self-consciousness: transcendental apperception and empirical apperception (or, approximately, inner sense). However, Kant sometimes claims that “I think,” the general expression of transcendental apperception, expresses an indeterminate empirical inner intuition (IEI), which differs in crucial ways from the empirical inner intuition produced by inner sense. Such claims undermine Kant’s conceptual framework and constitute a recalcitrant obstacle to understanding his theory of self-consciousness. This paper analyzes the relevant passages, evaluates the major interpretations of IEI, revisits the notion of pure apperception, and proposes an alternative reading: IEI is a ubiquitous, nonfocal, “obscure,” and empirical inner intuition that is built into all nonintrospective conscious states. This reading can successfully account for the peculiarities of IEI, resolving a major mystery in Kant’s theory of self-consciousness.

Study on the Resonance Characteristics and Active Damping Suppression Strategies of Multi-Inverter Grid-Connected Systems Under Weak Grid Conditions

When a multi-inverter grid-connected system is influenced by the parasitic parameters of LCL-type inverters and the impedance of the connected system’s lines, its resonance characteristics become more complex and difficult to predict. For LCL-type multi-inverter grid-connected systems, a mathematical model that considers the effects of parasitic parameters and line impedance has been established, leading to the derivation of the system’s Norton equivalent circuit and a general expression for the inverter output current. The resonance characteristics of multi-inverter grid-connected systems composed of inverters with the same and different parameters were analyzed under the influence of parasitic parameters and line impedance. To suppress the resonance in multi-inverter grid-connected systems and address the issue of traditional PI control not meeting grid requirements for LCL-type grid-connected inverters, a strategy combining superhelical sliding mode control with active damping was adopted. To verify the practical performance of the adopted resonance suppression strategy in complex environments, a grid-connected system model containing two LCL-type inverters was constructed using the MATLAB/Simulink software platform, followed by simulation analysis. The simulation results strongly confirm the feasibility and effectiveness of the adopted resonance suppression strategy, considering the effects of parasitic parameters and line impedance. This strategy demonstrates significant suppression effects in addressing resonance issues caused by parasitic parameters and line impedance, effectively enhancing the quality of grid-connected electrical energy.

Transcriptome Analysis of HNSCC by Aggregatibacter actinomycetemcomitans Extracellular Vesicles.

The role of extracellular vesicles (EVs), also known as outer membrane vesicles (OMVs), secreted by oral bacteria in the progression of head and neck squamous cell carcinomas (HNSCCs), is largely unexplored. This study aimed to investigate the influence of bacterial EVs, specifically those derived from Aggregatibacter actinomycetemcomitans (Aa), on the progression of HNSCC. FaDu and UMSCC1 cell lines were treated with Aa-derived EVs, and oncogenic activities were assessed. Comprehensive cellular and RNA-sequencing transcriptome analyses were conducted to assess the impact of these EVs on cell cycle progression and gene expression. Our findings reveal that Aa-derived EVs accelerate cell cycle progression through the S and G2 phases and enhance invasion in HNSCC cell lines. RNA-sequencing analysis showed that Aa-derived EVs exert a more significant effect on general transcript expression than on microRNA profiles, except for miR-146a, which is recognized as a key factor in both carcinogenesis and immune modulation. Bacterial EVs, particularly from periodontal pathogens like Aa, are significant modulators within the oral cancer environment, potentially affecting cellular behavior and gene expression profiles. This study highlights the complex relationship between periodontal health and oral carcinogenesis, emphasizing the significant role of bacterial EVs in HNSCC progression.

Impact of Circadian Clock PER2 Gene Overexpression on Rumen Epithelial Cell Dynamics and VFA Transport Protein Expression.

The circadian gene PER2 is recognized for its regulatory effects on cell proliferation and lipid metabolism across various non-ruminant cells. This study investigates the influence of PER2 gene overexpression on goat rumen epithelial cells using a constructed pcDNA3.1-PER2 plasmid, assessing its impact on circadian gene expression, cell proliferation, and mRNA levels of short-chain fatty acid (SCFA) transporters, alongside genes related to lipid metabolism, cell proliferation, and apoptosis. Rumen epithelial cells were obtained every four hours from healthy dairy goats (n = 3; aged 1.5 years; average weight 45.34 ± 4.28 kg), cultured for 48 h in vitro, and segregated into control (pcDNA3.1) and overexpressed (pcDNA3.1-PER2) groups, each with four biological replicates. The study examined the potential connection between circadian rhythms and nutrient assimilation in ruminant, including cell proliferation, apoptosis, cell cycle dynamics, and antioxidant activity and the expression of circadian-related genes, VFA transporter genes and regulatory factors. The introduction of the pcDNA3.1-PER2 plasmid drastically elevated PER2 expression levels by 3471.48-fold compared to controls (p < 0.01), confirming effective overexpression. PER2 overexpression resulted in a significant increase in apoptosis rates (p < 0.05) and a notable reduction in cell proliferation at 24 and 48 h post-transfection (p < 0.05), illustrating an inhibitory effect on rumen epithelial cell growth. PER2 elevation significantly boosted the expression of CCND1, WEE1, p21, and p16 (p < 0.05) while diminishing CDK4 expression (p < 0.05). While the general expression of intracellular inflammation genes remained stable, TNF-α expression notably increased. Antioxidant marker levels (SOD, MDA, GSH-Px, CAT, and T-AOC) exhibited no significant change, suggesting no oxidative damage due to PER2 overexpression. Furthermore, PER2 overexpression significantly downregulated AE2, NHE1, MCT1, and MCT4 mRNA expressions while upregulating PAT1 and VH+ ATPase. These results suggest that PER2 overexpression impairs cell proliferation, enhances apoptosis, and modulates VFA transporter-related factors in the rumen epithelium. This study implies that the PER2 gene may regulate VFA absorption through modulation of VFA transporters in rumen epithelial cells, necessitating further research into its specific regulatory mechanisms.

Two-dimensional P1 approximation (P1-2D) for the Description of the Radiant Field on Cylindrical Solar Photocatalytic Reactors

The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in polar coordinates with the P1 approximation approach (P1-2D) for the description of the radiant field in cylindrical solar photocatalytic reactors. A general expression of the LVRPA was formulated that can be employed on cylindrical photocatalytic reactors with an incident radiation constant along the reactor length. CPC and tubular photocatalytic reactors were used as reactor models and Lambert's cosine law (irradiance) was considered when using the boundary conditions. Simulations were carried out using the commercial TiO2-P25, its optical properties taken from the literature. The LVRPA was found to decrease exponentially from the reactor wall to its center. literature rate of photon absorption per unit of reactor length (VRPA/H) increased exponentially with the catalyst loading until a value where no significant increase was observed and was found to increase with reactor radius, information that agrees with the literature. The optimum catalyst loading with the CPC reactor was about 0.364 g/L with a reactor radius equal to 1.65 cm similar to that found in the literature when using the six-flux model in two dimensions (SFM-2D). The apparent optical thickness τ_App1 newly formulated with the P1 approximation was introduced for optimization purposes and was found more reliable than the optical thickness τ. This parameter not only removes the dependence of the optimum catalyst loading on the reactor's radius but also its dependence on catalyst albedo. τ_App1 was found about 9.73 and 14.6 for CPC and tubular reactors respectively and provides the optimum catalyst loading and the reactor radius that optimize the radiation absorption inside both reactors.

A System of Tensor Equations over the Dual Split Quaternion Algebra with an Application

In this paper, we propose a definition of block tensors and the real representation of tensors. Equipped with the simplification method, i.e., the real representation along with the M-P inverse, we demonstrate the conditions that are necessary and sufficient for the system of dual split quaternion tensor equations (A∗NX,X∗SC)=(B,D), when its solution exists. Furthermore, the general expression of the solution is also provided when the solution of the system exists, and we use a numerical example to validate it in the last section. To the best of our knowledge, this is the first time that the aforementioned tensor system has been examined on dual split quaternion algebra. Additionally, we provide its equivalent conditions when its Hermitian solution X=X∗ and η-Hermitian solutions X=Xη∗ exist. Subsequently, we discuss two special dual split quaternion tensor equations. Last but not least, we propose an application for encrypting and decrypting two color videos, and we validate this algorithm through a specific example.

Milky Way could invalidate the hypothesis of exotic matter and favor a gravitomagnetic solution to explain dark matter

We demonstrate a very general mathematical and physical expression of the rotation speed at the end of the galaxy (far from the vast majority of the galaxy’s baryonic mass) obtained from General Relativity without non-baryonic matter. We show the excellent agreement with measurements obtained for the Milky Way published in a recent article which confirms a significantly faster decline in the circular velocity curve at outer galactic radii up to 30 kpc compared to the inner parts. This relation comes from Linearized General Relativity (GRL). Some papers argue that the GRL solution cannot explain dark matter (DM). We demonstrate that this conclusion is too premature because they only consider mass currents of the galaxies which is not the most general theoretical solution. And because this GRL explanation suffers from the same defects as exotic matter, only direct measurement of the Lense-Thirring effect can objectively reject this solution. Current experiments are not yet precise enough to test this solution. But meanwhile, if the relevance of this expression were confirmed for most galaxies, this would strongly challenge exotic matter to explain DM and could drastically change the point of view on the DM component. Two known physical fields (contrary to an exotic matter) which are until now neglected or rather underestimated would then explain DM. The DM mystery would then consist for theory in understanding how the values of these fields can be larger than expected and for observation in being able to measure these two fields with sufficient precision. In addition, these fields allow obtaining the TULLY-FISHER relation and the MOND theory.

A novel mapping method for equivalent stiffness and equivalent damping of [formula omitted]-DOF series hydraulic robot

Impedance control is a commonly used approach for robots to interact with environments. At present, the impedance control is mostly implemented at the foot end, while the impedance control at the joint space offers faster response speed and is a more favorable option. However, due to the influence of installation position and moment arm of hydraulic drive unit (HDU), it is more complicated to establish the mapping relationship of equivalent stiffness and equivalent damping between the foot end and joint HDU. To address this challenge, this paper provides a general calculation expression of mapping matrices between the foot end and joint HDU, which also considers the influence of above nonlinear factors. Additionally, the accuracy of mapping matrices is verified through the impedance control, and the “finite difference method” (FDM) is used to enhance the accuracy of validation. Finally, the accuracy of mapping matrices is validated through the single leg of a 2-DOF series hydraulic robot.

An infralimbic cortex neuronal ensemble encoded during learning attenuates fear generalization expression.

Generalization allows previous experience to adaptively guide behavior when conditions change. The infralimbic (IL) subregion of the ventral medial prefrontal cortex plays a known role in generalization processes, although mechanisms remain unclear. A basic physical unit of memory storage and expression in the brain are sparse, distributed groups of neurons known as ensembles (i.e., the engram). Here, we set out to determine whether neuronal ensembles established in the IL during learning contribute to generalized responses. Generalization was tested in male and female mice by presenting a novel, ambiguous, tone generalization stimulus following Pavlovian defensive (fear) conditioning. The first experiment was designed to test a role for IL in generalization using chemogenetic manipulations. Results show IL regulates defensive behavior in response to ambiguous stimuli. IL silencing led to a switch in defensive state, from vigilant scanning to generalized freezing, while IL stimulation reduced freezing in favor of scanning. Leveraging activity-dependent "tagging" technology (ArcCreER T2 x eYFP system), a neuronal ensemble, preferentially located in IL Layer 2/3, was associated with the generalization stimulus. Remarkably, in the identical discrete location, fewer reactivated neurons were associated with the generalization stimulus at the remote timepoint (30 days) following learning. When an IL neuronal ensemble established during learning was selectively chemogenetically silenced, generalization increased. Conversely, IL neuronal ensemble stimulation reduced generalization. Overall, these data identify a crucial role for IL in suppressing generalized responses. Further, an IL neuronal ensemble, formed during learning, functions to later attenuate the expression of generalization in the presence of ambiguous threat stimuli.

Goos-Hänchen shift for an Airyprime beam.

We propose a comprehensive theory to analyze the Goos-Hänchen (GH) shift for an arbitrarily polarized Airyprime beam reflected at the air-dielectric interface. We derive general expressions for the spatial and angular GH shifts and establish a close relationship between the GH shift of the Airyprime beam and the GH shift of the Airy beam. We also predict the novel optical effects of a significantly enhanced spatial GH shift and an almost disappeared angular GH shift when the horizontally polarized Airyprime beam is reflected near Brewster's angle.

Leading two-point resistances from transfer matrices in cylindrical, spider web, axial and grid resistor networks

Resistor networks are increasingly being considered in heuristic research as models for natural or artificial matter. The equivalent resistance between two nodes, the Two-Point Resistance (TPR), can be calculated using a variety of methods. The transfer matrix (TM) method was originally considered as a numerical tool for estimating percolation thresholds in random networks with a repeating pattern. The TM method is revisited here as an efficient tool to obtain, in a fast and elegant way, iteration relations and exact explicit expressions for leading TPRs that include a node in the last repeated pattern. Several rotationally invariant networks are studied, such as simple cylindrical networks, spider web networks and cylindrical networks with a central resistive axis, in which case the TM matrices are circulant matrices. Examples of explicit expressions are given for orders of rotation ≤4 or 5, depending on the case. The method can be applied in a similar way to networks with less symmetry, such as grids. The general expressions of TPRs obtained using the TM method can provide quantitative guidelines for resistor networks developed in materials science, environmental issues or industrial applications.

Effect of leakage current on magnetoelectric effect of 0-3 multiferroic composites based on an equivalent circuit model

In 0-3 multiferroic composites, the content of ferromagnetic particles with conductive properties significantly influences their magnetoelectric (ME) performance. The occurrence of leakage current (Lc) at high contents is a crucial factor affecting the ME properties of such composites. Establishing a rational and effective theoretical model to analyze and predict the impact of Lc on their ME performance is of paramount theoretical significance for expanding the applications of these composites. In pursuit of this objective, by introducing conduction currents, magneto-electric-mechanical/electro-magnetic-mechanical coupling factor, and resistive components, an equivalent circuit model is built to analyze the direct and converse ME effects of this composites. Meanwhile, the general analytical expressions of various effective properties are obtained. By introducing factors with combined exponential and linear decay characteristics into the piezoelectric coefficient, our theoretically calculated results quantitatively agree with experimental data. On this basis and considering the effects of displacement current and conduction current, we utilized our equivalent circuit model to calculate the ME coefficients, which showed high consistency with experimental results. Especially at high volume fractions, our computed results accurately reflected the sharp decline characteristics of the ME coefficients caused by Lc. This demonstrates the accurate and reasonable explanation provided by our model for such ME problems. In addition, the optimal set of volume fractions and magnetic fields that maximize the direct ME coefficient is obtained. This study fills a theoretical gap in the equivalent circuit method for 0-3 multiferroic composites and gives an analytical solution for the ME coefficients and provides theoretical guidance and support for the application of this composites.

Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data

We explored how the Lorentz symmetry breaking parameter ℓ affects the Reissner-Nordstöm BH solution in the context of weak field deflection angle, and the black hole shadow. We aim to derive the general expression for the weak deflection angle using the non-asymptotic version of the Gauss-Bonnet theorem, and we presented a way to simplify the calculations under the assumption that the distance of the source and the receiver are the same. Through the Solar System test, ℓ is constrained from around orders of magnitude to 0, implying challenging detection of ℓ through the deflection of light rays from the Sun. We also studied the black hole shadow in an analytic way, where we applied the EHT results under the far approximation in obtaining an estimate expression for ℓ. Using the realistic values of the black hole mass and observer distance for Sgr. A* and M87*, it was shown that is satisfied, implying the relevance and potential promise of the spontaneous Lorentz symmetry breaking parameter's role on the shadow radius uncertainties as measured by the EHT. We find constraints for ℓ to be negatively valued, where the upper and lower bounds are ∼ - 1.94 and ∼ - 2.04, respectively.

Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling

This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement’s results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency.

Mean back relaxation for position and densities.

Correlation functions are a standard tool for analyzing statistical particle trajectories. Recently, a so-called mean back relaxation (MBR) has been introduced, which correlates positions at three time points. The deviation of its long-time value from 1/2 has been shown to be a marker for breakage of time-reversal symmetry for confined particles. Here, we extend the analysis of MBR in several ways, including discussion of a cutoff length used when evaluating MBR from trajectory data. Using a path integral approach, we provide a general expression for MBR in terms of multipoint density correlations. For Gaussian systems, this expression yields a relation between MBR and mean-squared displacement. We finally demonstrate that MBR can be applied to other stochastic observables besides particle position. Using it for microscopic densities, its deviation from 1/2 is a marker for broken detailed balance in confinement or in bulk systems.