Logarithmic Field Research Articles

Dynamics of U(1) gauged Q -balls in three spatial dimensions

We investigate the dynamics of U(1) gauged Q-balls using fully three-dimensional numerical simulations. We consider two different scenarios: first, the classical stability of gauged Q-balls with respect to generic three-dimensional perturbations, and second, the behavior of gauged Q-balls during head-on and off-axis collisions at relativistic velocities. With regard to stability, we find that there exist gauged Q-ball configurations which are classically stable in both logarithmic and polynomial scalar field models. With regard to relativistic collisions, we find that the dynamics can depend on many different parameters such as the collision velocity, relative phase, relative charge, and impact parameter of the colliding Q-balls. Published by the American Physical Society 2024

Fractional Einstein–Gauss–Bonnet Scalar Field Cosmology

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss–Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and α0=t0H0 and the fractional derivative order μ. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss–Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss–Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and α0, indicating that the solution is consistent with an accelerated expansion at late times with the values α0=1.38±0.05, m=1.44±0.05, and μ=1.48±0.17 (consistent with Ωm,0=0.311±0.016 and h=0.712±0.007), resulting in an age of the Universe t0=19.0±0.7 [Gyr] at 1σ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than ΛCDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.

Olfactory-based powered descent guidance for Mars methane plume exploration in long-time-average wind environment

This paper investigates an olfactory-based powered descent guidance method that enable a lander to autonomously locate and target the vent source of any methane plume in long-time-average wind environment on Mars. The episodic methane plumes emanating from the Martian surface invite the possibility of direct access to the subsurface methane reservoir to acquire pristine organic materials. Constrained by the insufficient knowledge of the accurate plume vent location, Mars landers must infer the target location — the plume source — autonomously during the powered descent. However, existing powered descent guidance methods require the target location as a terminal constraint, rendering them ineffective in plume exploration missions. We propose an olfactory-based powered descent guidance method that could steer a lander to target the methane vent source by tracking the gradient of methane concentration in long-time-average wind environment, imposing sub-optimal fuel consumption. A novel olfactory navigation method based on tracking the negative logarithmic concentration gradient, and the corresponding gradient measurement method, is proposed. By implementing the negative logarithmic gradient field, gradient-dependent dynamic equations for the powered descending lander are proposed. The gradient-dependent equations provide a way to transform the original optimal guidance problem, which is non-convex and terminal-free, into a convex and terminal-fixed problem. A suboptimal guidance law, similar to E-guidance, is then derived by solving this problem. The proposed guidance could target the vent source of any methane plume in long-time-average wind environment, imposing modest fuel consumption by feeding back the concentration gradient. Numerical simulations illustrate that, in comparison to the terminal-fixed E-guidance and the open-loop fuel-optimal guidance, the lander imposes additional fuel consumption of 2.57% and 12.15% respectively, using the proposed guidance law.

Development of Lead‐Free Defect Brownmillerite Perovskite Ceramic LiBiFeMnO5 Solid Solution for Electronic Devices

This article reports the fabrication (synthesis) and characterizations (structural, microstructural topographic surface, dielectric, transport, impedance, current–voltage, and resistive properties) of a complex lead‐free defect perovskite material of composition LiBiFeMnO5. A preliminary structural investigation of the X‐ray diffraction pattern using N‐TREOR09 methods shows monoclinic symmetry. The scanning electron microscopic spectrum examines the sample's microstructural topographic surface, fractal study, and roughness (using the standard ISO25178). The analysis of Maxwell–Wagner dielectric dispersion, relaxation, and transport mechanisms is investigated utilizing dielectric, impedance, and conductivity spectrum accumulated within the experimental frequency of (1 kHz–1 MHz) at different temperatures (30–500 °C). A nonoverlapping small polaron tunneling conduction mechanism and correlated barrier hopping mechanism in the material have helped to understand its conduction phenomena. The Ohmic and space–charge limited conduction mechanisms are investigated by the slope of the logarithmic electric field (E) and current density (J). The thermistor constant (β) is determined to be 1982.87. The temperature coefficient of resistance is found to be −0.00419, which may be suitable for negative temperature coefficient thermistors, sensors, and other related devices.

The perspective of the logarithmic field sprayer technology.

A logarithmic sprayer was suggested about 70 years ago, but it has not yet been seriously used in research and development, and subsequent registration of plant protection products. Logarithmic sprayers have resorted to mere demonstration experiments to show end users and others how plant protection products work. Fitting dose-response curves in field experiments, however, generates much essential information, e.g., extraction of various effective field rate levels (e.g., ED20, ED50, and ED80). One of the reasons for it rarely being used in the registration of plant protection products is that the dose-response curve regression was hitherto difficult to fit; the registration requirement solely focuses on analyses of variance. Another alleged obstacle is that the logarithmic plots have systematically, not randomly distributed field rates. This paper goes through some of the problems of how to non-randomly analyze field rates by taking autocorrelation into account to make the logarithmic sprayer palatable as registration documentation by assessing efficacy, selectivity, environmental side effects, general toxicity of plant protection products, and cost-effectiveness. The development in precision agriculture, drone technology, and automation of data capture and subsequent analysis could make the logarithmic sprayer a cost-effective alternative to numerous ANOVA experiments with very few fixed field rates to aid the precision spraying of pesticides and thus reduce unnecessary environmental side effects. © 2024 Society of Chemical Industry.

Generalized ghost dark energy model in Brans–Dicke theory with logarithmic scalar field

We study generalized ghost dark energy model in Brans–Dicke theory within the framework of flat Friedmann–Lemaitre–Robertson–Walker Universe. We assume the well-motivated logarithmic form of Brans–Dicke scalar field in terms of the scale factor to find the observational parameters such as equation of state parameter [Formula: see text] and deceleration parameter q. It is observed that the equation of state parameter crosses the phantom divide line [Formula: see text] for a suitable range of model parameters. We observe that the deceleration parameter is time-dependent which shows the recent phase transition from decelerated to accelerated expansion of the Universe. Moreover, the model shows that the Universe will go through two future phase transitions, recent accelerated expansion to decelerated expansion and again decelerated expansion to accelerated expansion. We have also plotted the trajectories of the model in the [Formula: see text] plane for different values of parameters and explored the freezing and thawing regions. Further, we apply the sound squared speed method to check the stability of the model and found that the model is stable for suitable range of parameters.

Multiple bump solutions to logarithmic scalar field equations

Multiple bump solutions to logarithmic scalar field equations

Observational constraints on a logarithmic scalar field dark energy model and black hole mass evolution in the Universe

We propose a logarithmic parametrization form of energy density for the scalar field dark energy in the framework of the standard theory of gravity, which supports the necessary transition from the decelerated to the accelerated behavior of the Universe. The model under consideration is constrained by available observational data, including cosmic chronometers data-sets (CC), Baryonic Acoustic Oscillation (BAO) data-sets, and Supernovae (SN) data-sets, consisting of only two parameters alpha and beta . The combined CC+BAO+SN data-sets yields a transition redshift of z_{tr}=0.79^{+0.02}_{-0.02}, where the model exhibits signature-flipping and is consistent with recent observations. For the combined data-sets, the present value of the deceleration parameter is calculated to be q_{0}=-0.43^{+0.06}_{-0.06}. Furthermore, the analysis yields constraints on both the parameter density value for matter and the present value of the Hubble parameter, with values of Omega _{m0}=0.25849^{+0.00026}_{-0.00025} and H_{0}=67.79_{-0.59}^{+0.59} km/s/Mpc, respectively, consistent with the results obtained from Planck 2018. Finally, the study investigates how the mass of a black hole evolves over time in a Universe with both matter and dark energy. It reveals that the black hole mass increases initially but stops increasing as dark energy dominates.

Representation of Motion Direction in Visual Area MT Accounts for High Sensitivity to Centripetal Motion, Aligning with Efficient Coding of Retinal Motion Statistics.

The overrepresentation of centrifugal motion in the middle temporal visual area (area MT) has long been thought to provide an efficient coding strategy for optic flow processing. However, this overrepresentation compromises the detection of approaching objects, which is essential for survival. In the present study, we revisited this long-held notion by reanalyzing motion selectivity in area MT of three macaque monkeys (two males, one female) using random-dot stimuli instead of spot stimuli. We found no differences in the number of neurons tuned to centrifugal versus centripetal motion; however, centrifugally tuned neurons showed stronger tuning than centripetally tuned neurons. This was attributed to the heightened suppression of responses in centrifugal neurons to centripetal motion compared with that of centripetal neurons to centrifugal motion. Our modeling implies that this intensified suppression accounts for superior detection performance for weak centripetal motion stimuli. Moreover, through Fisher information analysis, we establish that the population sensitivity to motion direction in peripheral vision corresponds well with retinal motion statistics during forward locomotion. While these results challenge established concepts, considering the interplay of logarithmic Gaussian receptive fields and spot stimuli can shed light on the previously documented overrepresentation of centrifugal motion. Significantly, our findings reconcile a previously found discrepancy between MT activity and human behavior, highlighting the proficiency of peripheral MT neurons in encoding motion direction efficiently.SIGNIFICANCE STATEMENT The efficient coding hypothesis states that sensory neurons are tuned to specific, frequently experienced stimuli. Whereas previous work has found that neurons in the middle temporal (MT) area favor centrifugal motion, which results from forward locomotion, we show here that there is no such bias. Moreover, we found that the response of centrifugal neurons for centripetal motion was more suppressed than that of centripetal neurons for centrifugal motion. Combined with modeling, this provides a solution to a previously known discrepancy between reported centrifugal bias in MT and better detection of centripetal motion by human observers. Additionally, we show that population sensitivity in peripheral MT neurons conforms to an efficient code of retinal motion statistics during forward locomotion.

Topologically nontrivial black holes of Lovelock gravity sourced by logarithmic electrodynamics

I investigate the topologically nontrivial black holes of Lovelock gravity sourced by logarithmic electrodynamics. To calculate the solution describing these black holes, additional constraints are also imposed on the base manifold of the higher dimensional spacetime. Relying on the selection of geometric mass, electric charge, and the nonlinearity parameter, this solution can be portrayed as a black hole with a single horizon, two horizons, or naked singularity. I also look into how the thermodynamical and conserved quantities of this solution are affected by the logarithmic electromagnetic field. Additionally, it is demonstrated that these quantities correspond to the first law of thermodynamics. At last, the local and global thermodynamic stabilities of the accomplished black hole are studied as well.

Logahoric Higgs torsors for a complex reductive group

In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group G, we introduce a notion of stability for logahoric $$\mathcal {G}_{\varvec{\theta }}$$ -Higgs torsors on a smooth algebraic curve X, where $$\mathcal {G}_{\varvec{\theta }}$$ is a parahoric group scheme on X. In the case when the group G is the general linear group $$\textrm{GL}_n$$ , we show that the stability condition of a parahoric torsor is equivalent to the stability of a parabolic bundle. A correspondence between semistable logahoric $$\mathcal {G}_{\varvec{\theta }}$$ -Higgs torsors and semistable equivariant logarithmic G-Higgs bundles allows us to construct the moduli space explicitly. This moduli space is shown to be equipped with an algebraic Poisson structure.

Dynamical evolution of U(1) gauged Q -balls in axisymmetry

We study the dynamics of $U(1)$ gauged Q-balls using fully non-linear numerical evolutions in axisymmetry. Focusing on two models with logarithmic and polynomial scalar field potentials, we numerically evolve perturbed gauged Q-ball configurations in order to assess their stability and determine the fate of unstable configurations. Our simulations suggest that there exist both stable and unstable branches of solutions with respect to axisymmetric perturbations. For solutions belonging to the stable branch, the gauged Q-balls respond to the perturbations by oscillating continuously or weakly radiating before returning to the initial configuration. For the unstable branch, the solutions are eventually destroyed and can evolve in several ways, such as dispersal of the fields to infinity or fragmentation into smaller gauged Q-balls. In some cases, we observe the formation of ring-like structures which we call "gauged Q-rings". We also investigate the stability of gauged Q-balls when the gauge coupling is small, finding that the behaviour of these configurations closely resembles that of ordinary (non-gauged) Q-balls.

Logarithmic Potential Field: A New Leader– Follower Robotic Control Mechanism to Enhance the Execution Speed and Safety Attributes

Logarithmic Potential Field: A New Leader– Follower Robotic Control Mechanism to Enhance the Execution Speed and Safety Attributes

Field synergy principle for compressible laminar flow and the application for drag reduction in microchannel

Considering the density variation of compressible fluid, the field synergy principle for compressible laminar flow is presented based on the incompressible flow field synergy principle. The flow resistance is related to the synergy of velocity field and density logarithmic gradient field. Based on the principle of minimum mechanical energy dissipation, the compressible laminar flow field synergy equation is derived. The field synergy principle is verified by an example of the microchannel with expansion cross section, and the structure is optimized. The results indicate that the viscous dissipation value in the entire flow domain of the optimized structure can be reduced by 13.5%, and the angle between the velocity vector and the gradient field of logarithm of density increases. In fluid flows, it will reduce the fluid flow drag to decrease the synergy angle between the velocity vector and the gradient field of logarithm of density.

Simplified approach for determination of parameters for Kostiakov's infiltration equation

Abstract Knowledge of soil infiltration characteristics is required increasingly for the proper design and efficient management of irrigation. Various empirical and physically based infiltration models have been used for several years, but the practical use of many is limited by parameter determination problems, which, in turn, are influenced by factors acting at the surface and within the soil, initial and boundary conditions, etc. In this study, a simplified approach for determining parameters for the Kostiakov equation was tested and validated. The equation's linearized form, using logarithmic transformation and field data collected from five sites, was employed. The results show that cumulative infiltration can be described well using the approach. Its quality is also confirmed by performance indices like R2 and standard error, whose values ranged from 0.985 to 0.999 and 0.020 to 0.005, respectively, suggesting that the simplified approach described is sufficient for practical purposes, when data are too scarce to apply other, complex methods to predict cumulative infiltration.

Calculation of the electron-optical scheme of a new type mirror energy analyzer of charged particles

Further studies of the electron-optical properties of electrostatic multipole-cylindrical fields, synthesized from the fields of a cylindrical mirror and circular multipoles, are continued in the work. The implementation of electron spectroscopy methods is based on the use of complex equipment, one of the main elements of which is an electron energy analyzer of low and medium energies. Application of the multipole approach to the synthesis of deflecting fields makes it possible to develop effective methods for energy analysis of charged particle beams. The electron-optical scheme of new type mirror energy analyzer of charged particle beams based on an electrostatic axially symmetric octupole-cylindrical field is proposed in the work. An axially symmetric octupole-cylindrical field is constructed as a superposition of a basic cylindrical field and a circular octupole. When the fields were added, the central circle of the octupole was combined with the zero equipotential of the logarithmic field. The motion of charged particles in the electrostatic octupole-cylindrical field. An integrodifferential equation for the motion of charged particles in an electrostatic octupolecylindrical field is derived. Calculation of trajectories in an energy analyzer with an octupole-cylindrical field was performed on the basis of the method of expansion into a fractional-power series of the particle motion equation presented in the integrodifferential form. Coefficients of the series, representing the trajectory of motion in an analytical form, accessible for further studies of the electron-optical characteristics of the octupole-cylindrical field, are obtained. Based on an octupole-cylindrical field, high luminosity energy analyzers can be built to determine the composition of charged particle beams with energies from units of eV to tens of keV in space plasma.

Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications

The central topic of the workshop was the notion of logarithmic vector fields along a divisor in a smooth complex analytic or algebraic variety, i.e., the vector fields on the ambient variety tangent to the divisor. Following their introduction by K. Saito for the purpose of studying the universal unfolding of an isolated singularity, this fundamental object has been the focus of studies in a wide range of mathematical fields such as algebra, algebraic geometry, singularity theory, root systems, (geometric) representation theory, combinatorics, (toric) topology, or symplectic geometry. In the last few years the logarithmic vector field approach has seen some unexpected and striking advances and deep applications. The aim of the workshop was to provide reports and to share these various new developments in the field.

Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions

We consider the (1+1)-dimensional Lorentz-symmetric field-theoretic model with logarithmic potential having a Mexican-hat form with two local minima similar to that of the quartic Higgs potential in conventional electroweak theory with spontaneous symmetry breaking and mass generation. We demonstrate that this model allows topological solutions — kinks. We analyze the kink excitation spectrum, and show that it does not contain any vibrational modes. We also study the scattering dynamics of kinks for a wide range of initial velocities. The critical value of the initial velocity occurs in kink-antikink collisions, which thus differentiates two regimes. Below this value, we observe the capture of kinks and their fast annihilation; while above this value, the kinks bounce off and escape to spatial infinities. Numerical studies show no resonance phenomena in the kink-antikink scattering.

Strong cosmic censorship for a scalar field in a logarithmic-de Sitter black hole

It has been shown that the quasinormal modes of perturebated fields can be used to investigate the validity of strong cosmic censorship (SCC). Relevant issues for Reissner–Nordstrom–de Sitter (RN-dS) black holes and Born–Infeld–de Sitter black holes have been discussed. In this paper, we investigate SCC in an asymptotic RN-dS black hole with logarithmic nonlinear electromagnetic field perturbed by massless scalar fields. It has been argued that SCC can be violated in a near-extremal RN-dS black hole. However, we find that the NLED effect can rescue SCC for a near-extremal logarithmic-de Sitter black hole. Compared with Born-Infeld model, we find that the NLED effect has similar behavior.

Concentration of nodal solutions for logarithmic scalar field equations

This paper studies sign-changing solutions and their concentration behaviors of logarithmic scalar field equations in the semiclassical setting. At a local minimum of the potential function we construct an unbounded sequence of sign-changing solutions concentrating near the local minimum. This resembles a localized phenomenon of an unbounded sequence of localized bound states in the studies of nonlinear eigenvalues and eigenfunctions.