Free Plane Research Articles

Dynamics of the Davydov’s soliton in external oscillating magnetic field

The influence of an external oscillating in time magnetic field on the dynamics of the Davydov’s soliton is studied. It is shown that soliton parameters depend on the amplitude and frequency of the magnetic field, as well as on the field orientation with respect to the molecular chain axis. Electron dynamics in the parallel magnetic field is a composition of the “free” soliton coherent propagation along the molecular chain and oscillatory movement in the transverse direction. The latter is described by the functions of the harmonic oscillator with the cyclotron frequency depending on the field frequency. In a perpendicular field the soliton dynamics is a superposition of (i) the free electron plane wave in the plane perpendicular to the molecular chain, and (ii) propagation along the chain which is described by the modified Nonlinear Schrödinger equation with an extra term depending on the field. This equation is solved using the nonlinear perturbation theory. It is shown that the soliton velocity and phase are given by expressions which include the terms oscillating in time with the frequency of the main harmonic, given by the external field frequency, and higher multiple harmonics. Such complex effects of external time-depending magnetic fields on the dynamics of solitons modify the charge transport in low-dimensional molecular systems, which in its turn, can affect the functioning of the devices based on such compounds. These results suggest also the physical mechanism of therapeutic effects of oscillating magnetic fields, based on the field influence on the dynamics of solitons which provide charge transport through biological macromolecules in the redox processes.

Deactivation and collective phasic muscular tuning for pointing direction: Insights from machine learning

Arm movements in our daily lives have to be adjusted for several factors in response to the demands of the environment, for example, speed, direction or distance. Previous research has shown that arm movement kinematics is optimally tuned to take advantage of gravity effects and minimize muscle effort in various pointing directions and gravity contexts. Here we build upon these results and focus on muscular adjustments. We used Machine Learning to analyze the ensemble activities of multiple muscles recorded during pointing in various directions. The advantage of such a technique would be the observation of patterns in collective muscular activity that may not be noticed using univariate statistics. By providing an index of multimuscle activity, the Machine Learning (ML) analysis brought to light several features of tuning for pointing direction. In attempting to trace tuning curves, all comparisons were done with respects to pointing in the horizontal, gravity free plane. We demonstrated that tuning for direction does not take place in a uniform fashion but in a modular manner in which some muscle groups play a primary role. The antigravity muscles were more finely tuned to pointing direction than the gravity muscles. Of note, was their tuning during the first half of downward pointing. As the antigravity muscles were deactivated during this phase, it supported the idea that deactivation is not an on-off function but is tuned to pointing direction. Further support for the tuning of the negative portions of the phasic EMG was provided by the observation of progressively improving classification accuracies with increasing angular distance from the horizontal. We also demonstrated that the durations of these negative phases, without information on their amplitudes, is tuned to pointing directions. Overall, these results show that the motor system tunes muscle commands to exploit gravity effects and reduce muscular effort. It quantitatively demonstrates that phasic EMG negativity is an essential feature of muscle control. The ML analysis was done using Linear Discriminant analysis (LDA) and Support Vector Machines (SVM). The two led to the same conclusions concerning the movements being investigated, hence showing that the former, computationally inexpensive technique is a viable tool for regular investigation of motor control.

Elasto-Thermodiffusive Microtemperature Model Induced by a Mechanical Ramp-Type of Nanoscale Photoexcited Semiconductor

ABSTRACT In this study, a novel theoretical approach to describe thermo-optical elastic materials is proposed. This formulation offers insights into the relationship between plasma waves and thermomechanical waves when the microtemperature properties of semiconductor materials such as silicon are taken into account. The proposed model involves incorporating the concept of microtemperature effect according to photothermal (PT) excitation processes in nonlocal photo-thermoelasticity. The investigation of the electron-hole interaction concerning the elasto-thermodiffusion (ETD) theory in the context of thermoelastic (TD) and electronic (ED) deformation is the main focus of the work. The advanced model is utilized to analyze how the mechanical loading of ramp-like structures impacts the unrestricted nonlocality semiconductor material on a free outer plane. The Laplace transform approach in one-dimensional (1D) provides an analytical solution for main non-dimensional thermo-photo-elastic fields (the hole charge carrier field, the displacement (acoustic) wave, thermal wave, and plasma wave (carrier density). The primary fields in the Laplace domain are obtained analytically, and boundary conditions are established using a mechanical ramp type. Using a numerical inverse Laplace transform, full time domain solutions for the fundamental fields are obtained numerically according to the Riemann-sum approximation approach. The graphical representations illustrate and discuss the outcomes of the main physical fields.

The Explosive Crack Propagation Mechanism of Layered Rock Mass

Layered joints significantly affect the propagation and attenuation of engineering blasting stress waves and have a significant influence on rock breakage. In this study, the explosion crack propagation mechanism of a stratified rock mass with weak or no cementation is analyzed. Multilayer plexiglass plates are employed to simulate a layered rock mass, establishing an experimental model to investigate the vertical interaction between explosive charges and layered rock masses. The extent of ruptures and damage within the charging and sealing sections of the rock mass is analyzed. The explosion cracks at the bottom of the hole are relatively dense, whereas those at the hole opening are relatively sparse. The range of the crushing and fracture zones around the gun hole in the charging section is larger than that in the blocking section. Moreover, as the blocking section approaches the free plane, the crushing zone size decreases. A notable area of rapid damage escalation is identified between the blocking and charging sections, leading to a significant increase in damage intensity. The numerical analysis results indicate that the cumulative explosive energy within the charging section surpasses that of the blocking section, and the rate of energy accumulation is notably higher in the charging region.

Asymmetric particle-antiparticle Dirac equation: first quantization

We derive a Dirac-like equation, the asymmetric Dirac equation, where particles and antiparticles sharing the same wave number have different energies and momenta. We show that this equation is Lorentz covariant under proper Lorentz transformations (boosts and spatial rotations) and also determine the corresponding transformation law for its wave function. We obtain a formal connection between the asymmetric Dirac equation and the standard Dirac equation and we show that by properly adjusting the free parameters of the present wave equation we can make it reproduce the predictions of the usual Dirac equation. We show that the rest mass of a particle in the theoretical framework of the asymmetric Dirac equation is a function of a set of four parameters, which are relativistic invariants under proper Lorentz transformations. These four parameters are the analog to the mass that appears in the standard Dirac equation. We prove that in order to guarantee the covariance of the asymmetric Dirac equation under parity and time reversal operations (improper Lorentz transformations) as well as under the charge conjugation operation, these four parameters change sign in exactly the same way as the four components of a four-vector. The mass, though, being a function of the square of those parameters remains an invariant. We also extensively study the free particle plane wave solutions to the asymmetric Dirac equation and derive its energy, helicity, and spin projection operators as well as several Gordon’s identities. The hydrogen atom is solved in the present context after applying the minimal coupling prescription to the asymmetric Dirac equation, which also allows us to appropriately obtain its non-relativistic limit.

Construction of Free Curves by Adding Lines to a Given Curve

In the present note we construct new families of free plane curves starting from a curve C and adding high order inflectional tangent lines of C, lines joining the singularities of the curve C, or lines in the tangent cone of some singularities of C. These lines L have in common that the intersection C∩L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C \\cap L$$\\end{document} consists of a small number of points. We introduce the notion of a supersolvable plane curve and conjecture that such curves are always free, as in the known case of line arrangements. Some evidence for this conjecture is given as well, both in terms of a general result in the case of quasi homogeneous singularities and in terms of specific examples. We construct a new example of maximizing curve in degree 8 and the first and unique known example of maximizing curve in degree 9. In the final section, we use a stronger version of a result due to Schenck, Terao and Yoshinaga to construct families of free conic-line arrangements by adding lines to the conic-line arrangements of maximal Tjurina number recently classified by Beorchia and Miró-Roig in arXiv:2303.04665

Asymptotic solutions for large fractures growing parallel to a free plane

Straight 2D and disc-like cracks situated close to a parallel free plane are considered and asymptotic solutions for the stress intensity factors (SIFs) and crack opening are developed. Two asymptotic terms with respect to the small ratio of distance from the surface to the crack length/radius are derived. The derivation is based on considering the material between the crack and the free surface as an elastically supported beam or circular plate. The crack is considered to be opened either by uniform tensile stress or a pair of concentrated forces or moments representing the action of central defects (these represent for instance the crack growth from initial inclined crack or pore under compression acting parallel to the free surface). A crack with non-interacting surfaces (the conventional crack) and a crack with linear links between the surfaces are considered. Interaction with the free surface is shown to considerably increase the crack opening and SIFs, while the presence of the elastic links can reduce these crack parameters. In particular, the opening and SIFs of a crack with linear links under a pair of concentrated forces/moments exponentially vanish with the crack dimensions tending to infinity. The obtained asymptotic solutions provide a simple and accurate tool for investigating mechanisms of surface delamination and spallation (including thermal spallation and strain rockbursts).

Reference Ranges and Development Patterns of Fetal Myocardial Function Using Speckle Tracking Echocardiography in Healthy Fetuses at 17 to 24 Weeks of Gestation.

The purposes of the study were to develop reference ranges and maturation patterns of fetal cardiac function parameters measured by speckle tracking echocardiography (STE) using multiple biometric variables at 17 to 24 weeks' gestation among Thai fetuses and to compare with other previous reports. The four-chamber view of the fetal heart in 79 healthy fetuses was suitably analyzed by STE to establish the best-fit regression model. The 95% reference intervals and Z-score equations of fetal cardiac function parameters were computed. The fractional area change of both ventricles, left ventricular (LV) end-diastolic and end-systolic volumes, LV stroke volume, LV cardiac output (CO), and LV CO per kilogram were all increased according to gestational age (GA) and five fetal biometric measurements. However, the global longitudinal strain, basal-apical length fractional shortening (BAL-FS), BAL annular free wall and septal wall FS, BAL free wall and septal wall annular plane systolic excursions, 24-segment transverse width FS, as well as LV ejection fraction were all independent of GA or other somatic characteristics. There were varying development patterns between fetal right and left ventricles of these cardiac function indices across the gestation period. Our study created Z-score and corresponding centile calculators, 5th and 95th centile reference tables, and corresponding graphs and determined the normal evolution across gestation using multiple somatic growth and age variables between 17 and 24 gestational weeks. These nomograms serve as an essential prerequisite for quantitatively evaluating fetal cardiac contractility and allow for precisely detecting early changes in the fetal heart function. · Most fetal cardiac function measurements were correlated with all the independent variables.. · Fetal ventricular function parameters have their own characteristic maturation changes.. · Racial variability may not occupy an important place for fetal myocardial function during these GA..

Gravitation-induced temperature of single atoms on atomic and cosmological scales

The experimental findings on the rate of transfer of a single Xe atom from the sample surface towards the tip in the low temperature STM, induced by voltage pulses, are understood by assuming a vibrational temperature for a single Xe atom. But temperature is introduced in standard quantum physics as a parameter in the Boltzmann distribution of a statistical ensemble consisting of large number of non-interacting exact copies of the dynamical system under investigation. This represents a problem, if the system under investigation is to be described by a single pure quantum state being a solution of Schrödinger’s equation. In the framework of a quantum field theory based on Einstein-Hilbert action in high dimensions (EHHD) we demonstrate that temperature for a single atom emerges if the atom is beabled in a warp resonance due to entanglement with local gravitons (gravonons), living in high spacetime dimensions (11D). Desorbing Xe atom in a limbo state in the tunnel gap, due to destruction of the beable via inelastic tunnelling, is in Boltzmann distribution over plane waves {| k〉} since the squared overlap of the warp resonance with free plane wave states varies like exp(–Ek/kBTvib ) where Ek is the energy of the free particle state and Tvib is the vibrational temperature of Xe calculated from the shape and the extension of the warp resonance. The nature of the warp resonance varies with the tip-sample voltage (becoming more contracted at higher tunnelling currents, as the tip approaches the sample) and raises its energy to higher values. More contracted warps at higher tunnelling currents imply stronger overlap with free states of higher energy, described by Boltzmann factors of higher temperature. The mechanism generating single atom temperature generalizes to other dynamical processes where temperature is completely determined by the nature of the warp resonance in the beables. For homogeneous and isotropic systems this implies a universal value of the temperature everywhere in the system. With these considerations the mechanism is also applied to intergalactic hydrogen-atom clusters, where it explains the observed temperature of the CMB radiation and the absence of the horizon problem.

Maximizing Curves Viewed as Free Curves

Abstract The aim of this paper is to provide a direct link between maximizing curves that occur in the construction of smooth algebraic surfaces having the maximal possible Picard numbers and reduced free plane curves with simple singularities. We also investigate odd degree plane curves with simple singularities having maximal total Tjurina number.

Photo-Thermoelasticity Heat Transfer Modeling with Fractional Differential Actuators for Stimulated Nano-Semiconductor Media

The term “optical thermoelasticity” is used to describe how the optical properties of a material change when it is heated or deformed mechanically. The issues of effective elastic and heat transfer symmetry are given particular focus. This study gives a new nonlocal theoretical formulation for a thermo-optical elastic material that can be used to describe how thermomechanical waves and plasma waves relate to the symmetry of semiconductor materials such as silicon or germanium. The suggested model includes the idea of nonlocal elasticity and a modified Moore–Gibson–Thompson (MGT) heat conduction equation with nonsingular fractional derivative operators. The heat transfer equation has been converted and generalized into a nonsingular fractional form based on the concepts of Atangana and Baleanu (AB) using the Mittag–Leffler kernel. The developed model is used to examine the effect of thermal loading by ramp-type heating on a free plane of unbounded semiconductor material symmetries. Using the Laplace transform approach, we may analytically obtain linear solutions for the investigated thermo-photo-elastic fields, such as temperature. The Discussion section includes a set of graphs that were generated using Mathematica to evaluate the impact of the essential parameters.

Correlated Two‐Photon Scattering in a 1D Waveguide Coupled to an N‐Type Four‐Level Emitter

AbstractCorrelated two‐photon scattering in a waveguide quantum electrodynamics system consisting of a four‐level ‐type emitter (4LE) sidely coupled to a one‐dimensional (1D) waveguide is studied. In the two‐photon regime, scattering eigenstates of the system are constructed by imposing an open boundary condition and defining the incident state as a free plane wave, which includes a photon–photon bound state that passes through the 4LE as a composite single particle. In the multilevel system, the bound state can be tuned by the interference to generate controllable types of interactions (attractive or repulsive) and interaction strengths. Photon‐induced tunneling (bunching) in transmission and photon blockade (antibunching) in reflection are found in the system. In addition, the scattering photon pair off the system is strongly entangled in momentum space.

Speckle Tracking Analysis in Fetuses with D-Transposition: Predicting the Need for Urgent Neonatal Balloon Atrial Septostomy.

Speckle tracking analysis of the endocardium of the right (RV) and left (LV) ventricles was used to evaluate the size, shape, and contractility of these chambers in fetuses with D-Transposition of the great arteries (D-TGA) to identify fetuses that would require emergent balloon atrial septostomy (BAS) after birth. This was a retrospective analysis of fetuses with D-TGA and intact ventricular septum that were divided into 2 groups. Group 1 underwent urgent BAS after birth because of a restrictive atrial septum and group 2 did not. Using speckle tracking analysis, the end-diastolic and end-systolic RV and LV areas, lengths, widths, sphericity indices, and contractility were computed. Logistic regression analysis was performed to identify fetuses who would require urgent neonatal BAS. Of the 39 fetuses with D-TGA, 55% (n = 22) required urgent neonatal BAS (group 1) and 45% (n = 17) (group 2) did not. When comparing D-TGA groups 1 and 2, differences were seen in RV and LV area, sphericity index for segment 1 of the LV, LV fractional area of change and free wall annular plane systolic excursion, fractional shortening for LV segment 12, and RV free wall strain. Regression analysis of these measurements identified 91% of neonates who underwent BAS, with a false-positive rate of 12%. Using speckle tracking analysis to evaluate the RV and LV, measurable differences were identified for the RV and LV size, shape, and contractility between fetuses who underwent neonatal urgent BAS vs. those who did not require this procedure.

Propagation of generalised Rayleigh wave at the surface of piezoelectric medium with arbitrary anisotropy

AbstractMathematical model for mechanical and electrical dynamics is solved for three‐dimensional propagation of harmonic plane waves in a piezoelectric medium with arbitrary anisotropy. A system of modified Christoffel equations is derived to explain the existence and propagation of bulk waves or decaying phases in the considered medium. At the free plane boundary, a superposition of decaying phases form a generalised Rayleigh wave, which is governed by a linear system of four homogeneous equations. A complex determinantal secular equation ensures a solution to this system. True surface wave at the boundary of the considered medium demands a real solution of this complex secular equation. The linear system of four equations is then transformed to replace the complex secular equation with a real one, which can be solved by standard numerical methods. A real solution of this real secular equation provides the phase velocity for generalised Rayleigh wave at the boundary of piezoelectric medium with arbitrary anisotropy. This phase velocity defines a complex slowness vector, which is used to calculate the motion of material particles and the wave‐induced electric field. A numerical example is considered to compute the phase velocity as well as group velocity for given (arbitrary) propagation directions of Rayleigh wave at the boundary. Variations in particle motion and electric field, induced by Rayleigh wave, are analysed at different depths for different propagation directions at the boundary.

Vision occlusion solution for line-structured light measurement system based on a plane mirror

To solve the problem of the measurement information loss caused by occlusion of the field of view in line-structured light measurement, a vision occlusion solution of the line-structured light measurement system based on a plane mirror is proposed in this work. In the system, a symmetrical structure between real and virtual images was created by the mirror. A checkerboard with a light stripe and its mirror image were captured by the camera in an image. The centers of the light stripe and its mirror image were corrected by the vanishing point constraint, and a calibration method of the free plane target was used to calibrate the real and virtual light planes. The real and virtual point clouds of the object were obtained by scanning with a linear guide. According to the ideal reflection model of the mirror, the real and virtual point clouds of the object were transformed into a common coordinate system, and an iterative closest point (ICP) algorithm was used to realize fine registration. As a result, the occluded parts can be compensated for each other. Compared with a standard ball, the mean/maximum absolute error of the measurement was 0.2553/0.3276 mm. The experimental results revealed that the proposed method can obtain the complete surface of the object, thus effectively solving the occlusion problem in the line-structured light measurement, and reducing the loss of the measurement information, which can meet the industrial measurement requirements.

Computable scott sentences for quasi–Hopfian finitely presented structures

We prove that every quasi-Hopfian finitely presented structure A has a d- $$\Sigma _2$$ Scott sentence, and that if in addition A is computable and Aut(A) satisfies a natural computable condition, then A has a computable d- $$\Sigma _2$$ Scott sentence. This unifies several known results on Scott sentences of finitely presented structures and it is used to prove that other not previously considered algebraic structures of interest have computable d- $$\Sigma _2$$ Scott sentences. In particular, we show that every right-angled Coxeter group of finite rank has a computable d- $$\Sigma _2$$ Scott sentence, as well as any strongly rigid Coxeter group of finite rank. Finally, we show that the free projective plane of rank 4 has a computable d- $$\Sigma _2$$ Scott sentence, thus exhibiting a natural example where the assumption of quasi-Hopfianity is used (since this structure is not Hopfian).

Speckle-Tracking Analysis in Fetuses With Tetralogy of Fallot: Evaluation of Right and Left Ventricular Contractility and Left Ventricular Function.

This study examines fetuses with tetralogy of Fallot (TOF) and evaluates the right (RV) and left (LV) ventricular contractility and LV function using speckle-tracking analysis of the endocardium. The study group consisted of 44 fetuses with TOF, of which 34% had pulmonary valve atresia (N=15) and 59% (N=26) had pulmonary valve stenosis. The RV and LV global fractional area change, longitudinal contractility (longitudinal strain, free wall strain, septal strain, free wall and septal annular fractional shortening, and free wall and septal wall annular plane systolic excursion), and transverse contractility (24-segment fractional shortening) as well as LV functional assessment (stroke volume, cardiac output, and ejection fraction) were measured using speckle-tracking analysis. The z-scores of the measurements were compared to 200 controls. Compared to controls, measurements of LV contractility in fetuses with TOF demonstrated significantly abnormal values for global contractility, longitudinal contractility, and transverse contractility of the mid and apical segments. LV function was abnormal for stroke volume (SV), cardiac output (CO), and ejection fraction (EF). In comparison, RV contractility demonstrated no significant difference between TOF and control z-score values for RV global contractility. Only two RV measurements were found to be abnormal: longitudinal contractility and transverse contractility of the apical segments. Using multiple measurement tools to evaluate global, longitudinal, and transverse contractility, this study identified significant differences between fetuses with TOF and healthy controls, with greater contractility abnormalities seen in the LV than in the RV.

Reflection of plane waves at the free surface of a magneto-thermoelastic medium with variable thermal conductivity and variable mass diffusivity

The present article deals with the propagation of plane waves in a magneto-thermoelastic medium under the effects of variable thermal conductivity and variable mass diffusivity. It is observed that three coupled longitudinal plane waves and one transverse wave travel in the medium with distinct speeds. The formulae for amplitude ratios and energy ratios corresponding to various reflected waves have been presented, when a set of coupled waves strikes obliquely at the boundary surface of the assumed model. To illustrate the analytical developments, the numerical solution is performed for a particular material and the results in respect of phase velocities, amplitude ratios and energy ratios are presented graphically. It is observed that the results depend upon the angle of incidence, frequency and the thermoelastic properties of the half-space. It is verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence and there is no energy dissipation at the free plane boundary. Results of some earlier workers have been deduced from the present formulation.

Geotechnical structure interpretation from borehole wall imagery at Mamput Block, Central Kalimantan, Indonesia

One of the considerations in mining excavation is geotechnical conditions especially structure orientation. Its observations can be done on the surface or through the drill core. However, if there is no free vertical plane on the surface and core observation, then it is difficult to find the direction of dip and strike, which then the televiewer technology is used. This study aims to reveal the structural conditions and to observe the strike and dip of rock layers using the High-Resolution Acoustic Televiewer (HIRAT) apparatus. This apparatus is an accurate and reliable method for recording structural data and has widely used in mining activity. Analysis of the structural conditions was carried out with a reading density of 0.20 m. The observations show that the discontinuity plane is generally trending to Northeast - Southwest, with a dip generally below 30°. The results of the structural interpretation of the borehole have various features that are bedding plane, filled fracture/joint, minor/major open joint, broken zone, and washout. This study gives many advantages especially in preparing data for project feasibility related to excavation, underground tunneling, or other constructions.

Long-Wave Vibrations and Long Waves in an Anisotropic Plate

Free vibrations and plane waves are analyzed in the linear approximation for a thin elastic, anisotropic infinite plate having constant thickness. A general anisotropy described by 21 elastic moduli is considered. It is assumed that the moduli of elasticity and density are independent in the tangential coordinates but can depend on the coordinate along the thickness of the plate. Multilayer and functionally gradient plates are also considered. Assuming that the wavelength significantly exceeds the thickness of the plate, an asymptotic power expansion is obtained for a small thickness parameter for a harmonic solution of the system using the three-dimensional equations in tangential coordinates provided by the elasticity theory. For fixed values of wave numbers, there are only three long-wave solutions available: one low-frequency bending and two shearing ones. Dispersion equations are obtained for these solutions with accuracy to the terms of the second order of smallness in the dimensionless thickness. Bending solutions are characterized by a strong dependence of frequency on the wavelength, while the tangential waves propagate with low dispersion. Particular types of anisotropy are considered.