Radial Wave Research Articles

On the Klein–Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu–Yang magnetic monopole

We consider Klein–Gordon (KG) particles in a global monopole (GM) spacetime within Eddington-inspired Born–Infeld gravity (EiBI-gravity) and in a Wu–Yang magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime settings. We propose a textbook power series expansion for the KG radial wave function that allows us to retrieve the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some conditionally exact, closed form, energy levels (through some parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar potential. We report the effects of the Eddington parameter κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}, GM-parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}, WYMM strength σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}, KG-oscillators’ frequency Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document}, and the coupling parameters of the Coulomb plus linear Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators at hand. Such effects are studied over a vast range of the radial quantum number nr≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_r\\ge 0$$\\end{document} and include energy levels clustering at κ>>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa>>1$$\\end{document} (i.e., extreme EiBI-gravity), and at |σ|>>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\sigma |>>1$$\\end{document} (i.e., extreme WYMM strength).

Spiral eutectic growth dynamics facilitated by space Marangoni convection and liquid surface wave

Eutectic alloys display excellent application performances since the essential function of coupled microstructures is quite different from that of single-phase and peritectic alloys. However, due to the strong natural convection within liquid alloys under normal gravity, the eutectic growth process on earth usually produces traditional rod-like or lamellar composite microstructures, which hinders the exploration of distinctive coupled growth patterns. Here, we carried out the rapid solidification of hypoeutectic Zr64V36 alloy to explore novel coupled growth dynamics aboard the China Space Station under a long-term stable microgravity condition. An extreme liquid undercooling of 253 K was achieved for this refractory alloy, displaying a strong metastability in outer space. We find that a radial coupled pattern grew out of the nucleation site, accompanying a ripple-like surface microstructure. This resulted from the rapid eutectic growth within a highly undercooled alloy in combination with a liquid surface wave excited by the electrostatic field under microgravity. Especially, a spiral coupled growth mode occurred during radial eutectic growth and surface wave spreading, which were controlled by the Marangoni convection effect on the fluid flow pattern and eutectic growth dynamics. Our findings contribute to the coupled growth investigation by modulating gravity levels to develop multi-pattern microstructures.

Dissociation cross sections of ψ(3770), ψ(4040), ψ(4160), and ψ(4415) mesons with nucleons

We study the dissociation of ψ(3770), ψ(4040), ψ(4160), and ψ(4415) mesons in collision with nucleons, which takes place in high-energy proton-nucleus collisions. The quark interchange between a nucleon and a cc¯ meson leads to the dissociation of the cc¯ meson. We consider the reactions: pR→Λc+D¯0 , pR→Λc+D¯*0 , pR→Σc++D− , pR→Σc++D*− , pR→Σc+D¯0 , pR→Σc+D¯*0 , pR→Σc*++D− , pR→Σc*++D*− , pR→Σc*+D¯0 , and pR→Σc*+D¯*0 , where R stands for ψ(3770), ψ(4040), ψ(4160), or ψ(4415). A reaction of a neutron and a cc¯ meson corresponds to a reaction of a proton and the cc¯ meson by replacing the up quark with the down quark and vice versa. Transition-amplitude formulas are derived from the S-matrix element. Unpolarized cross sections are calculated with the transition amplitudes for scattering in the prior form and in the post form. The cross sections relate to nodes in the radial wave functions of ψ(3770), ψ(4040), ψ(4160), and ψ(4415) mesons.

Electromagnetic Vibration and Noise Analysis of Linear Phase-Shifting Transformer

The advantages of adjustable angle phase-shifting and great expansibility make the linear phase-shifting transformer a novel type of power conversion device with a wide range of potential applications. However, during the procedure, there is a lot of noise. For the purposes of transformer design and vibration and noise reduction, it is crucial to investigate its electromagnetic vibration and noise. In this paper, the radial electromagnetic force wave considering the influence of the end effect as the source of the noise of the linear phase-shifting transformer was deduced and calculated. Based on this, the spectrum and space–time properties of the radial electromagnetic force waves were simulated and verified. Additionally, a finite element model was created using the Ansys Workbench 2022R1 platform to study the electromagnetic vibration and noise of the linear phase-shifting transformer. A joint simulation of the electromagnetic, structural, and sound fields was then performed. First, the transformer’s natural frequency was determined by modal analysis. After that, the transformer’s structure and the results of the transient electromagnetic field computation were combined and a harmonic response analysis was conducted to determine the vibration acceleration spectrum. Finally, in order to solve the sound pressure field, the transformer’s boundary vibration acceleration was coupled to the air domain. Furthermore, an analysis was conducted to determine the noise distribution surrounding the linear phase-shifting transformer. The joint simulation findings demonstrate that the linear phase-shifting transformer’s resonance, which produces larger electromagnetic vibration and noise, is indeed caused by the radial electromagnetic force. Simultaneously, the impact of the LPST core’s fixed components on the electromagnetic vibration and noise of the core was examined.

The effect of excitation current on radial electromagnetic force wave of tangential magnetizing parallel structure hybrid excitation synchronous motor

To study the influence of the magnitude of the excitation current on the radial electromagnetic force wave of the tangential magnetizing parallel structure hybrid excitation synchronous motor (TMPS-HESM) under different working conditions. Firstly, the basic structure of the motor and the rotor magnetic circuit model is introduced. Secondly, considering the influence of excitation current, the Maxwell stress tensor method is used to analyze the radial electromagnetic force wave of the motor and the source, frequency and order of the radial electromagnetic force wave that has a great influence on the electromagnetic vibration of the motor are qualitatively obtained. Then, the three-dimensional finite element method is used to calculate the variation law of the radial electromagnetic force wave when different excitation currents are applied under no-load and load conditions, revealing that the DC excitation will increase the amplitude of the radial electromagnetic force wave of a specific order. Meanwhile, the influence of load torque variation on the radial electromagnetic force wave is discussed, and it is found that the (2f, 8) and (6f, 24) order electromagnetic force waves are greatly affected by the armature reaction. The work provides a theoretical basis for further suppressing the electromagnetic vibration of this type of hybrid excitation motor.

Analytical solutions for the Klein–Gordon equation with combined exponential type and ring-shaped potentials

In this study, we have successfully obtained the analytical solutions for the Klein–Gordon equation with new proposed a non-central exponential potential Vr=D1-σ0coth(αr)2+(η1+η2cosθ)/r2sin2θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V\\left( r \\right) = D\\left[ {1 - \\sigma_{0} \\coth (\\alpha r)} \\right]^{2} + (\\eta_{1} + \\eta_{2} \\cos \ heta )/r^{2} \\sin^{2} \ heta$$\\end{document}. Our approach involves a proper approximation of the centrifugal term, with l′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${l}{\\prime}$$\\end{document} representing the generalized orbital angular momentum quantum number, and the utilization of the Nikiforov–Uvarov method. The resulting radial and angular wave functions are expressed in terms of Jacobi polynomials, and the corresponding energy equation is also derived. Our calculations of the eigenvalues for arbitrary quantum numbers demonstrated significant sensitivity to potential parameters and quantum numbers. Additionally, we evaluate the dependence of energy eigenvalues on screening parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} for arbitrary quantum numbers nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_{r}$$\\end{document} and N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N$$\\end{document} to establish the accuracy of our findings. Furthermore, we determine the non-relativistic limits of the radial wave function and energy equation, which align with corresponding previous results in the case where η1=η2=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta_{1} = \\eta_{2} = 0$$\\end{document}.

Short-term vascular responses to spring and fall daylight savings time shifts.

Daylight saving time (DST) is a Western biannual time transition, setting the clock back 1 h in the fall and forward 1 h in the spring. There is an epidemiological link between DST and acute myocardial infarction risk in the first week following the spring shift; however, the mechanisms underlying the effect of DST on cardiovascular function remain unclear. The purpose of this study was to explore the short-term cardiovascular changes induced by fall and spring shifts in DST in a convenience sample of healthy adults. We hypothesized that spring, but not fall, DST shifts would acutely increase central pulse wave velocity, the gold standard measurement of central arterial stiffness. Twenty-one individuals (fall: n = 10; spring: n = 11) participated in four visits, occurring 1 wk before and at +1, +3, and +5 days after spring and fall time transitions. Central, brachial, and radial pulse wave velocity as well as carotid augmentation index were assessed with applanation tonometry. Sleep quality and memory function were assessed via questionnaire and the Mnemonic Similarities Task, respectively. Neither fall or spring transition resulted in changes to cardiovascular variables (carotid-femoral pulse wave velocity, carotid-brachial pulse wave velocity, carotid-radial pulse wave velocity, heart rate, mean arterial pressure, or augmentation index), sleep quality, or cognitive function (all P > 0.05). Our findings do not provide evidence that DST shifts influence cardiovascular outcomes in healthy adults. This study emphasizes the need for further research to determine the mechanisms of increased cardiovascular disease risk with DST that help explain epidemiological trends.NEW & NOTEWORTHY The debate of whether to abolish daylight savings time (DST) is, in part, motivated by the population-level increase in all-cause mortality and incidence of cardiovascular events following DST; however, there is an absence of data to support a physiological basis for risk. We found no changes in pulse wave velocity or augmentation index during the subacute window of DST. Large multisite trials are necessary to address the small, but meaningful, effects brought on by a societal event.

A Wave-corrected Assessment of the Local Midplane

As the number of known Galactic structures mounts thanks to the Gaia Space Telescope, it is now pertinent to study methods for disentangling structures occupying the same regions of the Milky Way. Indeed, understanding the precise form of each individual structure and the interactions between structures may aid in understanding their origins and chronology. Moreover, accounting for known structures allows one to probe still finer Galactic structure. In order to demonstrate this, we have developed an odd low-pass filter (OLPF), which removes smaller, odd-parity structures like the vertical waves, and use the filtered data to examine the location of the Galaxy’s midplane. We find that the radial wave identified by Xu et al. continues inward to at least the Sun’s location, with an amplitude that decreases toward the inner, denser parts of the disk, consistent with a simple, qualitative simulation. Additionally, we employ the OLPF results to determine the solar offset, z ⊙, with smaller structures filtered out. We find that z ⊙ = 34.2 ± 0.3 pc.

Volume overload is a major characteristic in primary aldosteronism: a 3-year follow-up study.

We examined haemodynamics, focusing on volume balance and forward and backward wave amplitudes, before and after 2.8 years of targeted treatment of primary aldosteronism. Patients with essential hypertension and normotensive individuals were examined for comparison ( n = 40 in each group). Recordings were performed using radial artery pulse wave analysis and whole-body impedance cardiography. Unilateral aldosteronism was treated with adrenalectomy ( n = 20), bilateral aldosteronism with spironolactone-based medication ( n = 20), and essential hypertension with standard antihypertensive agents. Aortic SBP and DBP, forward and backward wave amplitudes, and systemic vascular resistance were equally elevated in primary aldosteronism and essential hypertension. All these haemodynamic variables were similarly reduced by the treatments. Primary aldosteronism presented with 1 litre (∼10%) extracellular water excess ( P < 0.001) versus the other groups, and this excess was normalized by treatment. Initial pulse wave velocity (PWV) was similarly increased in primary aldosteronism and essential hypertension, but final values remained higher in primary aldosteronism ( P < 0.001). In regression analyses, significant explanatory factors for treatment-induced forward wave amplitude reduction were decreased systemic vascular resistance ( β = 0.380) and reduced extracellular water volume ( β = 0.183). Explanatory factors for backward wave amplitude reduction were changes in forward wave amplitude ( β = 0.599), heart rate ( β = -0.427), and PWV ( β = 0.252). Compared with essential hypertension, the principal haemodynamic difference in primary aldosteronism was higher volume load. Volume excess elevated forward wave amplitude, which was subsequently reduced by targeted treatment of primary aldosteronism, along with normalization of volume load. We propose that incorporating extracellular water evaluation alongside routine diagnostics could enhance the identification and diagnosis of primary aldosteronism.

Kato's theorem and ultralong-range Rydberg molecules

We consider nonadiabatic coupling in the “trilobite”-like long-range Rydberg molecules created by perturbing degenerate high-ℓ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular nonadiabatic coupling. We find that the gap between the trilobite potential curve and neighboring “butterfly” or “dragonfly” potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the s-wave radial wave function. This is an unanticipated outcome of Kato's theorem. Published by the American Physical Society 2024

Numerical study on the self-pressurization capacity of radial gas wave refrigerator

Gas wave refrigeration technology is an innovative refrigeration technique that harnesses pressure waves to facilitate energy exchange. In this paper, the wave rotor undergoes a transformation from its original axial structure to a radial structure. The self-pressurization capability of radial structure is proven to facilitate autonomous gas circulation, obviating the necessity for a drive fan, according to numerical simulations. We explore two methods to regulate the cycling ability for improved adaptability: altering exhaust ports and controlling exhaust resistance. The former offers a broader range of adjustment, while the latter is suitable for fine-tuning due to associated throttling pressure loss. Additionally, the mechanism of radial heat transfer is probed, revealing its intensification correlating with rising rotational speeds. The study also delves into the power consumption dynamics unique to the radial configuration. Influenced by these two factors, the device attains its peak efficiency near the specific internal circulation state of φ=φi. The optimal rotational speed is determined to be 2750 rpm, which offers a balance between eddy current loss and power consumption. This study demonstrates that a radial gas wave refrigerator enables the integration of the pressurization and refrigeration processes. It serves as the foundation for subsequent structural optimization and experimental research on radial configurations.

(233) Perceptions and Use of Penile Regenerative and Aesthetic Therapy Among SMSNA Members

Abstract Introduction Wave therapy (WT) and platelet rich plasma (PRP) have been evaluated in multiple medical contexts, but there is paucity of long-term data to support their applications in erectile dysfunction (ED) and Peyronie’s disease (PD). Despite the American Urological Association and Sexual Medicine Society of North America (SMSNA) recommending against the use of these therapies for ED and PD outside of a clinical trial, many practices offer WT and PRP as penile regenerative therapies. Objective We aim to understand current perceptions and practice patterns of SMSNA members in offering penile regenerative and aesthetic therapies. Methods An anonymous online survey was deemed IRB exempt and administered to current members of SMSNA electronically from 4/2023 to 6/2023 asking practitioner’s demographics, practice information, their familiarity and offering of various types of penile regenerative therapy (focused shockwave therapy [fSWT], radial wave therapy [RWT], PRP, stem cell therapy [SCT], penile botulinum toxin [Botox] injection) and penile aesthetic procedures including girth and length-enhancement. We included current SMSNA members who are physicians in practice or Advance Practice Providers (APPs) that practice in the US. We excluded those who are trainees and practice outside the US. We conducted descriptive statistics using RedCap. Results Of the 500 active SMSNA members, 46 completed the survey (response rate 9%). Participants were predominantly male (N=42, 91%), physician (N=43, 93%), fellowship-trained (N=39, 85%), and in practice for a median of 5 years. Participants mostly practiced in academic settings (N=33, 72%), and saw 10 or more patients with ED weekly (N=35, 76%). Most respondents reported being comfortable describing the differences between types of wave therapy (N=28, 61%). A minority of respondents offered RWT (N=3, 7%) and most indicated that there was no to low evidence to support its use (N=31, 67%). Ten respondents offered fSWT (N=10, 22%) and only a minority reported no to low evidence to support the use of fSWT (N=18, 39%). Five respondents (11%) offered PRP and most reported that there was no or low evidence to support use of PRP (N=31, 67%). None of the respondents offered SCT and most reported that there was no to low evidence to support the use of SCT (N=26, 57%). One respondent (2%) reported offering penile botox treatment while 19 (41%) reported that there was no to low evidence to support its use. A minority of survey respondents offered girth-enhancement procedures with three respondents (7%) offering hyaluronic acid. For length-enhancing procedures, eight respondents (17%) offered cosmetic scrotoplasty and three (7%) offered suprapubic lipectomy. Conclusions Penile regenerative and aesthetic therapies are not common practice among SMSNA members. With the notable exception of fSWT, majority of survey respondents felt that there was little to no evidence supporting penile regenerative and aesthetic therapies. Further understanding the practice patterns of SMSNA members will help identify future opportunities for multi-institutional collaborations to further evaluate the efficacy of these experimental therapies. Disclosure No.

Model of slot antenna for MPECVD of carbon nanostructure

A model of a slotted waveguide antenna for microwave plasma enhanced chemical vapor deposition (MPECVD) of carbon nanostructures at low pressure is developed. The performance of two slot applicator for the production of dense plasma in the working gas (argon) at a frequency of 2.45 GHz is investigated by EM field simulator. Results show that dimensions of the symmetrical slots (length l ≤ λg/2, width of d = 6-10 mm) and optimized angle (φ=32° with respect to the waveguide central line) have a strong influence on the impedance matching of the waveguide to the dielectric window and plasma column (1.5 < SWR < 2.5), and on the radiation efficiency. The dielectric plate and plasma column density were taken into account in the model in the optimisation of the dimensions of the slots. The mode structure of standing surface waves in the plasma column is investigated at three values of plasma density and results for the radial (n=1) and azimuthal wave numbers (m=3, 4, 5) are in agreement with experimental results.

High-frequency dissipative MHD waves in straight magnetic cylindrical plasma: Coronal loops heating application

The theoretical model for analyzing the waves and oscillatory behavior in the structured solar corona using straight magnetic cylindrical geometry filled with uniform low-β plasma has been recognized as the most preferable classical model for the last few decades. A number of observations, since the first observation of the transition region and coronal explorer to the latest ones, have been adequately explained by adopting this model. In order to analytically formulate the oscillatory characteristics of magnetohydrodynamic (MHD) waves, most of the studies have considered the nature of plasma as an ideal fluid, particularly in the context of solar physics. However, a departure from ideal plasma consideration to non-ideal may lead to a number of modifications in the characteristics of the MHD waves, including its damping too. In what follows, we derive a more general analytical dispersion relation by extending the classical dispersion relation of [Edwin and Roberts, “Wave propagation in a magnetic cylinder,” Sol. Phys. 88, 179–191 (1983)] taking into account the effect of plasma viscosity as a non-ideal term in the existing formulations of the classical model. Consequently, the effects of viscosity on the damping of sausage and kink modes are examined in detail. Multiple trapped body waves of different frequencies exist for both kink and sausage modes in which trapped sausage body wave of comparatively high frequency is damped potentially to generate enough energy to balance the radiative losses of the coronal loop regions. For the coronal loop's plasma parameters, it is found that trapped first radial overtone body wave of sausage type is able to balance the radiative losses of coronal loop structure provided magnetic field strength does not exceed its value of more than 20G.

Exact scalar quasibound states solutions of f(R) theory's static spherically symmetric black hole

Following the recent developments in black holes' quasibound states exact solutions by Senjaya (2023b,c), in this letter, we present a novel exact solution of quasibound states of a scalar around a static spherically symmetric black hole solution of f(R) theory of gravity. We start with the relativistic scalar field wave equation, i.e. the Klein-Gordon equation, isolating the radial equation and finally successfully obtain the exact radial wave solutions in terms of General Heun functions. Having the exact solutions in hand, the energy levels expression is obtained from the radial wave polynomial conditions. In the last part of this letter, the Hawking radiation is investigated via the Damour-Ruffini method and the Hawking temperature is obtained from radiation distribution function.

A randomized trial of treatment for anterior cruciate ligament reconstruction by radial extracorporeal shock wave therapy

ObjectiveThe aim of this study was to explore the effects of radial extracorporeal shock wave therapy (rESWT) in patients with anterior cruciate ligament(ACL) reconstruction(ACLR).MethodsWe conducted a randomized, controlled trial involving 72 eligible patients with ACL reconstruction in which we compared two strategies: the experimental group was standard rehabilitation plus rESWT and the control group was standard rehabilitation plus sham rESWT. The outcome was the change from baseline to 24 weeks in the average score on Lysholm knee joint score (LKS), range of motion (ROM), visual analogue scale (VAS) and International Knee Literature Committee (IKDC).ResultsOf 36 subjects assigned to rehabilitation plus rESWT, 4 lost to follow up. Of 36 assigned to rehabilitation plus sham rESWT, 5 lost to follow up. The LKS, ROM and IKDC scores of the experimental group were markedly increased at 3 and 6 weeks after treatment (P < 0.001), and the VAS was notably decreased (P < 0.001). However, there were no significant differences in the LKS, ROM, IKDC and VAS between the groups at 24 weeks after treatment (P > 0.05).ConclusionThe strategy of rehabilitation plus rESWT had better functional outcomes after ACL reconstruction. As such, our study demonstrates that rESWT is essential for patients with ACL reconstruction. Early use of rESWT can improve joint function, pain relief and ability of daily living. rESWT has a positive effect on the overall rehabilitation of patients.

Energy spectrum and applications of Eckart plus Hellmann potential in hyperspherical coordinates

We investigate the approximate bound-state solutions of the N-dimensional Schrödinger equation with a combination of Eckart and Hellmann potentials via the asymptotic iteration approach. By the use of the Greene-Aldrich approximation, which is valid for small values of the screening parameter, we establish the N-dimensional energy spectrum and the N-dimensional radial wave function in approximate analytic form. In hyperspherical coordinates, the normalized radial wave function is expressed in terms of hypergeometric and Jacobi polynomials. To double-check the energy spectrum in hyperspherical coordinates, we utilize polynomial solutions in view of the asymptotic iteration approach. The expressions for the expectation values of inverse position, square of inverse position, kinetic energy, and square of momentum are derived in hyperspherical coordinates by using the Hellmann-Feynmann theorem. We also present the analytically calculated energy eigenvalues for Eckart plus Hellmann potential. We deduce special forms of the relevant potential, such as Eckart, Hellmann, and Hulthén potentials.

Numerical study on zero-power operation strategy of radial gas wave refrigerator

Radial gas wave refrigerators uniquely integrate pressurization and refrigeration processes. This paper emphasizes optimizing the device's structure to reduce power consumption. It is beneficial for the application in large-flow scenarios or areas with limited power resources. A transient numerical analysis methodology is developed for precise simulation. The mechanism of power consumption is revealed through the lenses of gas force and angular momentum. Strategies including nozzle inclination and curved channel design are proposed. The optimization process is steered by the principles of the Design of Experiments (DOE) methodology. The main results are presented as follows. Optimal oblique incidence of the driving gas can reduce power consumption by up to 59.6%. Implementing a curved channel yields a maximum 71.2% reduction in shaft work. The device attains self-driven operation by combining the inclined port with the backward-curved arched channel. The optimal parameters identified are α=120°, β=60°, and γ=50°. With these settings, the device produces 85 W of power to counteract mechanical friction and improves refrigeration efficiency by 16.5% compared to traditional designs. This study lays the groundwork for the practical application of radial gas wave refrigerators.

Histopathologic Examination Changes Observed as Mechanotransduction Following Focused and Radial Acoustic Wave Therapy

The author executed a series of self-biopsies following focused acoustic, and focused and radial acoustic wave therapy to examine the effectiveness of the two types of acoustic wave therapy and to identify and investigate mechanotransduction; the mechanism of action produced by acoustic wave therapy. A case of a 28-year-old patient’s acoustic wave therapy that improved a vascular malformation is reported as a successful example. The series of histopathologic examinations following acoustic wave therapy strongly suggest that mechanotransduction causes neither fatal damage nor critical degeneration of tissue, and rather create moderate changes; indicating that the treatment is safely effective. There are distinctive differences in histopathologic changes between the two types of acoustic waves; the combination of focused and radial acoustic wave therapy leads to a faster normalizing change with less infiltration of cells than that following only focused-acoustic wave therapy. Further research on the mechanism of acoustic wave therapy is awaited, and a clear elucidation of this mechanism will bring about widespread recognition of this modality as a promising treatment for skin tightening and rejuvenation.

Regeneration of the Patellar Tendon with Radial Pressure Waves in a Sharp Injury: Case Report

Patellar tendon ruptures are rare injuries and are more commonly associated with predisposing factors and previous surgical procedures than with direct trauma. Acute partial-thickness tears are usually treated with immobilization and rehabilitation. The literature recommends surgical management of partial ruptures of the patellar tendon after 6 months of failure of conservative treatments and in acute cases with a compromise &gt;50–55% of the tendon. Radial pressure wave therapy is a safe, non-invasive technique with scientific support in tissue regeneration; it is found as one of the therapeutic alternatives for the management of tendinopathy and partial ruptures of the patellar tendon. The present case report shows the effectiveness of radial pressure wave therapy in a shear injury of the patellar tendon, with a compromise of at least 70%. We have not found similar cases previously reported in the literature, highlighting its relevance. Keywords: Patellar tendon, Radial pressure waves, Patellar tendon rupture, Cutting injury