Quantum Mechanics: Harmonic Wave-Packets, Localized by Resonant Response in Dispersion Dynamics

From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity

Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over ＂fast＂ variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the ease without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.

Quasicrystals’ Resonant Response with Translational Symmetry

Diffraction in quasicrystals is in logarithmic order and icosahedral point group symmetry. Neither of these features are allowed in Bragg diffraction, so a special theory is required. The present work displays exact agreement between the analytic metric with a numeric description of diffraction in quasicrystals that is based on quasi-structure factors. So far, we treated the hierarchic structure as ideal;now, we detail the theory by including two significant features: firstly, the steady state wave function of the incident radiation demonstrates how harmonics, in metrical space and time, enable coherent interaction between the periodic wave packet and hierarchic quasicrystal;secondly, mapping of the hierarchic structure for any influence of defects will allow estimation of possible error margins in the analysis. The hierarchic structure has the required logarithmic periodicity: superclusters, containing about 103 atoms, convincingly map phase contrast images;while higher orders leave space for subsidiary speculation. The diffraction is completely explained for the first time.

Third-Order Nonlinear Optical Response near the Plasmon Resonance Band of Cu2-xSe Nanocrystals

The third-order nonlinear optical properties of water-soluble Cu Se nanocrystals are studied in the near infrared range of 700-980 nm using a femtosecond pulsed laser by the Z-scan technique. It is observed that the nonlinear optical response of Cu Se nanocrystals is sensitively dependent on the excitation wavelength and exhibits the enhanced nonlinearity compared with other selenides such as ZnSe and CdSe. The W-shaped Z-scan trace, a mixture of the reversed saturated absorption and saturated absorption, is observed near the plasmon resonance band of Cu Se nanocrystals, which is attributed to the state-filling of free carriers generated by copper vacancies (self-doping effect) of Cu Se nanocrystals as well as the hot carrier thermal effect upon intense femtosecond laser excitation. The large nonlinear optical response and tunable plasmonic band make Cu Se nanocrystals promising materials for applications in ultra-fast all-optical switching devices as well as nonlinear nanosensors.

Quantum Mechanics: Internal Motion in Theory and Experiment

Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E2 = p2c2 + m2c4. Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon;while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, vp⋅vg = c2 with vp ≥ c because vg ≤ c, as in relativity. The condition on the phase velocity is most noticeable when p≪mc. Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for vp = νλ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if vp is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy;h = Planck’s constant;ν = frequency;ω = angular momentum;p = momentum;λ = wavelength;k = wave vector;c = speed of light;m = particle rest mass;vp = phase velocity;vg = group velocity].

Ultrasonic Pulse Signal Resonance Features in Layered CFRP Within Voids

The ultrasonic pulse signal resonance features in layered carbon fiber reinforced plastic（CFRP） within voids were researched. The frequency domain model of acoustic wave propagation in multilayered medium was established. Then the reflection coefficient of multilayered CFRP within voids was numerically calculated. The results are as follows. When the CFRP laminate is tested by ultrasonic whose center frequency is close to the CFRP inherent resonant frequency, the ultrasonic may generate resonance phenomenon in CFRP. If CFRP contains evenly distributed voids, the frequency of resonant signal and its amplitude all decrease with the increase of porosity. For the thick section CFRP within local concentrated voids, the local concentrated voids near testing surface will cause signal frequency reduction and the decrease of its amplitude. But the voids which exist in layers far away from testing surface almost have no influence on signal resonance. The ultrasonic pulse echo testing was conducted for thick section CFRP specimen. The analysis results of testing signals were in accordance with the results of the numerical calculation, showing that the reflection coefficient frequency response model can effectively explain the ultrasonic resonance phenomenon in layered CFRP within voids.

Harmony Is Cause—Not Consequence—Of the Quantum

Einstein claimed Bohr’s theory is incomplete: “the wave function does not provide a complete description of the physical reality” [1]. Their views represent two physics in schism [2] [3]. Quanta are fundamental. The theory of diffraction in quasicrystals, that is summarized here, is falsifiable and verified. The quanta are not only harmonic;but harmonic in dual series: geometric and linear. Many have believed the quantum is real;rather than conceptual and axiomatic. The quasicrystal proves its reality.

Physical Quanta in Quasicrystal Diffraction

Diffraction in quasicrystals is in irrational and geometric series with icosahedral point group symmetry. None of these features are allowed in Bragg diffraction, so a special theory is required. By means of a hierarchic model, the present work displays exact agreement between an analytic metric, with a numeric description of diffraction in quasicrystals—one that is founded on quasi-structure-factors that are completely indexed in 3-dimensions. At the quasi-Bragg condition, the steady state wave function of incident radiation is used to show how resonant response, in metrical space and time, enables coherent interaction between the periodic wave packet and hierarchic quasicrystal. The quasi-Bloch wave is invariant about all translations , where is the quasi-lattice parameter. This is numerically derived, analyzed, measured, verified and complete. The hierarchic model is mapped in reverse density contrast, and matches the pattern and dimensions of phase-contrast, optimum-defocus images. Four tiers in the hierarchy of icosahedra are confirmed, along with randomization of higher order patterns when the specimen foil is oriented only degrees off the horizontal. This explains why images have been falsely described as having “no translational symmetry”.

Modified Lindstedt-Poincaré Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.

Real Quanta and Continuous Reduction

Previous theories of quasicrystal diffraction have called it “Bragg diffraction in Fibonacci sequence and 6 dimensions”. This is a misnomer, because quasicrystal diffraction is not in integral linear order n where nλ= 2dsin(θ) as in all crystal diffraction;but in irrational, geometric series τm, that are now properly indexed, simulated and verified in 3 dimensions. The diffraction is due not to mathematical axiom, but to the physical property of dual harmony of the probe, scattering on the hierarchic structure in the scattering solid. By applying this property to the postulates of quantum theory, it emerges that the 3rd postulate (continuous and definite) contradicts the 4th (instantaneous and indefinite). The latter also contradicts Heisenberg’s “limit”. In fact, the implied postulates of probability amplitude describe hidden variables that are universally recognized, in all sensitive measurement, by records of error bars. The hidden variables include momentum quanta, in quasicrystal diffraction, that are continuous and definite. A revision of the 4th postulate is proposed.

Specific metabolic impairments indicate loss of sustained liver improvements in metabolic dysfunction-associated steatotic liver disease treatment

Background:High liver fat content(LFC)induces increased risks of both hepatic and extrahepatic progression in metabolic dysfunction-associated steatotic liver disease(MASLD),while maintaining a significant decline in magnetic resonance imaging-based proton density fat fraction(MRI-PDFF)(≥30%decline relative to baseline)without worsening fibrosis results in improved histological severity and prognosis.However,the factors associated with the loss of sustained responses to treatment remain unclear,and we aim to identify them.Methods:Consecutive treatment-naïve MASLD patients between January 2015 and February 2022,with follow-up until April 2023,were included in this prospective cohort study.LFC quantified by MRI-PDFF and liver stiffness measurements(LSM)determined by two-dimensional shear wave elastography(2D-SWE)were evaluated at weeks 0,24 and 48.MRI-PDFF response was defined as a≥30%relative decline in PDFF values,and LSM response was defined as a≥1 stage decline from baseline.Results:A total of 602 MASLD patients were enrolled.Of the 303 patients with a 24-week MRI-PDFF response and complete follow-up of 48 weeks,the rate of loss of MRI-PDFF response was 29.4%,and multivariable logistic regression analyses showed that 24-week insulin resistance(IR),still regular exercise and caloric restriction after 24 weeks,and the relative decline in LFC were risk factors for loss of MRI-PDFF response.Loss of LSM response at 48 weeks occurred in 15.9%of patients,and multivariable analysis confirmed 24-week serum total bile acid(TBA)levels and the relative decline in TBA from baseline as independent predictors.No significant association was found at 48 weeks between loss of MRI-PDFF response and loss of LSM response.Conclusions:MASLD patients with IR and high TBA levels are at higher risks of subsequent diminished sustained improvements of steatosis and fibrosis,respectively.

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωPg respectively. In the case of ωe?ωg, the PEMFs are manifested as the EM wave beams with frequency ωe and a standing EM wave with ωg. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ωg?ωe, all PEMFs are expressed as the standing EM waves with frequency ωg. The resonant response occurs in two cases of ωe = 1/2 ωg andωe, = ωg only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10-33 - 10-35 and λg = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.

Relationship between local damage and structural dynamic behavior

Damage in the structures alters the structural dynamic behavior. Damage generally occurs locally in the components of structures, and its effect often exhibits in the changes of both local and global characteristics of structures. Better understanding of this relationship helps to monitor and assess the condition of structures and develop dynamics-based structural health monitoring techniques. In this study, the relationship between the local damage and structural dynamic behavior is investigated. To validate the concept, an experiment of a three-dimensional (3-D) steel frame structure with different magnitudes of local damage is illustrated. The experimental results indicate that the change of global resonant response between the intact and damage structure is not obvious. The change of local resonant responses measured near the location of saw-cut crack damage is quite significant. The experimental study conducted indicates that the local resonant responses at the low order resonance can be used as an effective damage identification method to detect and quantify the local damage in the 3D frame structures.

Structural topology optimization on sound radiation at resonance frequencies in thermal environments

Thermal and acoustic environments pose severe challenges to find optimal design that exhibits ideal acoustic characteristics the structural design of hypersonic vehicles. One of them is to in a frequency band, which is discussed in this paper through topology optimization aiming at resonance sound radiation in thermal environments. The sound radiation at resonance fre- quencies is the main component of response, minimization on which is likely to provide a satisfactory design. A bi-material plate subjected to uniform temperature rise and excited by harmonic loading is studied here. Thermal stress is first evaluated and considered as prestress in the following dynamic analysis; radiated sound power is then calculated through Rayleigh inte- gral. Sensitivity analysis is carried out through adjoint method considering the complicated relationship between stress-induced geometric stiffness and design variables. As the resonance frequency is constantly changing during the optimization, its sensi- tivity should be considered. It is also noticed that mode switching may occur, so mode tracking technique is employed in this work. Some numerical examples are finally discussed.

Versatile nanocomposite augments high-intensity focused ultrasound for high-efficacy sonodynamic therapy of glioma

High-intensity focused ultrasound(HIFU),with inherent advantages of improved ultrasonic depth and low off-target damage,holds the promising capability for glioma treatment,but the relatively long therapeutic time and potential physical complications may hamper its clinical application.Herein,a bovine serum albumin(BSA)-based nanoplatform with in situ growth of MnO_(2) was synthesized,and Protoporphyrin IX(PpIX)was further anchored to obtain a versatile PpIX@MnO_(2)@BSA nanoplatform(denoted as BMP).By employing HIFU as the exogenous irradiation source,a high-efficacy sonodynamic therapy(SDT)is developed,in which the excited BMP enables the production of tumoricidal reactive oxygen species(ROS).The inherent tumor microenvironment(TME)-responsive property of MnO_(2) endows BMP with specific T1-weighted magnetic resonance imaging(MRI)by releasing Mn2+,and the simultaneously generated O_(2) facilitates hypoxia alleviation as well as ^(1)O_(2) generation.Compared with HIFU therapy alone,suppression of glioma growth and improved survival benefits are achieved through the designed TMEresponsive nanocomposite under HIFU exposure.The high-efficacy SDT strategy combining BMP and HIFU demonstrated favorable TME-responsive T1-weighted MRI,hypoxic environment alleviation,and anti-tumor capability,providing a perspective paradigm for MRI-guided glioma treatment.