Primary Assumptions and Guidance Laws in Wave Mechanics

In an article written by Louis de Broglie in 1959 (30 years after the Nobel prize rewarding his foundation of Wave Mechanics), the most challenging problem raised by the Bohr, Heisenberg and Born Standard Quantum Mechanics (SQM) was pointed out in the renunciation to describe “a permanent localization in space, and therefore a well-defined trajectory” for any moving particle. This challenge is taken up in the present paper, showing that de Broglie’s Primary Assumption p=hk, predicting the wave-particle duality, does also allow to obtain from the energy-dependent form of the Schrödinger and/or Klein-Gordon equations the Guidance Laws piloting particles along well-defined trajectories. The energy-independent equations, on the other hand, may only give rise—both in SQM and in the Bohmian approach—to probabilistic descriptions, overshadowing the role of de Broglie’s matter waves in physical space.

Proposed Wave Momentum Source for Generating the 22-Year Solar Cycle

For the 22-year solar cycle oscillation there is no external time dependent source. A nonlinear oscillation, the solar cycle must be generated internally, and Babcock-Leighton models apply an artificial nonlinear source term that can simulate the observations—which leaves open the question of the actual source mechanism for the solar cycle. Addressing this question, we propose to take guidance from the wave mechanism that generates the 2-year Quasi-biennial Oscillation (QBO) in the Earth atmosphere. Upward propagating gravity waves, eastward and westward, deposit momentum to generate the observed zonal wind oscillation. On the Sun, helioseismology has provided a thorough understanding of the acoustic p-waves, which propagate down into the convective envelope guided by the increasing temperature and related propagation velocity. Near the tachocline with low turbulent viscosity, the waves propagating eastward and westward can produce an axisymmetric 22-year oscillation of the zonal flow velocities that can generate the magnetic solar dynamo. Following the Earth model, waves in opposite directions can generate in the Sun wind and magnetic field oscillations in opposite directions, the proposition of a potential solar cycle mechanism.

Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of Wave Mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum Mechanics, when Schrödinger proved that the Matrix Mechanics independently developed by Werner Heisenberg was equivalent to Wave Mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

The Dynamics of Wave-Particle Duality

Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and interference process. In the case of Wave Mechanics, de Broglie’s merging of Maupertuis’s and Fermat’s principles (see Section 3) provides, without resorting to the probability-based guidance-laws and flow-lines of the Bohmian theory, the simple law addressing particles along the Helmholtz rays of the relevant matter waves. The purpose of the present research was to derive the exact Hamiltonian ray-trajectory systems concerning, respectively, classical electromagnetic waves, non-relativistic matter waves and relativistic matter waves. We faced then, as a typical example, the numerical solution of non-relativistic wave-mechanical equation systems in a number of numerical applications, showing that each particle turns out to “dances a wave-mechanical dance” around its classical trajectory, to which it reduces when the ray-coupling is neglected. Our approach reaches the double goal of a clear insight into the mechanism of wave-particle duality and of a reasonably simple computability. We finally compared our exact dynamical approach, running as close as possible to Classical Mechanics, with the hydrodynamic Bohmian theory, based on fluid-like “guidance laws”.

Unstable Tropical Air-Sea Interaction Waves and Their Physical Mechanisms

In this paper, the tropical air-sea interaction is discussed by using a simple air-sea coupled model, in which the inertia-gravity waves are filtered off and only the equatorial Rossby waves are reserved in both the atmosphere and the ocean. There exist two kinds of air-sea interaction waves in the coupled model, that is, the high-frequency fast waves and the low-frequency slow waves. The phase speed of the fast waves is westward and the frequencies are close to those of the equatorial Rossby waves in the atmosphere. The slow waves propagate westward in the part of short wavelengths and eastward in that of long wavelengths. There exist instabilities for both the westward and eastward propagating slow waves. If the fast waves are filtered off, there is little effect on the slow waves which have great influence on the long range process in the tropical air-sea coupled system. According to the tropical air-sea interaction waves we obtain here, a possible explanation to the propagating process of ENSO events is given.

Numerical modelling of nonlinear extreme waves in presence of wind

A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are numerically generated by a piston-type wave maker, and the wind-excited pressure is introduced into dynamic boundary conditions using a pressure distribution over steep crests, as defined by Jeffreys＇ sheltering mechanism.A boundary value problem is solved by a higher-order boundary element method（HOBEM） and a mixed Eulerian-Lagrangian time marching scheme. The proposed model is validated through comparison with published experimental data from a focused wave group. The influence of wind on extreme wave properties,including maximum extreme wave crest, focal position shift, and spectrum evolution, is also studied. To consider the effects of the wind-driven currents on a wave evolution, the simulations assume a uniform current over varying water depth. The results show that wind causes weak increases in the extreme wave crest, and makes the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide a comparison to demonstrate the shifts at focal points, considering the combined effects of the winds and the wind-driven currents.

Sediment mathematical model for sand ridges and sand waves

A new theoretical model is formulated to describe internal movement mechanisms of the sand ridges and sand waves based on the momentum equation of a solid-liquid two-phase flow under a shear flow. Coupling this equation with two-dimensional shallow water equations and wave reflection-diffraction equation of mild slope, a two-dimensional coupling model is established and a validation is carried out by observed hydrogeology, tides,waves and sediment. The numerical results are compared with available observations. Satisfactory agreements are achieved. This coupling model is then applied to the Dongfang 1-1 Gas Field area to quantitatively predict the movement and evolution of submarine sand ridges and sand waves. As a result, it is found that the sand ridges and sand waves movement distance increases year by year, but the development trend is stable.

A Topological Transformation of Quantum Dynamics

In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.

Sedimentation Rate Rhythms:Evidence from Filling of the Tarim Basin,Northwest China

Variations of sedimentation rate within a basin over geologic time are a time series that can be filtered into several cyclic wave curves. Based on back-stripping and the empirical mode decomposition method, the cores from 14 wells in the Tarim Basin were selected to do filtering analysis. Four cycles or quasi-cycles （33 Ma, 64.4 Ma, 103.6 Ma, and 224 Ma） were obtained. Among these, the 33 Ma period, which was related to the internal earth activity, an external force, or a combination of the two, was the most obvious. The 64.4 Ma period corresponded to the solar system crossing the galaxy plane or the periodic melting of inner-earth material. The 103.6 Ma period was related with plate collisional tectonism around the Tarim Plate. The 224 Ma period was related to one galaxy year and may also be related to the aesthenospherical convection cycle.

Reservoir-induced landslides and risk control in Three Gorges Project on Yangtze River,China

The Three Gorges region in China was basically a geohazard-prone area prior to construction of the Three Gorges Reservoir （TGR）. After construction of the TGR, the water level was raised from 70 m to 175 m above sea level （ASL）, and annual reservoir regulation has caused a 30-m water level difference after impoundment of the TGR since September 2008. This paper first presents the spatiotemporal distribution of landslides in six periods of 175 m ASL trial impoundments from 2008 to 2014. The results show that the number of landslides sharply decreased from 273 at the initial stage to less than ten at the second stage of impoundment. Based on this, the reservoir-induced landslides in the TGR region can be roughly classified into five failure patterns, i.e. accumulation landslide, dip-slope landslide, reversed bedding landslide, rockfall, and karst breccia landslide. The accumulation landslides and dip-slope landslides account for more than 90%. Taking the Shuping accumulation landslide （a sliding mass volume of 20.7 × 106 m^3） in Zigui County and the Outang dip-slope landslide （a sliding mass volume of about 90 × 106 m^3） in Fengjie County as two typical cases, the mechanisms of reactivation of the two landslides are analyzed. The monitoring data and factor of safety （FOS） calculation show that the accumulation landslide is dominated by water level variation in the reservoir as most part of the mass body is under 175 m ASL, and the dip-slope landslide is controlled by the coupling effect of reservoir water level variation and precipitation as an extensive recharge area of rainfall from the rear and the front mass is below 175 m ASL. The characteristics of landslide-induced impulsive wave hazards after and before reservoir impoundment are studied, and the probability of occurrence of a landslide-induced impulsive wave hazard has increased in the reservoir region. Simulation results of the Ganjingzi landslide in Wushan County indicate the strong relationship between landslide-induced surge and water variation with high potential risk to shipping and residential areas. Regarding reservoir regulation in TGR when using a single index, i.e. 1-d water level variation, water resources are not well utilized, and there is also potential risk of disasters since 2008. In addition, various indices such as 1-d, 5-d, and 10-d water level variations are proposed for reservoir regulation. Finally, taking reservoir-induced landslides in June 2015 for example, the feasibility of the optimizing indices of water level variations is verified.

Effect of Microfocused Ultrasound on Facial Rejuvenation: Clinical and Histological Evaluation

Introduction: Micro focused ultrasound (MFU) is formed by mechanical waves emitted in a focused manner, concentrating thermal energy on a certain point or region, promoting a clinical improvement in wrinkles. Objective: evaluate the effects of micro focused ultrasound on facial rejuvenation. Methodology: This is an experimental study. The sample consisted of 30 volunteers, who were evaluated before treatment, 45 and 90 days after its beginning. A single application of the MFU was performed across the facial region. The parameters used were: 10 MHz cartridge with depth of 1.5 mm, 7 MHz with depth of 3 mm, and 4 MHz with focal depth of 4.5 mm;doses ranged from 0.1 to 2.0 J, according to the sensitivity of the volunteers treated, and the application time was of approximately 90 minutes. Clinical photographic analysis and facial symmetry analysis using Dolphin Imaging software were performed, and validated questionnaires. Two volunteers were submitted to blepharoplasty surgery, and one to rhytidoplasty surgery 45 days after the application of the MFU. Samples of the treated skin were taken after the surgical procedures and submitted to histological and immunohistochemical analyses. The volunteers answered a questionnaire to assess adverse reactions and satisfaction. Results: We observed a visible clinical improvement on the images by photography, and an improvement of facial symmetry in the measurements of the paralateronasal projection (p = 0.007), left lateral mandibular (p = 0.01), and right lateral mandibular (p = 0.008). The histological analysis showed an increase in the amount of fibroblasts (p = 0.02), blood vessels (p = 0.0062) and inflammatory cells (p = 0.0036), in addition to the production of type 1 collagen. In the immunohistochemical analysis, we observed the presence of the macrophage marker IHQ: CD68, indicating phagocytosis of adipose tissue and the presence of fibrosis. In the analysis of adverse reactions, only transient hyperemia was observed with the presence of pain during application. Additionally, the volunteers expressed high level of satisfaction (93%) with the treatment Conclusion: The MFU promoted the production of collagen, reorganization of the dermis and, clinically, a reduction of sagging and wrinkles, with increased facial symmetry.

What is the wave function in quantum mechanics？

Quantum mechanics,is a pillar of modern science and technology,and has benefited human society for a century.Quantum mechanics works well,its predictions agree amazingly well with experiments,and its mathematical structure is beautiful.However,the debate on the meaning of quantum mechanics has remained a hot topic to date.In the past 100 years,what most people did was‘‘Shut up and calculate',and wave functions always gave us a correct probability list of measurement outcomes.

Gamma-Ray Bursts: Afterglows and Central Engines

Gamma-ray bursts (GRBs) are the most intense transient gamma-ray events in the sky; this, together with the strong evidence (the isotropic and inhomogeneous distribution of GRBs detected by BASTE) that they are located at cosmological distances, makes them the most energetic events ever known. For example, the observed radiation energies of some GRBs are equivalent to the total convertion into radiation of the mass energy of more than one solar mass. This is thousand times stronger than the energy of a supernova explosion. Some unconventional energy mechanism and extremely high conversion efficiency for these mysterious events are required. The discovery of host galaxies and association with supernovae at cosmological distances by the recently launched satellite of BeppoSAX and ground based radio and optical telescopes in GRB afterglow provides further support to the cosmological origin of GRBs and put strong constraints on their central engine. It is the aim of this article to review the possible central engines, energy mechanisms, dynamical and spectral evolution of GRBs, especially focusing on the afterglows in multi-wavebands.

Slow Relaxation and Memory Effect in Ti_(50)Ni_(47)Fe_3 Shape Memory Alloy

The slow relaxation of resistance and memory effect in TisoNi_(47)Fe_3 shape memory alloy(SMA) are found for the first time.An evidence for CDW mechanism of incommensurate and commensurate phases in SMA was provided.

The secular effect of gravitational radiation damping on the periastronadvance of binary stars in second order perturbation theory

The second order perturbation effect of gravitational radiation damping on the periastron advance of binary stars is studied.The second order analytic solution is obtained based on the first order theory in the 2014 article by Li.Theoretical results show that secular variation exists in the periastron advance of binary stars in the second order theory,but secular variation does not exist in the first order perturbation theory.Numerical results for two compact binary stars(PSR J0737–3039 and M33 X-7)are given,demonstrating the theoretical significance even though the effect is very small.

The focal mechanism solution of the Ms6.5 Wuding earthquake in Yunnan Province of October 24,1995

The focal mechanism of Wuding earthquake with magnitude M =6.5 on October 24, 1995 is estimated by the method of inversion of seismic tensor in this paper. The two principal axes are nearly horizontal, the principal compressive axis is about N30°E, the nodal plane which strikes about N105°E (N75°W) is probably consistent with the actual rupture plane.

Dynamic Mechanical Characteristics and Damage Evolution Model of Granite

By using the technique of the split Hopkinson pressure bar（ SHPB）,impact tests at different stress wavelengths（ 0. 8-2. 0 m） and strain rates（ 20-120 s^（-1）） were conducted to study the dynamic mechanical properties and damage accumulation evolution lawof granite. Test results showthat the dynamic compressive strength and strain rate of granite have a significantly exponential correlation;the relationship between peak strain and strain rate is approximately linear,and the increase of wavelengths generally makes the level of peak strain uplift. The multiple-impacts test at a lowstrain rate indicates that at the same wavelength,the cumulative damage of granite shows an exponential increasing form with the increase of strain rate; when keeping the increase of strain rate constant and increasing the stress wavelength,the damage accumulation effect of granite is intensified and still shows an exponential increasing form; under the effect of multiple impacts,the damage development trend of granite is similar overall,but the increase rate is accelerating. Therefore the damage evolution model was established on the basis of the exponential function while the physical meaning of parameters in the model was determined. The model can reflect the effect of the wave parameters and multiple impacts. The validity of the model and the physical meaning of the parameters were verified by the test,which further offer a reference for correlational research and engineering application for the granite.

Study on generation mechanism of anomalous acoustic-gravity waves before the 2011 Beijing earthquake(M_L=3.0)

Observation results of abnormal acoustic-gravity waves before a Beijing earthquake （ML =3.0） are presented. During this period, abnormalities of earth surface tilt variations were also recorded. The cross-correlations between the both values are high, which reach maximal values of 0.5 in the area close to the epicenter. The correlations decrease with increasing distances from the epicenter. It was proposed that generation of the anomalous waves may be associated with the pressure and wind perturbations in the air flow caused by slowly shaking mountains during slow surface motion preceding the earthquake in Beijing. Based on the wind velocity data taken from a 350 m meteorological tower in Beijing, the propagation of ducted acoustic-gravity waves in a two-layer model of the atmosphere was numerically simulated. It is shown that characteristic periods, amplitudes and velocities of the simulated phases which were assumed from non-stationary air flow relative to mountains are approximate to the observed phases. A consistency between the simulated results and observation data indicates that a slow surface motion may be a possible source of the anomalous acoustic-gravity waves observed prior to the earthquake.