ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.

Probing the electric double layer structure at nitrogen-doped graphite electrodes by constant-potential molecular dynamics simulations

Electric double layer(EDL)is a critical topic in electrochemistry and largely determines the working performance of lithium batteries.However,atomic insights into the EDL structures on heteroatom-modified graphite anodes and EDL evolution with electrode potential are very lacking.Herein,a constant-potential molecular dynamics(CPMD)method is proposed to probe the EDL structure under working conditions,taking N-doped graphite electrodes and carbonate electrolytes as an example.An interface model was developed,incorporating the electrode potential and atom electronegativities.As a result,an insightful atomic scenario for the EDL structure under varied electrode potentials has been established,which unveils the important role of doping sites in regulating both the EDL structures and the following electrochemical reactions at the atomic level.Specifically,the negatively charged N atoms repel the anions and adsorb Li~+at high and low potentials,respectively.Such preferential adsorption suggests that Ndoped graphite can promote Li~+desolvation and regulate the location of Li~+deposition.This CPMD method not only unveils the mysterious function of N-doping from the viewpoint of EDL at the atomic level but also applies to probe the interfacial structure on other complicated electrodes.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.

Elementary Fermions: Strings, Planck Constant, Preons and Hypergluons

Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism which is proportional to Planck’s constant. This may be the result of two massless bosons (hypergluons) coupled by a preon (prequark) exchange. It also gives a physical explanation to the origin of the Planck constant, and origin of spin.

Study of the Physical and Mechanical Properties of Titanium in Volume by the MEAM Method

In this work we present the results of our study on the physical and mechanical properties of titanium in volume. The work consisted in determining its physical and mechanical properties under different crystallographic structures (HCP, FCC, BCC and SC) using the Modified Embedded Atom Method (MEAM) and the MEAM potential of titanium. We used the LAMMPS calculation code, based on classical molecular dynamics, to determine the most stable structure of titanium, which is the hexagonal compact structure (HCP) with crystal parameters a = 2.952 Å and c = 4.821 Å and a cohesion energy of -4.87 eV. This structure is seconded by the cubic centred structure (BCC) with a lattice parameter a = 3.274 Å and a cohesive energy of -4.84 eV. It was shown that titanium can crystallise into a third structure which is the face-centred cubic (FCC) structure with a lattice parameter a = 4.143 Å and a cohesive energy of -4.82 eV. The results obtained in this study were compared with the theoretical results and showed considerable agreement.

Gedankenexperiment for Modified ZPE and Planck’s “Constant”, h, in the Beginning of Cosmological Expansion, Partly Due to NLED

We initially look at a non singular universe representation of entropy, based in part on what was brought up by Muller and Lousto. This is a gateway to bringing up information and computational steps (as defined by Seth Lloyd) as to what would be available initially due to a modified ZPE formalism. The ZPE formalism is modified as due to Matt Visser’s alternation of k (maximum) ~ 1/(Planck length), with a specific initial density giving rise to initial information content which may permit fixing the initial Planck’s constant, h, which is pivotal to the setting of physical law. The settings of these parameters depend upon NLED.

The Extremal Universe Exact Solution from Einstein’s Field Equation Gives the Cosmological Constant Directly

Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

New Approach to Synchronize General Relativity and Quantum Mechanics with Constant “K”-Resulting Dark Matter as a New Fundamental Force Particle

Planck scale plays a vital role in describing fundamental forces. Space time describes strength of fundamental force. In this paper, Einstein’s general relativity equation has been described in terms of contraction and expansion forces of space time. According to this, the space time with Planck diameter is a flat space time. This is the only diameter of space time that can be used as signal transformation in special relativity. This space time diameter defines the fundamental force which belongs to that space time. In quantum mechanics, this space time diameter is only the quantum of space which belongs to that particular fundamental force. Einstein’s general relativity equation and Planck parameters of quantum mechanics have been written in terms of equations containing a constant “K”, thus found a new equation for transformation of general relativity space time in to quantum space time. In this process of synchronization, there is a possibility of a new fundamental force between electromagnetic and gravitational forces with Planck length as its space time diameter. It is proposed that dark matter is that fundamental force carrying particle. By grand unification equation with space-time diameter, we found a coupling constant as per standard model “αs” for that fundamental force is 1.08 × 10-23. Its energy calculated as 113 MeV. A group of experimental scientists reported the energy of dark matter particle as 17 MeV. Thorough review may advance science further.

Upsilon Constants and Their Usefulness in Planck Scale Quantum Cosmology

This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.

The Planck Constant and Its Relation to the Compton Frequency

The Planck constant is considered one of the most important universal constants of physics, and despite all we know much about it, the physical nature of it has not been fully understood. Further investigation and new perspectives on the Planck constant should therefore be of interest. We demonstrate that the Planck constant also can be directly linked to the Compton frequency of one, which again is divided by the Compton frequency in one kg. If this is right, it means also the Planck constant is linked to quantization of matter, not only energy. However, as we will show the frequency of one when expressed in relation to kg will be observational time dependent. This means the missing mass gap surprisingly both is equal to the Planck mass, which is larger than any known particle and also it is linked to a very small mass that again is equal to what has been suggested as the photon mass in the existing literature. This new view could be an important step forward in understanding the physical nature of the Planck constant as well as the mass gap and even the rest mass of a photon.

Introducing a 2nd Universal Space-Time Constant Can Explain the Observed Age of the Universe and Dark Energy

The purpose of this paper is to introduce new theoretical concepts as opposed to accepting the existence of dark entities, such as dark energy. This research sought to introduce a 2nd universal space-time constant, besides having a finite speed constant (speed of light in vacuum c). A finite universal age constant b is introduced. Namely, this paper shows that the changes in the Earth’s anomalistic year duration over time support the hypothesis of the age of the universe correlating with a maximum number of orbital revolutions constant. Neglecting the gravitational influence of other cosmological entities in the proximity of the Earth, the constant maximum number of revolutions is herewith determined solely by the Earth’s orbital revolutions around the Sun. The value of the universal age constant b is calculated to be around 13.8 billion orbital revolutions, derived out of an equation related to the changes in the Earth’s anomalistic year duration over time and the so-called Hubble tension. The above-mentioned calculated value b correlates well with the best fit to measured data of the cosmic microwave background radiation (CMBR) by the Planck spacecraft, the age of the observed universe is measured to be approximately 13.787 ± 0.020 billion years (2018 final data release). Developing a theory with this 2nd universal space-time constant b, being covariant with respect to the Lorentz transformations when time spans are large, gives results such as: A confirmation of the measured CMBR value of 13.787 ± 0.020 billion years. Correlating well with the observed expansion rate of the universe (dark energy). The universe’s expansion accelerating over the last four to five billion years.

A Number Theoretic Analysis of the Enthalpy, Enthalpy Energy Density, Thermodynamic Volume, and the Equation of State of a Modified White Hole, and the Implications to the Quantum Vacuum Spacetime, Matter Creation and the Planck Frequency

In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.

A Solution to the Cosmological Constant Problem Using the Holographic Principle (A Brief Note)

This paper integrates a quantum conception of the Planck epoch early universe with FSC model formulae and the holographic principle, to offer a reasonable explanation and solution of the cosmological constant problem. Such a solution does not appear to be achievable in cosmological models which do not integrate black hole formulae with quantum formulae such as the Stephan-Boltzmann law. As demonstrated herein, assuming a constant value of Lambda over the great span of cosmic time appears to have been a mistake. It appears that Einstein’s assumption of a constant, in terms of vacuum energy density, was not only a mistake for a statically-balanced universe, but also a mistake for a dynamically-expanding universe.

Robust Nonlinear Current Sensorless Control of the Boost Converter with Constant Power Load

The boost converter feeding a constant power load (CPL) is a non-minimum phase system that is prone to the destabilizing effects of the negative incremental resistance of the CPL and presents a major challenge in the design of stabilizing controllers. A PWM-based current-sensorless robust sliding mode controller is developed that requires only the measurement of the output voltage. An extended state observer is developed to estimate a lumped uncertainty signal that comprises the uncertain load power and the input voltage, the converter parasitics, the component uncertainties and the estimation of the derivative of the output voltage needed in the implementation of the controller. A linear sliding surface is used to derive the controller, which is simple in its design and yet exhibits excellent features in terms of robustness to external disturbances, parameter uncertainties, and parasitics despite the absence of the inductor’s current feedback. The robustness of the controller is validated by computer simulations.

Stoichiometry and Stability Constant Values for Copper (II) Chelates with Ethylene Diamine in Deep Eutectic Solvents (DES) (Ethaline) Solutions

In this study we used the deep eutectic solvents (ionic liquids) to investigate the reaction between copper (II) with ethylene diamine (en). Two of the existing methods for analyzing spectrophotometric measurements have been applied for establishing, the stoichiometry and whenever possible, the stability constants of the chelates formed. The method of continuous variations was necessary to determine first whether, the metal ion and the ligand ethylene diamine form one or more than one chelate, when more than one chelate formed, the results obtained depend on the wavelength and for meaningful conclusions the wavelengths were carefully selected. The empirical formulae of the chelates were further substantiated by the molar ratio method. The effect of time and temperature on the formation and stability of these chelates in solution is also studied. The stability constants, K1 and K2 for the copper (II) chelates were calculated, though reliable, and are comparable to literature values.

Comparison of undrained behaviors of granular media using fluidcoupled discrete element method and constant volume method

The fluid-coupled discrete element method(DEM)and the constant volume method as two types of discrete modeling methods for fundamental study of undrained responses of granular materials,have been discussed by many researchers.The fluid-coupled DEM,which couples the motions of discrete particles with pore fluid movements,is theoretically robust although it requires a large amount of computation time.As a substitution for the complex fluid-coupled DEM,the constant volume method simulates an undrained condition for a saturated granular material by simply preserving the total volume of a granular assembly without considering interactions between fluids and particles;hence,the validity of its results is questionable.In this paper,the undrained behaviors of granular assemblies simulated using the aforementioned two methods are compared.Based on a comparison of both macroscopic and microscopic responses given by the two methods,it is demonstrated that the constant volume method may reasonably simulate the responses of a loose saturated granular material with very coarse grains,which has a high permeability,and thus a rapid pore pressure equalization.However,it is ineffective in simulating the responses of a loose material with fine components due to its failure to capture the process of a slow dissipation of the excess pore pressure among the individual pores.With regard to the dense material adopted,similar behaviors at the early and intermediate shearing stages given by the two methods are displayed.

Sliding modes of fault activation under constant normal stiffness conditions

Fault activation has been the focus of research community for years.However,the studies of fault activation remain immature,such as the fault activation mode and its major factors under constant normal stiffness(CNS)conditions associated with large thickness of fault surrounding rock mass.In this study,the rock friction experiments were conducted to understand the fault activation modes under the CNS conditions.Two major parameters,i.e.the initial normal stress and loading rate,were considered and calibrated in the tests.To reveal the response mechanism of fault activation,the local strains near the fault plane were recorded,and the macroscopic stresses and displacements were analyzed.The testing results show that the effect of displacement-controlled loading rate is more pronounced under the CNS conditions than that under constant normal load(CNL)conditions.Both the normal and shear stresses drop suddenly when the stick-slip occurs.The decrease and increase of the normal stress are synchronous with the shear stress in the regular stick-slip scenario,but mismatch with the shear stress during the chaotic stick-slip process.The results are helpful for understanding the fault sliding mode and the prediction and prevention of fault slip.

An improved constant volume cycle model for performance analysis and shape design of PDRE nozzle

An improved constant volume cycle （CVC） model is developed to analyze the nozzle effects on the thrust and specific impulse of pulse detonation rocket engine （PDRE）. Theoretically, this model shows that the thrust coefficient/specific impulse of PDRE is a function of the nozzle contraction/expansion ratio and the operating frequency. The relationship between the nozzle contraction ratio and the operation frequency is obtained by introducing the duty ratio, by which the key problem in the theoretical design can be solved. Therefore, the performance of PDRE can be accessed to guide the preliminary shape design of nozzle conveniently and quickly. The higher the operating frequency of PDRE is, the smaller the nozzle contraction ratio should be. Besides, the lower the ambient pressure is, the larger the expansion ratio of the nozzle should be. When the ambient pressure is 1.013 × 105 Pa, the optimal expansion ratio will be less than 2.26. When the ambient pressure is reduced to vacuum, the extremum of the optimal thrust coefficient is 2.236 9, and the extremum of the specific impulse is 321.01 s. The results of the improved model are verified by numerical simulation.

Quantization Heat Capacity Equations at Constant Volume According to Energy Levels and Planck Constant

The quantization thermal excitation isotherms based on the maximum triad spin number (G) of each energy level for metal cluster were derived as a function of temperature by expanding the binomial theorems according to energy levels. From them the quantized geometric mean heat capacity equations are expressed in sequence. Among them the five quantized geometric heat capacity equations, fit the best to the experimental heat capacity data of metal atoms at constant pressure. In the derivations we assume that the triad spin composed of an electron, its proton and its neutron in a metal cluster become a basic unit of thermal excitation. Boltzmann constant (kB) is found to be an average specific heat of an energy level in a metal cluster. And then the constant (kK) is found to be an average specific heat of a photon in a metal cluster. The core triad spin made of free neutrons may exist as the second one additional energy level. The energy levels are grouped according to the forms of four spins throughout two axes. Planck constant is theoretically obtained with the ratio of the internal energy of metal (U) to total isotherm number (N) through Equipartition theorem.