Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method(DEM)modelling.The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions.A side wall node loading method is used to exert bi-directional shear of various angles.The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials.However,the relationship between bidirectional shear and mechanical responses relies on loading conditions,i.e.constant vertical stress or constant volume conditions.The stress states induced by static shear consolidation are affected by loading angles,which are enlarged by subsequent shear,consistent with the relationship between bidirectional shear and principal stresses.It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials.The presence of bi-directional principal stress rotation(PSR)is demonstrated,which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction.Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts,but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts.It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions.Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined,providing further insights into understanding granular behaviour under bi-directional shear.

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.

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.

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.

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.

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.

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.

Predicting High Precision Hubble Constant Determinations Based on a New Theoretical Relationship between CMB Temperature and H0

Based on considerable progress made in understanding the Cosmic Microwave Background (CMB) temperature from a deep theoretical perspective, this paper demonstrates a useful and simple relationship between the CMB temperature and the Hubble constant. This allows us to predict the Hubble constant with much higher precision than before by using the CMB temperature. This is of great importance, since it will lead to much higher precision in various global parameters of the cosmos, such as the Hubble radius and the age of the universe. We have improved uncertainty in the Hubble constant all the way down to 66.8712 ± 0.0019 km/s/Mpc based on data from one of the most recent CMB studies. Previous studies based on other methods have rarely reported an uncertainty much less than approximately ±1 km/s/Mpc for the Hubble constant. Our deeper understanding of the CMB and its relation to H0seems to be opening a new era of high-precision cosmology, which may well be the key to solving the Hubble tension, as alluded to herein. Naturally, our results should also be scrutinized by other researchers over time, but we believe that, even at this stage, this deeper understanding of the CMB deserves attention from the research community.

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.

The Gravitational Constant as the Function of the Cosmic Scale

This paper uses the cosmic evolution picture constructed by the principal and associated fiber bundles and, with the help of gauge invariance, systematically proposes the γfactor theory that the Newton’s law of universal gravitation and the cosmological constant of Einstein’s equation must be corrected in the large-scale space-time structure of the universe. That is, it is found that the calculated value of Newton’s universal gravitation in space-time above the scale of galaxies must be multiplied by 1/γto be consistent with the measured value, and the cosmological constant of Einstein’s equation is no longer a constant but a function that increases with the increase of the scale of cosmic regions. Therefore, the cyclic hypothesis of cosmic evolution is proposed, and it is further found that the gravitational constant that people think is natural is not a constant but a function that changes with the scale of cosmic regions. Therefore, the reason for the dark matter and dark energy hypothesis may be that the gravitational constant is a variable. The existence of actual dark matter and dark energy may be just an illusory hypothesis, and their origin comes from the understanding that the gravitational constant is constant.

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.

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.

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.

Rail-to-rail op-amp with constant transconductance,SR and gain

A novel general-purpose low-voltage rail-to-rail CMOS （ complementary metal-oxide-semiconductor transistor ） operational amplifier （op-amp）is introduced, which obtains constant transconductance, slew rate and constant high gain over the entire input common mode voltage range. The proposed scheme has the potential for applications in deep submicrometer technology, as the operation of the circuit does not exclusively rely on the square-law or the linear-law of transistors. The scheme is compact and suitable for applications as VLSI cell. The rail-to- rail op-amp has been implemented in DPDM 0. 6 μm mixedsignal process. The simulations show that in the entire range of input common mode voltage, the variations in transconductance, SR and gain are 1%, 2. 3%, 1.36 dB, respectively. Based on this, the layout and tape-out are carded out. The area of layout is 0. 072 mm^2. The test results are basically consistent with the circuit simulation.

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.

Numerical simulation of rockburst disaster and control strategy of constant resistance and large deformation anchor cable in Gaoloushan tunnel

The Gaoloushan Tunnel in Longnan City,Gansu Province,China,frequently experiences rockburst disasters due to high in-situ stress.Managing rockburst in deep-buried tunnels remains a challenging issue.This paper employs RFPA(Rock Failure Process Analysis)software to establish a calculation model of constant resistance and large deformation(CRLD)anchorages and analyzes the effects of different support methods and pre-stress levels on rockburst.We simulate the process of tunnel rockburst disasters and find that ordinary anchor support incurs rockburst on the right arch waist and arch top,forming a V-shaped explosion pit.CRLD anchor support has several advantages in rockburst control,such as more uniform stress distribution in the surrounding rock,a uniform distribution of plastic zones,less noticeable damage to the tunnel,and effective control of the arch top displacement.The effectiveness of the CRLD anchor support under varying pre-stress conditions shows that a higher prestress results in a smaller plastic zone of the surrounding rock and arch top displacement and a lower number of acoustic emission signals,which better explains the excavation compensation effect.Moreover,adding long anchorages in the deep surrounding rock area can better control rockburst and reduce surrounding rock deformation.Based on these findings,we propose a comprehensive control system that combines long and short anchorages and provides the optimal scheme based on calculations.Therefore,by using high-prestress CRLD anchor support and the combination of long and short anchorages at critical positions,we can enhance the integrity of the surrounding rock,effectively absorb the energy released by the surrounding rock deformation,and reduce the incidence of rockburst disasters.

CONSTANT DISTANCE BOUNDARIES OF THE t-QUASICIRCLE AND THE KOCH SNOWFLAKE CURVE

LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, Γ_(λ) is a Jordan curve whenζ=1/2 and Γ_(λ) is a quasicircle when 0<ζ<1/2.We introduce the(ζ,r_(0),t)-chordal property,which generalizes the(ζ,r_(0))-chordal property,and we show that under the condition thatΓis(ζ,r_(0),√t)-chordal with 0<ζ<r_(0)^(1−√t)/2,there existsε>0 such that Γ_(λ) is a t-quasicircle once Γ_(λ) is a Jordan curve when 0<λ<ε.In the last part of this paper,we provide an example:Γis a kind of Koch snowflake curve which does not have the(ζ,r_(0))-chordal property for any 0<ζ<1/2,however Γ_(λ) is a Jordan curve whenλis small enough.Meanwhile,Γhas the(ζ,r_(0),√t)-chordal property with 0<ζ<r_(0)^(1−√t)/2 for any t∈(0,1/4).As a corollary of our main theorem, Γ_(λ) is a t-quasicircle for all 0<t<1/4 whenλis small enough.This means that our(ζ,r_(0),t)-chordal property is more general and applicable to more complicated curves.

LOCAL BIFURCATION OF STEADY ALMOST PERIODIC WATER WAVES WITH CONSTANT VORTICITY

In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal direction.Using conformal mappings,one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition.By virtue of the Hilbert transform,the problem is equivalent to a quasilinear pseudodifferential equation for an almost periodic function of one variable.The bifurcation theory ensures that we can obtain an existence result.Our existence result generalizes and covers the recent result in[15].Moreover,our result implies a non-uniqueness result at the same bifurcation point.

Experimental Studies on Cyclic Shear Behavior of Steel-Clay Interface Under Constant Normal Load

The degradation of the shear stress between pile-clay interface caused by undrained cyclic jacking affects the jacking force.A series of large displacement monotonic shear,cyclic shear and post-cyclic monotonic steel plate-clay interface shear te sts were performed under the constant normal load(CNL)condition to inve stigate the effects of normal stre ss,cyclic amplitude,and number of cycles on a steel plate-clay interface using the GDS multi-function interface shear tester.Based on the experimental results,in monotonic shear tests,change of shear stress took place in the specimen,the shear stress rapidly reached the peak value at shear displacement of 1 mm,and then abruptly decreased to the residual value.In cyclic shear te sts,accumulated displacement was a better parameter to describe the soil degradation characteristics,and the degradation degree of shear stress became greater with the increasing of normal stress and accumulated displacement.Shear stress in post-cyclic monotonic shear tests did not generate a peak value and was lower than that in monotonic shear tests under the same normal stress.The soil was completely disturbed and reached the residual strength when the cumulative displacement approached 6 m.An empirical equation to evaluate shear stress degradation mechanism was formulated and the procedure of parameter identification was presented.

An Experimental Study on Constant Current Load Test of Reinforced Concrete based on 3D Paraffin Isolation

Aiming at the complex corrosion degradation factors of reinforced concrete and clearing the deterioration mechanism in the constant stress state,a new type of constant current accelerated corrosion method in the saline soil environment was developed.The three-dimensional paraffin isolation specimens and the three-dimensional penetration specimens were taken as the research objects,and the Cl−content and AC impedance Bode diagram were measured.The macro morphology and micro analysis were also used to evaluate the corrosion degradation laws of the two groups of specimens.A constant current three-factor system accelerated model was established for the current acceleration factor,chloride ion,and sulfate ion acceleration factor.The experimental results show that,in the constant stress test of the saline soil environmental conditions,the paraffin isolation layer can effectively isolate corrosive chloride ions,which is a brand-new research method of single factor variable control in the constant stress test.According to the basic corrosion data,the law of constant current acceleration test is summarized and divided into five corrosion degradation stages,and each stage has significant changes in the accelerated corrosion efficiency.The corrosion degradation of a constant stress test is the combined effect of constant current,positive and negative penetration of chloride ions and sulfate ions.