scholarly journals Pair production and gravity as the weakest force

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Eduardo Gonzalo ◽  
Luis E. Ibáñez
Keyword(s):  
Pair Production ◽  
Relative Strength ◽  
Alternative Formulation ◽  
Long Distance ◽  
Pair Annihilation ◽  
Second Derivatives ◽  
The Stability ◽  
Bps States ◽  
Derivatives Of ◽  
Extremal Black Holes

Abstract The Weak Gravity Conjecture (WGC) is usually formulated in terms of the stability of extremal black-holes or in terms of long distance Coulomb/Newton potentials. However one can think of other physical processes to compare the relative strength of gravity versus other forces. We argue for an alternative formulation in terms of particle pair production at threshold or, equivalently, pair annihilation at rest. Imposing that the production rate by any force mediator (photon or scalar) of pairs of charged particles be larger or equal to graviton production, we recover known conditions for the U(1) WGC and its extensions. Unlike other formulations though, threshold pair production is sensitive to short range couplings present in scalar interactions and gives rise to a Scalar WGC. Application to moduli scalars gives rise to specific conditions on the trilinear and quartic couplings which involve first and second derivatives of the WGC particle mass with respect to the moduli. Some solutions saturating equations correspond to massive states behaving like BPS, KK and winding states which feature duality invariance and are in agreement with the Swampland distance conjecture. Conditions for N = 2 BPS states saturate our bounds and we discuss specific examples of BPS states which become massless at large Kahler moduli in Type IIA N=2, D=4 CY and orbifold compactifications. We study possible implications for potentials depending on moduli only through WGC massive states. For some simple classes of potentials one recovers constraints somewhat similar but not equivalent to a Swampland dS conjecture.

scholarly journals Advanced analysis in epidemiological modeling: Detection of wave

2021 ◽  
Author(s):  
Abdon Atangana ◽  
Seda IGRET ARAZ
Keyword(s):  
Simple Model ◽  
Reproductive Number ◽  
Second Derivative ◽  
Mathematical Concepts ◽  
Epidemiological Modeling ◽  
Derivative Analysis ◽  
Second Derivatives ◽  
Advanced Analysis ◽  
The Stability ◽  
Derivatives Of

Some mathematical concepts have been used in the last decades to predict the behavior of spread of infectious diseases. Among them, the reproductive number concept has been used in several published papers for study the stability of the spread. Some conditions were suggested to predict there would be either stability or instability. An analysis was also suggested to determine conditions under which infectious classes will increase or die out. Some authors pointed out limitations of the reproductive number, as they presented its inability to fairly help understand the spread patterns. The concept of strength number and analysis of second derivatives of the mathematical models were suggested as additional tools to help detect waves. In this paper, we aim at applying these additional analyses in a simple model to predict the future. Keywords: Strength number, second derivative analysis, waves, piecewise modeling.

Time-Dependent Ginzburg-Landau Equation in Car Following Model Considering the Traffic Interruption Probability

2012 ◽  
Vol 198-199 ◽  
pp. 843-847
Author(s):  
Yi Qiang Zhang ◽  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Landau Equation ◽  
Reductive Perturbation Method ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Car Following ◽  
Second Derivatives ◽  
Spinodal Line ◽  
Car Following Model ◽  
The Stability ◽  
Derivatives Of

This paper focuses on a car-following model which involves the effects of traffic interruption probability. The stability condition of the model is obtained through the linear stability analysis. The time-dependent Ginzburg-Landau (TDGL) equation is derived by the reductive perturbation method. In addition, the coexisting curve and the spinodal line are obtained by the first and second derivatives of the thermodynamic potential. The analytical results show that the traffic interruption probability indeed has an influence on driving behaviour.

Quintessence compact stars satisfying Karmarkar condition

2019 ◽  
Vol 97 (4) ◽  
pp. 374-381 ◽  
Author(s):  
G. Abbas ◽  
Shahid Qaisar ◽  
Wajiha Javed ◽  
W. Ibrahim
Keyword(s):  
Radial Pressure ◽  
Compact Stars ◽  
Field Equations ◽  
Anisotropic Parameter ◽  
Proposed Model ◽  
Second Derivatives ◽  
Metric Functions ◽  
The Stability ◽  
Quintessence Field ◽  
Derivatives Of

In this research article, the authors have presented the modelling of quintessence compact stars, which satisfies the Karmarkar conditions. For this purpose, we have formulated the set of Einstein field equations with the static metric, anisotropic perfect fluid, and quintessence field. The equation of state pr= αρ and Karmarkar condition have been used to solve the set of field equations. The unknown constant in the metric functions (appearing due to the Karmarkar conditions) have been found by matching the interior metric with the Schwarzschild exterior metric. The observed value of mass and radius of some well-known classes of stars has been used. The fluid variables density, radial and transverse pressures, and anisotropic parameter have been plotted graphically. The first and second derivatives of density and radial pressure have been evaluated to discuss the regularity of the model. The speed of sound for the radial and transverse directions determines the stability of the proposed model. Moreover, the redshift for the proposed model of the star has been discussed.

THE TDGL EQUATION FOR CAR-FOLLOWING MODEL WITH CONSIDERATION OF THE TRAFFIC INTERRUPTION PROBABILITY

2012 ◽  
Vol 23 (07) ◽  
pp. 1250053 ◽  
Author(s):  
HONG-XIA GE ◽  
YI-QIANG ZHANG ◽  
HUA KUANG ◽  
SIU-MING LO
Keyword(s):  
Traffic Flow ◽  
Reductive Perturbation Method ◽  
Ginzburg Landau ◽  
Car Following ◽  
Second Derivatives ◽  
Spinodal Line ◽  
Car Following Model ◽  
Tdgl Equation ◽  
The Stability ◽  
Derivatives Of

A car-following model which involves the effects of traffic interruption probability is further investigated. The stability condition of the model is obtained through the linear stability analysis. The reductive perturbation method is taken to derive the time-dependent Ginzburg–Landau (TDGL) equation to describe the traffic flow near the critical point. Moreover, the coexisting curve and the spinodal line are obtained by the first and second derivatives of the thermodynamic potential, respectively. The analytical results show that considering the interruption effects could further stabilize traffic flow.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

Binding of calcium and lead ions to carboxystarch prepared by action of nitrogen dioxide on native starch and its 2,3-dialdehyde derivatives

1986 ◽  
Vol 51 (6) ◽  
pp. 1340-1351 ◽  
Author(s):  
Rudolf Kohn ◽  
Karol Tihlárik
Keyword(s):  
Nitrogen Dioxide ◽  
Alkaline Medium ◽  
Binding Capacity ◽  
Lead Ions ◽  
Carbonyl Groups ◽  
Weakly Alkaline ◽  
Exchange Cations ◽  
Counter Ions ◽  
The Stability ◽  
Derivatives Of

The binding of calcium and lead ions to carboxy derivatives of starch prepared by allowing nitrogen dioxide to act on native maize starch (procedure A) and on starch 2,3-dialdehyde derivatives of degrees of oxidation DO(d.a.) ≥ 0.94 (procedure B) was studied. The carboxy group content of the samples in the H+ form was 4.6 - 12.1 mmol g-1. The effect of alkaline medium on the stability of the carboxy derivatives and on their ability to bind and exchange cations was examined. The Ca2+ → 2K+ exchange was evaluated in terms of the decrease in the electrostatic free enthalpy Δ(Gel/N)KCa, determined by alkalimetric potentiometric titrations, and the binding of Pb2+ ions was evaluated in terms of the activity of the Pb2+ counter-ions determined in suspensions of Pb salts of the carboxy derivatives by means of an ion specific electrode. The IR and CD spectra revealed that the carboxystarch preparations obtained by procedure A contained, in addition to free carboxy groups, a considerable amount of carbonyl groups. During the conversion of the latter groups to the former, even in a weakly alkaline medium, the carboxy derivatives undergo an appreciable degradation and lose, to a great extent, their ability to bind and exchange cations. Procedure B, on the other hand, leads to highly selective starch and amylose carboxy derivatives, exhibiting a small amount of carbonyl groups and featuring a relative stability towards alkaline medium; their binding capacity is as high as 12 milliequivalents of cations per g of sample.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

scholarly journals Antioxidant Network Based on Sulfonated Polyhydroxyalkanoate and Tannic Acid Derivative

2021 ◽  
Vol 8 (1) ◽  
pp. 9
Author(s):  
Laura Brelle ◽  
Estelle Renard ◽  
Valerie Langlois
Keyword(s):  
Gallic Acid ◽  
Tannic Acid ◽  
Water Soluble ◽  
Gel Formation ◽  
Ene Reaction ◽  
Inorganic Cations ◽  
Medium Chain Length ◽  
Physically Crosslinked ◽  
The Stability ◽  
Derivatives Of

A novel generation of gels based on medium chain length poly(3-hydroxyalkanoate)s, mcl-PHAs, were developed by using ionic interactions. First, water soluble mcl-PHAs containing sulfonate groups were obtained by thiol-ene reaction in the presence of sodium-3-mercapto-1-ethanesulfonate. Anionic PHAs were physically crosslinked by divalent inorganic cations Ca2+, Ba2+, Mg2+ or by ammonium derivatives of gallic acid GA-N(CH3)3+ or tannic acid TA-N(CH3)3+. The ammonium derivatives were designed through the chemical modification of gallic acid GA or tannic acid TA with glycidyl trimethyl ammonium chloride (GTMA). The results clearly demonstrated that the formation of the networks depends on the nature of the cations. A low viscoelastic network having an elastic around 40 Pa is formed in the presence of Ca2+. Although the gel formation is not possible in the presence of GA-N(CH3)3+, the mechanical properties increased in the presence of TA-N(CH3)3+ with an elastic modulus G’ around 4200 Pa. The PHOSO3−/TA-N(CH3)3+ gels having antioxidant activity, due to the presence of tannic acid, remained stable for at least 5 months. Thus, the stability of these novel networks based on PHA encourage their use in the development of active biomaterials.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

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