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siavash sohrab

Northwestern University, Mechanical Engineering, Faculty Member

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Papers by siavash sohrab

SHORT COMMUNICATION Some Examples of Hysteresis Phenomena in Combustion

Combustion Science and Technology, 2007

In the present experimental study, some examples of hysteresis phenomena in combustion systems ar... more In the present experimental study, some examples of hysteresis phenomena in combustion systems are described. In particular, the onset of acoustic instability of premixed flames in stagnation-point flow is investigated. It is found that for a given nozzle speed, transition from acoustic to non-acoustic burning regime is history dependent. The critical molar fuel concentrations X FU and X FL corresponding to the onset and termination of acoustic flames as a function of the mean exit velocity of the gas at the nozzle are determined which show the hysteresis band. In the study, additional example of such hysteresis effects in terms of the extinction and re-establishment of combustion of premixed flames in the stagnation-point flow is examined. Finally. the hysteresis effects associated with the onset and termination of rotation of polyhedral butane Bunsen flames as a function of the velocity of a co-flowing nitrogen stream is investigated. The possible significance of the results to the modeling of flamelet dynamics in turbulent combustion is discussed.

Modified van der Waals Equation of State

WSEAS Transactions on Biology and Biomedicine, 2004

A modified form of the van der Waals equation of state is presented that is valid for general val... more A modified form of the van der Waals equation of state is presented that is valid for general values of the critical compressibility factor. The resulting modified law of corresponding states is shown to lead to closer agreement with the experimental data. The model also suggests a finite value of vacuum pressure pv, such that the pressure of the anti-matter pam and the matter pm fields will be bonded from below and above by the pressure of the white-hole pWH and the black-hole pBH, WH BH am v m 0 p p p p p        , that constitute two singularities of the field.

Solution of Ancient Greek Problem of Trisection of Arbitrary Angle

Chaotic Modeling and Simulation, 2019

A solution of the ancient Greek problem of trisection of an arbitrary angle employing only c... more A solution of the ancient Greek problem of trisection of an arbitrary angle employing only compass and straightedge that avoids the need for two marks on Archimedes marked ruler is presented. It is argued that although Wantzel [1-5] 1837 theory concerning non-existence of rational roots of Descartes-Wantzel cubic equation is correct it does not imply impossibility of trisection of 60o angle. This is because according to the construction method introduced herein square of cosine of the trisected angle cos2α is related to cosine of its double cos2α thus requiring extraction of square root that is constructible rather than cubic root requiring rational solution of Descartes- Wantzel equation. In addition, the earlier formulation of the problem by Descartes the father of algebraic geometry is discussed. If one assumes that the ruler and compass
employed in the geometric constructions are Platonic ideal instruments then the trisection solution proposed herein should be exact.

Invariant Model of Boltzmann Statistical Mechanics and its Implications to Hydrodynamic Model of Electromagnetism, Physical Foundations of Quantum Mechanics, Relativity, Quantum Gravity and Quantum Cosmology

Journal of open systems evolution problems, Nov 30, 2023

Some implications of an invariant model of Boltzmann statistical mechanics to quantum nature of (... more Some implications of an invariant model of Boltzmann statistical mechanics to quantum nature of (space, time, mass), physical foundations of quantum mechanics, relativity, electromagnetism and Maxwell equations, quantum gravity and quantum cosmology will be discussed. In harmony with Huygens&#39; analogy between propagation of sound in air and light in ether, propagation of light wave is shown to involve an exceedingly thin longitudinal component besides its Maxwellian transverse polarizations. Following Maxwell and Lorentz, an invariant hydrodynamic model of electromagnetism is presented. It is expected that time-dependence of the speed of light, identified as root-mean-square velocity of gravitons, could be determined by measurement of changes in period of geological events caused by periodic cosmic radiation bursts from sources such as pulsars. New interpretation of physi cal foundation of quantum mechanics, Dirac wave equation, pilot waves of de Broglie-Bohm model will be described. Identifying physical space, Aristotle fifth element or Casimir vacuum, as a tachyonic compress ible fluid, in harmony with Huygens and Planck compressible ether, Lorentz-FitzGerald contractions becomes causal (Pauli) leading to Poincare-Lorentz dynamic as opposed to Einstein kinematic theory of relativity. Invariant forms of conservation equations lead to hydrodynamics of universe governed by quantum gravity as a dissipative deterministic dynamic system proposed by &#39;t Hooft. The thermodynam ics of universe suggests possible relevance of classical Nordstrom scalar, and Abraham vector theories of gravitation beside Einstein tensor theory. Also, some implications of the model to quantum cosmology, loop quantum gravity (LQG), and Everett multiverse are discussed.

Some Implications of a Scale Invariant Model of Statistical Mechanics, Kinetic Theory of Ideal Gas, and Riemann Hypothesis

Book Publisher International (a part of SCIENCEDOMAIN International), Jul 16, 2021

To derive invariant forms of conservation equations, a scale invariant statistical mechanics mode... more To derive invariant forms of conservation equations, a scale invariant statistical mechanics model is used. A modified form of the Cauchy stress tensor for fluid is presented, which leads to a modified Stokes assumption and thus a finite bulk viscosity coefficient. Brownian motion is defined as the state of equilibrium between suspended particles and molecular clusters that also have Brownian motion. Physical space, also known as the Casimir vacuum, is a tachyonic fluid that is Dirac's "stochastic ether" or de Broglie's "hidden thermostat," and it is compressible according to Planck's compressible ether. The stochastic definitions of the Planck h and Boltzmann k constants are shown to be related to the spatial and temporal aspects of vacuum fluctuations, respectively. As a result, a modified definition of thermodynamic temperature is introduced, resulting in predicted sound velocity that agrees with observations. Boltzmann combinatoric method was employed to derive invariant forms of Planck energy and Maxwell-Boltzmann speed distribution functions. In addition, the universal gas constant is identified as a modified value of the Joule-Mayer mechanical equivalent of heat known as De Pretto number 8338, which appeared in his mass-energy equivalence equation. Invariant versions of Boltzmann, Planck, and Maxwell-Boltzmann distribution functions for equilibrium statistical fields, including those of isotropic stationary turbulence, are determined using Boltzmann's combinatoric methods. The latter leads to the definitions of (electron, photon, neutrino) as the most likely equilibrium sizes of (photon, neutrino, tachyon) clusters, respectively. The physical basis for the coincidence of the Riemann zeta function's normalized spacing between zeros and the normalized Maxwell-Boltzmann distribution, as well as its connections to the Riemann hypothesis are investigated. Through Euler's golden key, the zeros of the Riemann zeta function are related to the zeros of particle velocities or "stationary states," providing a physical explanation for the location of the critical line. It is proposed that, because the energy spectrum of the Casimir vacuum will be determined by the Schrodinger equation of quantum mechanics, physical space should be characterised by noncommutative spectral geometry of Connes in light of Heisenberg matrix mechanics. Invariant forms of transport coefficients implying finite values of gravitational viscosity, as well as hierarchies of vacua and absolute zero temperatures, are described. Some of the implications of the results for the problem of thermodynamic irreversibility and the Poincare recurrence theorem are discussed. An invariant modified form of the first law of thermodynamics is obtained, as well as a modified definition of entropy, which closes the gap between radiation and gas theory. Finally, in quantum mechanics, new paradigms for the hydrodynamic foundations of both Schrodinger and Dirac wave equations, as well as transitions between Bohr stationary states, are examined.

Some Implications of a Scale-Invariant Model of Statistical Mechanics to Classical and Black Hole Thermodynamics

Bulletin of the American Physical Society, Apr 17, 2016

Submitted for the APR16 Meeting of The American Physical Society Some Implications of a Scale-Inv... more Submitted for the APR16 Meeting of The American Physical Society Some Implications of a Scale-Invariant Model of Statistical Mechanics to Classical and Black Hole Thermodynamics. SIAVASH SOHRAB, Northwestern University-A scale-invariant model of statistical mechanics is applied to described modified forms of four laws of classical thermodynamics. Following de Broglie formula λ rk = h/m k v rk , frequency of matter waves is defined as ν rk = k/m k v rk leading to stochastic definitions of (Planck, Boltzmann) universal constants (h = m k < λ rk > c, k = m k < ν rk > c), λ rk ν rk = c, relating to spatiotemporal Casimir vacuum fluctuations. Invariant Mach number M a β = v/v rβ is introduced leading to hierarchy of "supersonic" flow separated by shock front, viewed as "event-horizon" EH β , from subsonic flow that terminates at surface of stagnant condensate of "atoms" defined as "black-hole" BH β at scale β thus resulting in hierarchy of embedded "black holes" at molecular-atomic-, electron-, photon-, tachyon-.. . scales, ad infinitum. Classical black hole will correspond to solid phase photon or solid-light. It is argued that Bardeen-Carter-Hawking (1973) first law of black hole mechanics δM = (κ/8π)δA + Ω H δJ + Φ H δQ, instead of dE = T dS − P dV suggested by Bekenstein (1973), is analogous to first law of thermodynamics expressed as T dS = P dV + dE such that entropy of black hole, rather than to its horizon surface area, will be related to its total energy hence enthalpy H = T S leading to S BH = 4kN in exact agreement with prediction of Major and Setter , Class. Quant. Grav. 18(2-3), 5125 (2001).

Implications of a scale invariant model of statistical mechanics to nonstandard analysis and the wave equation

International Conference on Applied Mathematics, Mar 22, 2007

Lobachevsky-Poincaré-Dirac Space and Quantum Nature of Internal Spacetime versus External Space and Time in Cosmology

Bulletin of the American Physical Society, Apr 16, 2019

Some implications of the modified forms of the first and the second laws of thermodynamics and the variational principles in chemically reactive systems

International Conference on Systems, Jul 11, 2005

Derivation of invariant forms of conservation equations from the invariant Boltzmann equation

A scale-invariant model of statistical mechanics is described and applied to introduce the invari... more A scale-invariant model of statistical mechanics is described and applied to introduce the invariant Boltzmann equation and the corresponding invariant Enskog equation of change. The invariant forms of the mass, energy, linear momentum, and angular momentum conservation equations are then derived. An invariant definition of the reaction rate for any scale within the hierarchy of statistical fields is defined. A modified form of the total stress tensor for fluids

Extinction of Counterflow Premixed Flames Under Periodic Variation of the Rate of Stretch

Combustion Science and Technology, 1995

SHORT COMMUNICATION The Influence of Rotation on Premixed Flames in Stagnation-Point Flow

Combustion Science and Technology, May 1, 1987

Abstract-Premixed flames stabilized in a rotating stagnation-point flow is considered. A descript... more

Modified theories of laminar flow around a rigid cylinder and flow outside and inside a liquid cylinder in uniform and counterflow gaseous jets

International Conference on Applied Mathematics, May 11, 2005

The scale-invariant forms of conservation equations in reactive fields are described. The modifie... more The scale-invariant forms of conservation equations in reactive fields are described. The modified form of the Helmholtz vorticity equation is solved to determine laminar flow outside a rigid cylinder and flow inside and outside of a cylindrical liquid body in a uniform gaseous stream or at the stagnation-point of two symmetric gaseous planar counterflow jets. For the former problem, a modified solution for flow around rigid cylinder is presented that resolves the Stokes paradox and is harmonious with the Oseen's classical solution. For the latter problem, parallel to the classical Hill spherical vortex, the solution describing two cylindrical vortex lines is presented. Also, the stream functions representing flow within two concentric immiscible liquid cylinders in uniform or planar counterflow gaseous streams are presented.

Solutions of Modified Equation of Motion for Laminar Flow across (within) Rigid (Liquid) Sphere and Cylinder and Resolution of Stokes Paradox: Scientific Explanation

Book Publisher International (a part of SCIENCEDOMAIN International), Aug 6, 2021

The scale-invariant forms of conservation equations are employed to describe solutions of modifie... more The scale-invariant forms of conservation equations are employed to describe solutions of modified form of equation of motion for the problems of laminar viscous flow across (within) rigid (liquid) sphere and cylinder. Analytical solutions of modified equation of motion in all three regions for both spherical and cylindrical geometry are presented. New solutions for laminar viscous flow across rigid sphere and cylinder are presented with the latter resolving the Stokes paradox for flow across cylinder.

Quantum Nature of Physical Space, Aristotle Fifth Element or Casimir Vacuum, Connects Constants of Chaos Theory (δ, α) in Mathematics to Universal Gas Constant and Atomic Mass Unit (R o , amu) in Physics

APS April Meeting Abstracts, 2018

Some Implications of Invariant Boltzmann Statistical Mechanics to Quantum Gravity and Noncommutative Geometry of Physical Space and its Fractal Spectral Dimension

Bulletin of the American Physical Society, Apr 18, 2020

to invariant Boltzmann statistical mechanics [1], Kelvin absolute temperature T [K] is identified... more to invariant Boltzmann statistical mechanics [1], Kelvin absolute temperature T [K] is identified as Wien wavelength λ wβ−1 [m] of thermal oscillations leading to internal measures of spacetime (λ wβ−1 , τ wβ−1) and external measures of space and time (x β = N x λ wβ−1 , t β = N t τ wβ−1). Therefore, temperature of space or Casimir vacuum fixes local measures of spacetime (λ wβ−1 , τ wβ−1)that are not independent because v ws = λ ws /τ ws must satisfy the vacuum temperature. Since Wien displacement law λ w T = 0.29 cm-K = 0.0029 [m 2 ] requires the change of units [m/cm] = 100, the classical temperature conversion formula becomes T [m] = o C[m] + 2.731 with 2.731 close to Penzias-Wilson [1965] cosmic microwave background radiation temperature T CM B ≃ 2.73 [m]. The role of analytic functions, Cauchy-Riemann conditions, and possible imaginary nature of internal spacetime coordinates, due to connections to Riemann surfaces at lower scale β −1, on path-independence of trajectories of quantum transitions and Heisenberg equation of motion are discussed. Finally, some implications of the hydrodynamic model to quantum gravity as a dissipative deterministic system [2] and fractal spectral dimension of noncommutative geometry of space [3] are examined.

Influence of radiative heat loss on flammability limits

On Radiative Cooling and Temperature Profiles of Counterflow Premixed Flames

ABSTRACT Axial and radial temperature profiles of the gaseous slab in between two symmetric count... more ABSTRACT Axial and radial temperature profiles of the gaseous slab in between two symmetric counterflow premixed flames of methane are measured. The results indicate that for widely separated lean and rich flames, there exists a temperature dip which is accounted for on the basis of radiative heat loss. For lean flames, the dependence of the temperature dip on the flame separation distance, and hence volume of the emitting gas, is determined. The calculated total radiant loss from the transparent gas volume, based on CO2H2O emissivities obtained from Hottel&#39;s curves, results in average temperature drops which closely agree with the measured values. The data are also in favorable agreement with the previously developed theory for radiatively cooled counterflow premixed flames. Also reported is the influence of the thermocouple coating thickness on the measured temperatures. Potential application of the present experimental method to the evaluation of effective emissivities of luminous and nonluminous slabs of combustion products of different fuels is discussed.

Kelvin Absolute Temperature Scale Identified as Length Scale and Related to de Broglie Thermal Wavelength

Bulletin of the American Physical Society, Mar 15, 2016

dβ = h/m β v rβ and frequency ν dβ = k/m β v rβ of matter waves and stochastic definitions of Pla... more dβ = h/m β v rβ and frequency ν dβ = k/m β v rβ of matter waves and stochastic definitions of Planck h = h k = m k < λ rk > c and Boltzmann k = k k = m k < ν rk > c constants, λ rk ν rk = c, that respectively relate to spatial (λ) and temporal (ν) aspects of vacuum fluctuations. Photon massm k =

Effects of Air-Side Oxygen Addition on Soot Formation in Methane Coflow Diffusion Flame

Combustion Science and Technology, Oct 1, 1990

SHORT COMMUNICATION Some Examples of Hysteresis Phenomena in Combustion

Combustion Science and Technology, 2007

In the present experimental study, some examples of hysteresis phenomena in combustion systems ar... more In the present experimental study, some examples of hysteresis phenomena in combustion systems are described. In particular, the onset of acoustic instability of premixed flames in stagnation-point flow is investigated. It is found that for a given nozzle speed, transition from acoustic to non-acoustic burning regime is history dependent. The critical molar fuel concentrations X FU and X FL corresponding to the onset and termination of acoustic flames as a function of the mean exit velocity of the gas at the nozzle are determined which show the hysteresis band. In the study, additional example of such hysteresis effects in terms of the extinction and re-establishment of combustion of premixed flames in the stagnation-point flow is examined. Finally. the hysteresis effects associated with the onset and termination of rotation of polyhedral butane Bunsen flames as a function of the velocity of a co-flowing nitrogen stream is investigated. The possible significance of the results to the modeling of flamelet dynamics in turbulent combustion is discussed.

Modified van der Waals Equation of State

WSEAS Transactions on Biology and Biomedicine, 2004

A modified form of the van der Waals equation of state is presented that is valid for general val... more A modified form of the van der Waals equation of state is presented that is valid for general values of the critical compressibility factor. The resulting modified law of corresponding states is shown to lead to closer agreement with the experimental data. The model also suggests a finite value of vacuum pressure pv, such that the pressure of the anti-matter pam and the matter pm fields will be bonded from below and above by the pressure of the white-hole pWH and the black-hole pBH, WH BH am v m 0 p p p p p        , that constitute two singularities of the field.

Solution of Ancient Greek Problem of Trisection of Arbitrary Angle

Chaotic Modeling and Simulation, 2019

A solution of the ancient Greek problem of trisection of an arbitrary angle employing only c... more A solution of the ancient Greek problem of trisection of an arbitrary angle employing only compass and straightedge that avoids the need for two marks on Archimedes marked ruler is presented. It is argued that although Wantzel [1-5] 1837 theory concerning non-existence of rational roots of Descartes-Wantzel cubic equation is correct it does not imply impossibility of trisection of 60o angle. This is because according to the construction method introduced herein square of cosine of the trisected angle cos2α is related to cosine of its double cos2α thus requiring extraction of square root that is constructible rather than cubic root requiring rational solution of Descartes- Wantzel equation. In addition, the earlier formulation of the problem by Descartes the father of algebraic geometry is discussed. If one assumes that the ruler and compass
employed in the geometric constructions are Platonic ideal instruments then the trisection solution proposed herein should be exact.

Invariant Model of Boltzmann Statistical Mechanics and its Implications to Hydrodynamic Model of Electromagnetism, Physical Foundations of Quantum Mechanics, Relativity, Quantum Gravity and Quantum Cosmology

Journal of open systems evolution problems, Nov 30, 2023

Some implications of an invariant model of Boltzmann statistical mechanics to quantum nature of (... more Some implications of an invariant model of Boltzmann statistical mechanics to quantum nature of (space, time, mass), physical foundations of quantum mechanics, relativity, electromagnetism and Maxwell equations, quantum gravity and quantum cosmology will be discussed. In harmony with Huygens&#39; analogy between propagation of sound in air and light in ether, propagation of light wave is shown to involve an exceedingly thin longitudinal component besides its Maxwellian transverse polarizations. Following Maxwell and Lorentz, an invariant hydrodynamic model of electromagnetism is presented. It is expected that time-dependence of the speed of light, identified as root-mean-square velocity of gravitons, could be determined by measurement of changes in period of geological events caused by periodic cosmic radiation bursts from sources such as pulsars. New interpretation of physi cal foundation of quantum mechanics, Dirac wave equation, pilot waves of de Broglie-Bohm model will be described. Identifying physical space, Aristotle fifth element or Casimir vacuum, as a tachyonic compress ible fluid, in harmony with Huygens and Planck compressible ether, Lorentz-FitzGerald contractions becomes causal (Pauli) leading to Poincare-Lorentz dynamic as opposed to Einstein kinematic theory of relativity. Invariant forms of conservation equations lead to hydrodynamics of universe governed by quantum gravity as a dissipative deterministic dynamic system proposed by &#39;t Hooft. The thermodynam ics of universe suggests possible relevance of classical Nordstrom scalar, and Abraham vector theories of gravitation beside Einstein tensor theory. Also, some implications of the model to quantum cosmology, loop quantum gravity (LQG), and Everett multiverse are discussed.

Some Implications of a Scale Invariant Model of Statistical Mechanics, Kinetic Theory of Ideal Gas, and Riemann Hypothesis

Book Publisher International (a part of SCIENCEDOMAIN International), Jul 16, 2021

To derive invariant forms of conservation equations, a scale invariant statistical mechanics mode... more To derive invariant forms of conservation equations, a scale invariant statistical mechanics model is used. A modified form of the Cauchy stress tensor for fluid is presented, which leads to a modified Stokes assumption and thus a finite bulk viscosity coefficient. Brownian motion is defined as the state of equilibrium between suspended particles and molecular clusters that also have Brownian motion. Physical space, also known as the Casimir vacuum, is a tachyonic fluid that is Dirac's "stochastic ether" or de Broglie's "hidden thermostat," and it is compressible according to Planck's compressible ether. The stochastic definitions of the Planck h and Boltzmann k constants are shown to be related to the spatial and temporal aspects of vacuum fluctuations, respectively. As a result, a modified definition of thermodynamic temperature is introduced, resulting in predicted sound velocity that agrees with observations. Boltzmann combinatoric method was employed to derive invariant forms of Planck energy and Maxwell-Boltzmann speed distribution functions. In addition, the universal gas constant is identified as a modified value of the Joule-Mayer mechanical equivalent of heat known as De Pretto number 8338, which appeared in his mass-energy equivalence equation. Invariant versions of Boltzmann, Planck, and Maxwell-Boltzmann distribution functions for equilibrium statistical fields, including those of isotropic stationary turbulence, are determined using Boltzmann's combinatoric methods. The latter leads to the definitions of (electron, photon, neutrino) as the most likely equilibrium sizes of (photon, neutrino, tachyon) clusters, respectively. The physical basis for the coincidence of the Riemann zeta function's normalized spacing between zeros and the normalized Maxwell-Boltzmann distribution, as well as its connections to the Riemann hypothesis are investigated. Through Euler's golden key, the zeros of the Riemann zeta function are related to the zeros of particle velocities or "stationary states," providing a physical explanation for the location of the critical line. It is proposed that, because the energy spectrum of the Casimir vacuum will be determined by the Schrodinger equation of quantum mechanics, physical space should be characterised by noncommutative spectral geometry of Connes in light of Heisenberg matrix mechanics. Invariant forms of transport coefficients implying finite values of gravitational viscosity, as well as hierarchies of vacua and absolute zero temperatures, are described. Some of the implications of the results for the problem of thermodynamic irreversibility and the Poincare recurrence theorem are discussed. An invariant modified form of the first law of thermodynamics is obtained, as well as a modified definition of entropy, which closes the gap between radiation and gas theory. Finally, in quantum mechanics, new paradigms for the hydrodynamic foundations of both Schrodinger and Dirac wave equations, as well as transitions between Bohr stationary states, are examined.

Some Implications of a Scale-Invariant Model of Statistical Mechanics to Classical and Black Hole Thermodynamics

Bulletin of the American Physical Society, Apr 17, 2016

Submitted for the APR16 Meeting of The American Physical Society Some Implications of a Scale-Inv... more Submitted for the APR16 Meeting of The American Physical Society Some Implications of a Scale-Invariant Model of Statistical Mechanics to Classical and Black Hole Thermodynamics. SIAVASH SOHRAB, Northwestern University-A scale-invariant model of statistical mechanics is applied to described modified forms of four laws of classical thermodynamics. Following de Broglie formula λ rk = h/m k v rk , frequency of matter waves is defined as ν rk = k/m k v rk leading to stochastic definitions of (Planck, Boltzmann) universal constants (h = m k < λ rk > c, k = m k < ν rk > c), λ rk ν rk = c, relating to spatiotemporal Casimir vacuum fluctuations. Invariant Mach number M a β = v/v rβ is introduced leading to hierarchy of "supersonic" flow separated by shock front, viewed as "event-horizon" EH β , from subsonic flow that terminates at surface of stagnant condensate of "atoms" defined as "black-hole" BH β at scale β thus resulting in hierarchy of embedded "black holes" at molecular-atomic-, electron-, photon-, tachyon-.. . scales, ad infinitum. Classical black hole will correspond to solid phase photon or solid-light. It is argued that Bardeen-Carter-Hawking (1973) first law of black hole mechanics δM = (κ/8π)δA + Ω H δJ + Φ H δQ, instead of dE = T dS − P dV suggested by Bekenstein (1973), is analogous to first law of thermodynamics expressed as T dS = P dV + dE such that entropy of black hole, rather than to its horizon surface area, will be related to its total energy hence enthalpy H = T S leading to S BH = 4kN in exact agreement with prediction of Major and Setter , Class. Quant. Grav. 18(2-3), 5125 (2001).

Implications of a scale invariant model of statistical mechanics to nonstandard analysis and the wave equation

International Conference on Applied Mathematics, Mar 22, 2007

Lobachevsky-Poincaré-Dirac Space and Quantum Nature of Internal Spacetime versus External Space and Time in Cosmology

Bulletin of the American Physical Society, Apr 16, 2019

Some implications of the modified forms of the first and the second laws of thermodynamics and the variational principles in chemically reactive systems

International Conference on Systems, Jul 11, 2005

Derivation of invariant forms of conservation equations from the invariant Boltzmann equation

A scale-invariant model of statistical mechanics is described and applied to introduce the invari... more A scale-invariant model of statistical mechanics is described and applied to introduce the invariant Boltzmann equation and the corresponding invariant Enskog equation of change. The invariant forms of the mass, energy, linear momentum, and angular momentum conservation equations are then derived. An invariant definition of the reaction rate for any scale within the hierarchy of statistical fields is defined. A modified form of the total stress tensor for fluids

Extinction of Counterflow Premixed Flames Under Periodic Variation of the Rate of Stretch

Combustion Science and Technology, 1995

SHORT COMMUNICATION The Influence of Rotation on Premixed Flames in Stagnation-Point Flow

Combustion Science and Technology, May 1, 1987

Abstract-Premixed flames stabilized in a rotating stagnation-point flow is considered. A descript... more

Modified theories of laminar flow around a rigid cylinder and flow outside and inside a liquid cylinder in uniform and counterflow gaseous jets

International Conference on Applied Mathematics, May 11, 2005

The scale-invariant forms of conservation equations in reactive fields are described. The modifie... more The scale-invariant forms of conservation equations in reactive fields are described. The modified form of the Helmholtz vorticity equation is solved to determine laminar flow outside a rigid cylinder and flow inside and outside of a cylindrical liquid body in a uniform gaseous stream or at the stagnation-point of two symmetric gaseous planar counterflow jets. For the former problem, a modified solution for flow around rigid cylinder is presented that resolves the Stokes paradox and is harmonious with the Oseen's classical solution. For the latter problem, parallel to the classical Hill spherical vortex, the solution describing two cylindrical vortex lines is presented. Also, the stream functions representing flow within two concentric immiscible liquid cylinders in uniform or planar counterflow gaseous streams are presented.

Solutions of Modified Equation of Motion for Laminar Flow across (within) Rigid (Liquid) Sphere and Cylinder and Resolution of Stokes Paradox: Scientific Explanation

Book Publisher International (a part of SCIENCEDOMAIN International), Aug 6, 2021

The scale-invariant forms of conservation equations are employed to describe solutions of modifie... more The scale-invariant forms of conservation equations are employed to describe solutions of modified form of equation of motion for the problems of laminar viscous flow across (within) rigid (liquid) sphere and cylinder. Analytical solutions of modified equation of motion in all three regions for both spherical and cylindrical geometry are presented. New solutions for laminar viscous flow across rigid sphere and cylinder are presented with the latter resolving the Stokes paradox for flow across cylinder.

Quantum Nature of Physical Space, Aristotle Fifth Element or Casimir Vacuum, Connects Constants of Chaos Theory (δ, α) in Mathematics to Universal Gas Constant and Atomic Mass Unit (R o , amu) in Physics

APS April Meeting Abstracts, 2018

Some Implications of Invariant Boltzmann Statistical Mechanics to Quantum Gravity and Noncommutative Geometry of Physical Space and its Fractal Spectral Dimension

Bulletin of the American Physical Society, Apr 18, 2020

to invariant Boltzmann statistical mechanics [1], Kelvin absolute temperature T [K] is identified... more to invariant Boltzmann statistical mechanics [1], Kelvin absolute temperature T [K] is identified as Wien wavelength λ wβ−1 [m] of thermal oscillations leading to internal measures of spacetime (λ wβ−1 , τ wβ−1) and external measures of space and time (x β = N x λ wβ−1 , t β = N t τ wβ−1). Therefore, temperature of space or Casimir vacuum fixes local measures of spacetime (λ wβ−1 , τ wβ−1)that are not independent because v ws = λ ws /τ ws must satisfy the vacuum temperature. Since Wien displacement law λ w T = 0.29 cm-K = 0.0029 [m 2 ] requires the change of units [m/cm] = 100, the classical temperature conversion formula becomes T [m] = o C[m] + 2.731 with 2.731 close to Penzias-Wilson [1965] cosmic microwave background radiation temperature T CM B ≃ 2.73 [m]. The role of analytic functions, Cauchy-Riemann conditions, and possible imaginary nature of internal spacetime coordinates, due to connections to Riemann surfaces at lower scale β −1, on path-independence of trajectories of quantum transitions and Heisenberg equation of motion are discussed. Finally, some implications of the hydrodynamic model to quantum gravity as a dissipative deterministic system [2] and fractal spectral dimension of noncommutative geometry of space [3] are examined.

Influence of radiative heat loss on flammability limits

On Radiative Cooling and Temperature Profiles of Counterflow Premixed Flames

ABSTRACT Axial and radial temperature profiles of the gaseous slab in between two symmetric count... more ABSTRACT Axial and radial temperature profiles of the gaseous slab in between two symmetric counterflow premixed flames of methane are measured. The results indicate that for widely separated lean and rich flames, there exists a temperature dip which is accounted for on the basis of radiative heat loss. For lean flames, the dependence of the temperature dip on the flame separation distance, and hence volume of the emitting gas, is determined. The calculated total radiant loss from the transparent gas volume, based on CO2H2O emissivities obtained from Hottel&#39;s curves, results in average temperature drops which closely agree with the measured values. The data are also in favorable agreement with the previously developed theory for radiatively cooled counterflow premixed flames. Also reported is the influence of the thermocouple coating thickness on the measured temperatures. Potential application of the present experimental method to the evaluation of effective emissivities of luminous and nonluminous slabs of combustion products of different fuels is discussed.

Kelvin Absolute Temperature Scale Identified as Length Scale and Related to de Broglie Thermal Wavelength

Bulletin of the American Physical Society, Mar 15, 2016

dβ = h/m β v rβ and frequency ν dβ = k/m β v rβ of matter waves and stochastic definitions of Pla... more dβ = h/m β v rβ and frequency ν dβ = k/m β v rβ of matter waves and stochastic definitions of Planck h = h k = m k < λ rk > c and Boltzmann k = k k = m k < ν rk > c constants, λ rk ν rk = c, that respectively relate to spatial (λ) and temporal (ν) aspects of vacuum fluctuations. Photon massm k =

Effects of Air-Side Oxygen Addition on Soot Formation in Methane Coflow Diffusion Flame

Combustion Science and Technology, Oct 1, 1990

Examples of Applications of an Invariant Statistical Theory of Field to Cosmology, Astrophysics, Hydrodynamics, Electrodynamics, and Photonics

15th Chaotic Modeling and Simulation International Conference, Springer Proceedings in Complexity, 2023

Some examples of application of a scale-invariant statistical theory of

Examples of Applications of an Invariant Statistical Theory of Field to Cosmology, Astrophysics, Hydrodynamics, Electrodynamics, and Photonics

C. H. Skiadas and Y. Dimotikalis (eds.), 15th Chaotic Modeling and Simulation International Conference, Springer Proceedings in Complexity,, 2023

Some examples of application of a scale-invariant statistical theory of

Universality of Boltzmann Statistical Mechanics, Thermodynamics, Quantum Mechanics, and Shannon Information Theory

C. H. Skiadas and Y. Dimotikalis (eds.), 14th Chaotic Modeling and Simulation International Conference, Springer Proceedings in Complexity,, 2021

Universal nature of Boltzmann statistical mechanics, generalized thermodynamics, quantum mechanic... more Universal nature of Boltzmann statistical mechanics, generalized thermodynamics, quantum mechanics, spacetime, black hole mechanics, Shannon information theory, Faraday lines of force, and Banach-Tarski paradox (BTP) are studied. The nature of matter and Dirac anti-matter are described in terms of states of compression and rarefaction of physical space, Aristotle fifth element, or Casimir vacuum identified as a compressible tachyonic fluid. The model is in harmony with perceptions of Plato who believed that the world was formed from a formless primordial medium that was initially in a state of total chaos or "Tohu Vavohu" (Sohrab, in Int J Mech 8:873-84, [1]. Hierarchies of statistical fields from photonic to cosmic scales lead to universal scale-invariant Schrödinger equation thus allowing for new perspectives regarding connections between classical mechanics, quantum mechanics, and chaos theory. The nature of external physical time and its connections to internal thermodynamics time and Rovelli thermal time are described. Finally, some implications of renormalized Planck distribution function to economic systems are examined. Keywords Thermodynamics. Quantum mechanics. Anti-matter. Spacetime. Thermal time. Information theory. Faraday lines of force. Banach-Tarski paradox. T.O.E.

Connecting Bernoulli and Schrödinger Equations and its Impact on Quantum-Mechanic Wave Function and Entanglement Problems

C. H. Skiadas and Y. Dimotikalis (eds.), 13th Chaotic Modeling and Simulation International Conference, Springer Proceedings in Complexity,

An invariant model of Boltzmann statistical mechanics is applied to derive invariant Schrödinger ... more An invariant model of Boltzmann statistical mechanics is applied to derive invariant Schrödinger equation of quantum mechanics from invariant Bernoulli equation of hydrodynamics. The results suggest new perspectives regarding quantum mechanics wave function and its collapse, stationary versus propagating wave functions, and waveparticle duality. The invariant hydrodynamic model also leads to the definition of generalized shock waves in "supersonic" flows at molecular-, electro-, and chromodynamic scales with (Mach, Lorentz, and Michelson) numbers exceeding unity. The invariant internal hydro-thermo-diffusive structure of such generalized "shock" waves are described.

Connecting Bernoulli and Schrödinger Equations and its Impact on Quantum-Mechanic Wave Function and Entanglement Problems

13th Chaotic Modeling and Simulation International Conference, 2021

An invariant model of Boltzmann statistical mechanics is applied to derive invariant Schrödinger ... more An invariant model of Boltzmann statistical mechanics is applied to derive invariant Schrödinger equation of quantum mechanics from invariant Bernoulli equation of hydrodynamics. The results suggest new perspectives regarding quantum mechanics wave function and its collapse, stationary versus propagating wave functions, and waveparticle duality. The invariant hydrodynamic model also leads to the definition of generalized shock waves in "supersonic" flows at molecular-, electro-, and chromodynamic scales with (Mach, Lorentz, and Michelson) numbers exceeding unity. The invariant internal hydro-thermo-diffusive structure of such generalized "shock" waves are described.