scholarly journals Relating the deBroglie and Compton Wavelengths to the Velocity of Light?

2018 ◽  
Vol 10 (4) ◽  
pp. 102
Author(s):  
Gordon R. Kepner
Keyword(s):  
Order Differential Equation ◽  
Free Particle ◽  
The Other ◽  
Time Dependent ◽  
Uncertainty Relations ◽  
Fundamental Relation ◽  
Compton Wavelength ◽  
Velocity Of Light ◽  
Velocity Wave ◽  
Empirical Constants

No report in the literature has directly described this relation. New constants for particles are presented. One relates to the Compton wavelength, called here the “mass-wave” constant for all particles. The other relates to the deBroglie wavelength, called here the “velocity-wave” constant for a particle. An equation is derived based on these two constants encapsulating a fundamental relation between the matter-states, particle and wave, to the velocity of light. New approaches to the Uncertainty relations are shown. The basic Schrodinger equation is derived from the perspective of a non-dimensional second-order differential equation free of any assumed empirical constants. The resulting time-dependent wave equation for a free particle was then expressed in terms of the particle velocity and deBroglie wavelength.

FRW viscous fluid cosmological model with time-dependent inhomogeneous equation of state

2017 ◽  
Vol 15 (01) ◽  
pp. 1830001 ◽  
Author(s):  
G. S. Khadekar ◽  
Deepti Raut
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Quadratic Form ◽  
State Parameter ◽  
The Other ◽  
Time Dependent ◽  
Inhomogeneous Equation ◽  
Field Equations ◽  
Equation Of State Parameter ◽  
Viscous Models

In this paper, we present two viscous models of non-perfect fluid by avoiding the introduction of exotic dark energy. We consider the first model in terms of deceleration parameter [Formula: see text] has a viscosity of the form [Formula: see text] and the other model in quadratic form of [Formula: see text] of the type [Formula: see text]. In this framework we find the solutions of field equations by using inhomogeneous equation of state of form [Formula: see text] with equation of state parameter [Formula: see text] is constant and [Formula: see text].

Correlations of substituent effects on proton and fluorine chemical shifts with inverse ionization potentials

1967 ◽  
Vol 45 (24) ◽  
pp. 3143-3151 ◽  
Author(s):  
T. Schaefer ◽  
F. Hruska ◽  
H. M. Hutton
Keyword(s):  
Electric Fields ◽  
Chemical Shifts ◽  
Substituent Effects ◽  
Group Iv ◽  
The Other ◽  
Ionization Potentials ◽  
Time Dependent ◽  
Practical Application ◽  
Methyl Proton ◽  
Proton Chemical Shifts

The fluorine and proton chemical shifts in some geminally disubstituted vinylidene fluorides and ethylenes are discussed. For these compounds, at least, there are difficulties with an interpretation based on intramolecular time-dependent electric fields. On the other hand, the shifts correlate with the inverse ionization potentials of the substituents, indicating a paramagnetic effect arising from the second term in Ramsey's expression. It is suggested that the effect operates via the bonds and not across space. Methyl proton shifts in a series of substituted methyl compounds of group IV, V, and VI elements show similar correlations. A practical application of the correlation to spectral analysis problems is given.

A note on disturbances in a layered medium containing a magnetic field

1964 ◽  
Vol 54 (6A) ◽  
pp. 1771-1777
Author(s):  
D. K. Sinha
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Layered Medium ◽  
Present Note ◽  
Infinite Medium ◽  
The Other ◽  
Time Dependent ◽  
The Earth ◽  
Propagation Of Waves ◽  
Initial Magnetic Field

abstract In recent years, Kaliski has contributed a series of papers on the interaction of elastic and magnetic fields and some of them, [1], [2], [3] are concerned with the propagation of waves in a semi-infinite medium either loaded or conditioned otherwise, at its free surface. Such problems, as Kaliski [1] has remarked, may have relevance in the practical seismic problem of detecting the mechanical explosions inside the earth. Moreover, their geophysical implications have also been examined by Knopoff [4[, Cagniard [5], Banos [6], and Rikitake [7]. The present note seeks to investigate disturbances in a medium consisting of two layers (one finite and the other infinite) of elastic medium intervened by a thin layer of vacuum. The vacuum is traversed by an initial magnetic field. The disturbances in the medium are assumed to have been produced by a time-dependent load on the free surface of the medium. The method of Laplace transform has been used to facilitate the solution of the problem.

Simulation of time-dependent radiative heat motion over a stretching/shrinking sheet of hybrid Nanofluid: Stability analysis for dual solutions

2022 ◽  
pp. 239779142110690
Author(s):  
Seema Tinker ◽  
SR Mishra ◽  
PK Pattnaik ◽  
Ram Prakash Sharma
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Dual Solutions ◽  
The Other ◽  
Time Dependent ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Heat Transfer Characteristics ◽  
Suction Parameter ◽  
Transfer Characteristics

The heat transfer characteristics for the flow of a time-dependent hybrid nanofluid with thermal radiation and source/sink over a stretching/shrinking sheet are examined in the current investigation. We have transformed the governing equations of the presented study into the similarity equations utilizing similarity variables. However, a numerical solution is obtained by using in-build MATLAB code bvp5c. The mass and energy profiles for diverse values of thermophysical parameters are studied together with their physical quantities. It is observed that dual solutions exist, that is, one is upper, and the other is lower branch solution for a definite choice of the unsteadiness parameter. Also, stability analysis is executed to determine the long-term stability of dual solutions, indicating that out of the two, only one is stable and the other is unstable. It is revealed that comparatively, the first solution shows stability, while the second solution shows instability. There is a considerable influence of second-order slip on the problem’s respective flow and heat transfer characteristics. Further, major outcomes also show the dimensionless frictional stress and the magnitude of conventional heat transfer enhancement with growing suction parameter values.

Quantum Mechanics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Variational Principles ◽  
Free Particle ◽  
Uncertainty Relations ◽  
Probabilistic Interpretation ◽  
Historical Account ◽  
Potential Wells ◽  
Harmonic Oscillator Potential ◽  
Ground State Energies

In this chapter, the main features of quantum theory are presented. The chapter begins with a historical account of the invention of quantum mechanics. The meaning of position and momentum in quantum mechanics is discussed and non-commuting operators are introduced. The Schrödinger equation is presented and solved for a free particle and for a harmonic oscillator potential in one dimension. The meaning of the wavefunction is considered and the probabilistic interpretation is presented. The mathematical machinery and language of quantum mechanics are developed, including Hermitian operators, observables and expectation values. The uncertainty principle is discussed and the uncertainty relations are presented. Scattering and tunnelling by potential wells and barriers is considered. The use of variational principles to estimate ground state energies is explained and illustrated with a simple example.

scholarly journals Comparative Evaluation of Intestinal Absorption and Functional Value of Iron Dietary Supplements and Drug with Different Delivery Systems

Molecules ◽  
2020 ◽  
Vol 25 (24) ◽  
pp. 5989
Author(s):  
Paolo Pastore ◽  
Marco Roverso ◽  
Erik Tedesco ◽  
Marta Micheletto ◽  
Etienne Mantovan ◽  
...  
Keyword(s):  
Side Effects ◽  
Dietary Supplements ◽  
Iron Absorption ◽  
Therapeutic Targets ◽  
Iron Bioavailability ◽  
The Other ◽  
Time Dependent ◽  
Nutritional Deficiencies ◽  
Deficiency Anemia ◽  
Iron Supplements

Iron is a fundament micronutrient, whose homeostasis is strictly regulated. Iron deficiency anemia is among the most widespread nutritional deficiencies and its therapy, based on dietary supplement and drugs, may lead to severe side effects. With the aim of improving iron bioavailability while reducing iron oral therapy side effects, novel dietary supplements based on innovative technologies—microencapsulation, liposomes, sucrosomes—have been produced and marketed. In the present work, six iron dietary supplements for different therapeutic targets were compared in terms of bioaccessibility, bioavailability, and safety by using an integrated in vitro approach. For general-purpose iron supplements, ME + VitC (microencapsulated) showed a fast, burst intestinal iron absorption kinetic, which maintained iron bioavailability and ferritin expression constant over time. SS + VitC (sucrosomes), on the other side, showed a slower, time-dependent iron absorption and ferritin expression trend. ME + Folate (microencapsulated) showed a behavior similar to that of ME + VitC, albeit with a lower bioavailability. Among pediatric iron supplements, a time-dependent bioavailability increase was observed for LS (liposome), while PIC (polydextrose-iron complex) bioavailability is severely limited by its poor bioaccessibility. Finally, except for SS + VitC, no adverse effects on intestinal mucosa vitality and barrier integrity were observed. Considering obtained results and the different therapeutic targets, microencapsulation-based formulations are endowed with better performance compared to the other formulations. Furthermore, performances of microencapsulated products were obtained with a lower iron daily dose, limiting the potential onset of side effects.

Electrophysiological Characteristics of Classes of Neuron in the HVc of the Zebra Finch

1998 ◽  
Vol 80 (2) ◽  
pp. 914-923 ◽  
Author(s):  
Michinori Kubota ◽  
Ikuo Taniguchi
Keyword(s):  
Action Potential ◽  
Zebra Finch ◽  
Action Potential Duration ◽  
The Other ◽  
Time Dependent ◽  
Inward Rectification ◽  
Type I ◽  
Type Ii ◽  
Type Iii ◽  
Type Iv

Kubota, Michinori and Ikuo Taniguchi. Electrophysiological characteristics of classes of neuron in the HVc of the zebra finch. J. Neurophysiol. 80: 914–923, 1998. Whole cell recordings were made from zebra finch HVc neurons in slice preparations. Four distinct classes of neuron were found on the basis of their electrophysiological properties. The morphological characteristics of some of these neurons were also examined by intracellular injection of Lucifer yellow. Type I neurons (21 of 65 cells) had longer time-to-peak of an afterhyperpolarization following an action potential than the other classes. They exhibited both fast and time-dependent inward rectification and an initial high-frequency firing followed by a slower constant firing. Type I neurons had large somata and thick dendrites with many spines. The axons of some of the neurons in this class projected in the direction of area X of the parolfactory lobe. Type II neurons (30 of 65 cells) had a more negative resting membrane potential than the other classes. They exhibited fast inward rectification. Type II neurons could be divided into two subclasses by the absence (IIa; 22 cells) and the presence (IIb; 8 cells) of a low-threshold transient depolarization. Type IIa neurons had relatively small somata and thin, spiny dendrites. The axons of some of the neurons in this class projected in the direction of the robust nucleus of the archistriatum (RA). Type IIb neurons had relatively large somata and thick dendrites with many spines. Type III neurons (6 of 65 cells) had a shorter action-potential duration than the other classes. They exhibited prominent time-dependent inward rectification and a regular tonic firing with little or no accommodation. Type III neurons had beaded, aspiny dendrites. Type IV neurons (8 of 65 cells) had a longer action-potential duration, a much larger input resistance, and longer membrane time constant than the other classes. Type IV neurons had small somata and thin, short, sparsely spiny dendrites. The axons of some of the neurons in this class projected in the direction of the RA. These classes of neuron may play distinct roles in song production and representation in the HVc.

scholarly journals Fractional-Derivative Approximation of Relaxation in Complex Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Kin M. Li ◽  
Mihir Sen ◽  
Arturo Pacheco-Vega
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
System Identification ◽  
Complex Systems ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Initial Conditions ◽  
Time Dependent ◽  
Fractional Order Differential Equation

In this paper, we present a system identification (SI) procedure that enables building linear time-dependent fractional-order differential equation (FDE) models able to accurately describe time-dependent behavior of complex systems. The parameters in the models are the order of the equation, the coefficients in it, and, when necessary, the initial conditions. The Caputo definition of the fractional derivative, and the Mittag-Leffler function, is used to obtain the corresponding solutions. Since the set of parameters for the model and its initial conditions are nonunique, and there are small but significant differences in the predictions from the possible models thus obtained, the SI operation is carried out via global regression of an error-cost function by a simulated annealing optimization algorithm. The SI approach is assessed by considering previously published experimental data from a shell-and-tube heat exchanger and a recently constructed multiroom building test bed. The results show that the proposed model is reliable within the interpolation domain but cannot be used with confidence for predictions outside this region. However, the proposed system identification methodology is robust and can be used to derive accurate and compact models from experimental data. In addition, given a functional form of a fractional-order differential equation model, as new data become available, the SI technique can be used to expand the region of reliability of the resulting model.

A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows

1971 ◽  
Vol 8 (04) ◽  
pp. 708-715 ◽  
Author(s):  
Emlyn H. Lloyd
Keyword(s):  
Functional Equation ◽  
Explicit Formula ◽  
Generating Function ◽  
Present Theory ◽  
The Other ◽  
Time Dependent ◽  
Independent Sequence ◽  
Time Dependent Solution ◽  
Infinite Reservoir ◽  
Stationary Behaviour

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).

Unsteady convective diffusion with interphase mass transfer

1973 ◽  
Vol 333 (1592) ◽  
pp. 115-132 ◽  
Keyword(s):  
Dispersion Model ◽  
Reaction Rates ◽  
The Other ◽  
Time Dependent ◽  
Transport Systems ◽  
Exchange Coefficient ◽  
Dispersion Coefficients ◽  
Interfacial Transport ◽  
Order Of Magnitude ◽  
Proper Values

The theory of miscible dispersion is extended to interphase transport systems. As a specific example miscible dispersion in laminar flow in a tube in the presence of interfacial transport due to an irreversible first-order reaction at the wall is analysed by an exact procedure. A new exact dispersion model which accounts for dispersion with interphase transport is derived from first principles. The new concept of an ‘exchange coefficient’ arises naturally. This coefficient depends strongly on the rate of interfacial transport. Such transport also affects the convection and dispersion coefficients significantly. A general expression is derived which shows clearly the time-dependent nature of the coefficients in the dispersion model. The complete time-dependent expression for the exchange coefficient is obtained explicitly and is independent of the velocity distribution in the flow; however, it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large-time evaluations are made for the convection and dispersion coefficients, but these are sufficient to give useful physical insight into the nature of the problem. When the rate of the wall reaction approaches zero the exchange coefficient also approaches zero and the other two coefficients approach their proper values in the absence of interfacial transport. At the other extreme of rapid wall reaction rates, the convection coefficient is more than 50 % larger than its value in the absence of interfacial transport and the dispersion coefficient is an order of magnitude smaller than that for zero interphase transport.

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