[19] **viXra:1510.0482 [pdf]**
*submitted on 2015-10-28 20:31:46*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 12 Pages.

The generation of Chaos in Electronics has largely been implemented using the Chua circuits, where the initial conditions are described by system parameters such as resistors and capacitors. The present work provides a radical shift in approach by proposing signal based chaos generators. The essential design here is the coupling of two sinusoidal signal sources to a CMOS inverter circuit, which is seen to exhibit nonlinear behavior thanks to its transfer characteristics and non-quasi static behavior. The Standard Circle Map, ideally suited to describing nonlinear coupling of oscillations with competing frequencies is studied and a ‘frequency map’ is derived from it. The latter is studied using bifurcation and cobweb plots. A second perspective, the amplitude map is created by forming a difference equation using the CMOS inverter transfer function. This map is explored using the bifurcation plots and phase portraits. Finally, the proposed design is implemented experimentally and the generated chaotic output is validated using phase portraits and Fourier spectra. The effect of driving frequency on the output is characterized using Kolmogorov Entropy and Lyapunov Exponents, giving rise to the term ‘Frequency Dependent Chaos’. The fresh perspectives of a signal oriented chaos discussed in the present work exhibits the advantages of simple circuitry and easy tunability, and this forms the novelty of the present work.

**Category:** Mathematical Physics

[18] **viXra:1510.0479 [pdf]**
*submitted on 2015-10-28 20:35:13*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 8 Pages.

The fluctuations accompanying the DC offset in a photovoltaic cell open circuit voltage waveform are studied. Nonlinear analyses performed on these waveforms ascertain the presence of a highly unstable chaotic behavior. The results are validated using various parameters such as Kolmogorov Entropy, Fractal Dimension and Lyapunov Exponent. It is observed that the chaotic behavior responds to atmospheric and cosmic disturbances and hence can be used to study such effects. The information and inferences about the chaotic behavior coupled with proper synchronization techniques could potentially lead to cost effective means of enhancing the solar cell output.

**Category:** Mathematical Physics

[17] **viXra:1510.0468 [pdf]**
*submitted on 2015-10-28 08:01:16*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 6 Pages.

The present work pertains to the generation of a chaotic signal by taking the inverse Fourier Transform of a Fractal Spectral Profile. The presence of chaos is ascertained and characterized using phase portraits, recurrence plots, Lyapunov exponents and Kolmogorov entropies. This signal is modulated by a hyperbolic secant solitary pulse to formulate the “Fractal Chaotic Solitary Wavelet” (FCSW), the analysis of which reveals vanishing higher moments, translating to efficient capabilities of burst and discontinuity detection, apart from the advantage of security owing to the induced unpredictability of chaos. This results in the proposed Fractal Chaotic Solitary Wavelets having potential applications in secure communications and encryption.

**Category:** Mathematical Physics

[16] **viXra:1510.0467 [pdf]**
*submitted on 2015-10-28 08:02:21*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

Chaotic signals serve as ideal candidates as carriers in secure communication systems. The present work proposes the generation of a ‘digital’ chaotic signal using a frequency dependent iterative map. The proposed design is implemented using Field Programmable Gate Array and nonlinear characterization using Lyapunov exponent confirms the presence of chaos. A proof-of-concept communication system is then numerically designed and evaluated using the Mean Square Error, which reveals the sensitivity of the system to perfect decryption. The simplicity of the design, coupled with the high level of security obtained form the highlights of the present work.

**Category:** Mathematical Physics

[15] **viXra:1510.0466 [pdf]**
*submitted on 2015-10-28 08:03:01*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

The present work pertains to the exploration of signal based chaos generation in the Microwave X-Band frequency range. Specifically, two reflex klystrons are used as sources to two ports of the magic tee, while a third port is terminated. By taking the output from the fourth port, the envelope waveforms and phase portraits are seen to exhibit reasonable degree of richness and complexity. The presence of chaos is quantitatively ascertained using Lyapunov Exponents and Kolmogorov Entropies. The results outlined in the present work offer a far simpler alternative to generate easy-to-tune signal dependent chaos, suitable for telecommunication applications.

**Category:** Mathematical Physics

[14] **viXra:1510.0459 [pdf]**
*submitted on 2015-10-28 09:19:22*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

The basic components for most secure computing and communication systems of today are random number generators. The present work purports to a radically novel approach to the design and implementation of random number generators. Firstly, a nonlinear analysis of the photovoltaic cell open circuit voltage is performed, and the presence of chaos is ascertained using standard measures such as Lyapunov Exponents. Following this, the chaotic output is adapted into a bit stream and randomness tests from the NIST Suite are performed. It is seen that the chaotic output indeed passes all the randomness tests. The histogram of the output reveals similarities with Gaussian Normal Distributions, confirming the stochastic nature. Thus, the photovoltaic cell output is a potential power generating random number generator, drastically differing from the conventional power dissipative random number generators.

**Category:** Mathematical Physics

[13] **viXra:1510.0452 [pdf]**
*submitted on 2015-10-28 09:29:42*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 7 Pages.

A two-dimensional photonic crystal based on a lattice of silicon rods in air with a photonic bandgap in the visible and near-ultraviolet spectra is proposed, by removing some of the silicon rods or resizing their radius, to create a monotonically varying tapered line defect, thereby pertaining to a case of structure-based nonlinearity and making it possible to operate with low input powers. By properly manipulating the length of the line defect, pulse compression and consequent adiabatic amplification is seen, along with bunching/anti-bunching of pulses. For certain modes of operation, field confinement is observed, and this leads to the formation of discrete pulses, or light bullets. Following this, by appropriate use of cavity defects, the localization of discrete pulses is obtained, with the ‘gate’-output transfer curve resembling optical bistability. Such a structure can be used as a multi-functional device, with some of the functionalities being optical non-pumped amplification, frequency upconversion, memory writing, matched termination and slow wave guiding, that form the major conclusions of the work.

**Category:** Mathematical Physics

[12] **viXra:1510.0451 [pdf]**
*submitted on 2015-10-28 09:30:32*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 6 Pages.

A simplified photonic crystal design for an all-optical NAND gate operating in the visible spectrum is proposed and validated with numerical experiments using Finite Difference Time Domain method. Considering the NAND gate as a optical four-port network, the scattering matrix is determined. Also, two-dimensional autocorrelation-based leakage analysis is done and temporal analysis of the output pulse is performed. From the above mentioned valuations, one can obtain the optimal performance of the NAND gate structure with minimal loss and distortion, which forms the novelty of the present work.

**Category:** Mathematical Physics

[11] **viXra:1510.0450 [pdf]**
*submitted on 2015-10-28 09:31:42*

**Authors:** Sai Venkatesh Balasubramanian, Ganapathy R, Porsezian K

**Comments:** 3 Pages.

A ‘T-shaped’ defect is introduced in a two-dimensional photonic crystal lattice made of silicon, and for a small-signal optical input, this structure thus acts as an optical amplifier. A detailed analysis yields optimal linear and nonlinear performance of the optical amplifier operating in the visible region with minimal leakage and distortion.

**Category:** Mathematical Physics

[10] **viXra:1510.0355 [pdf]**
*submitted on 2015-10-22 09:44:59*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 13 Pages.

A frequency dependant chaos generator offering the twin advantages of simplicity of implementation and easy control and tunability is proposed using an iterative map based on the circle map and characterized using bifurcation diagrams. The nonlinearity of a single MOS transistor is effectively harnessed and is used to design a frequency dependant chaos generator using ring oscillators for the driving signals. The proposed design is implemented at the deep submicron VLSI level at 180nm CMOS Technology using SPICE Simulation. The generated chaos is characterized qualitatively using waveforms, spectra and phase portrait. Quantitative characterization using Lyapunov Exponent, Kolmogorov Entropy and Fractal Dimension ascertain the chaotic nature. Finally, the dependance of the nature of chaos generated on the power supply and on the driving signal frequency is characterized. The simplicity of circuitry coupled with the frequency dependence and low power dissipation form the key highlights of the present work. The chaotic signal generated in the present work serve as a potential candidate as a carrier in secure communication systems and encryption techniques.

**Category:** Mathematical Physics

[9] **viXra:1510.0346 [pdf]**
*submitted on 2015-10-21 07:23:12*

**Authors:** Nicolae Mazilu; Maricel Agop

**Comments:** 23 Pages.

The extended matter should be first characterized by a surface of separation from the empty space. This surface cannot be neatly, i.e. purely geometrically, defined. When it comes to extended particles, which are the fundamental structural units of the matter, the physical evidence is that they are not even stable: they are in a continuous transformation, and so are their limits of separation from space. The present work describes a concept of extended particle with special emphasis on this limit of separation. It turns out that the properties of inertia, as classically understood, are intrinsically related to the spin properties of quantum origin. Thus, the extended particle model cannot be but “holographic” when it comes to imbedding it in a physical structure. The spin properties turn out to be essential, inasmuch as they decide the forces of interaction issuing from the particle.

**Category:** Mathematical Physics

[8] **viXra:1510.0340 [pdf]**
*submitted on 2015-10-20 18:28:10*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 4 Pages.

Will the physics of GRS look similar or different from current physics [primarily strings]?

**Category:** Mathematical Physics

[7] **viXra:1510.0322 [pdf]**
*replaced on 2015-10-30 16:32:53*

**Authors:** Andrew Nassif

**Comments:** 6 Pages.

We will be taking a look at analyzing different papers from the Cambridge University Press on Computational Mathematics, Theoretical Physics, and Mathematical Physics. We will be reviewing them through a literary, rhetorical, and ofcourse scientific perspective. Overall we will do this through an Annotated Bibliography.

**Category:** Mathematical Physics

[6] **viXra:1510.0145 [pdf]**
*replaced on 2015-10-20 20:14:59*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 7 Pages.

Merriam-Webster's Collegiate Dictionary, Eleventh Edition, gives a technical definition of curvature, "the rate of change of the angle through which the tangent to a curve turns in moving along the curve and which for a circle is equal to the reciprocal of the radius". That precisely describes a curve's intuitive curvature, but the Riemann "curvature" tensor is zero for all curves! We work out the natural extension of intuitive curvature to hypersurfaces, based on the rates that their tangents develop components which are orthogonal to the local tangent hyperplane. Intuitive curvature is seen to have the form of a second-rank symmetric tensor which cannot be algebraically expressed in terms of the metric tensor and a finite number of its partial derivatives. The Riemann "curvature" tensor contrariwise is a fourth-rank tensor with both antisymmetric and symmetric properties that famously is algebraically expressed in terms of the metric tensor and its first and second partial derivatives. Thus use of the word "curvature" with regard to the Riemann tensor is misleading, and since it can't encompass intuitive curvature, Gauss-Riemann "geometry" oughtn't be termed differential geometry either. That "geometry" is no more than the class of the algebraic functions of the metric and any finite number of the metric's partial derivatives, which it is convenient to organize into generally covariant entities such as the Riemann tensor because those potentially play a role in generally-covariant metric-based field theories.

**Category:** Mathematical Physics

[5] **viXra:1510.0130 [pdf]**
*submitted on 2015-10-15 04:14:17*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 13 Pages.

A novel kind of classical bracket of classical observables is proposed. This bracket is used directly as a derivation* of the commutator of the quantum mechanical observables that are simply obtained by Dirac quantization of the classical observables. Light bending in the presence of a massive object in Schwarzschild’s metric is considered and the above bracket is used to obtain a second quantized equation of the wave function of the photon in this situation via the Dirac quantization.

**Category:** Mathematical Physics

[4] **viXra:1510.0111 [pdf]**
*submitted on 2015-10-13 11:04:50*

**Authors:** V.A.Budarin

**Comments:** 7 Pages. MSC 76D09, doi:10.15587/1729-4061.2015.39886

The paper considers transformation of the equation of motion in stresses for an incompressible Newtonian fluid. The aim of the transformation is to obtain more detailed equations that account for the impact of vortex (rotational) and linear (forward) flows on the process of viscous friction. The transformation method is based on adding zero to the expressions for shear stresses with subsequent distinguishing of rotor velocity function and derivatives characterizing the linear flow. This approach as a form of recording the original equation does not require any additional restrictions. The transformation has resulted in new systems of equations for viscous vortex and vortex-free flows as well as three-dimensional vortex. The obtained equations allow obtaining the known exact solution for the laminar flow (Poiseuille’s formula) and Euler’s differential equation for an ideal fluid. We have shown that the Navier-Stokes equation is a separate case of a more general equation for Newtonian fluid motion. The obtained equations and connections between them allow improvement of the mathematical description of the incompressible fluid flow.

**Category:** Mathematical Physics

[3] **viXra:1510.0104 [pdf]**
*replaced on 2015-10-18 15:08:59*

**Authors:** Algirdas Antano Maknickas

**Comments:** 2 Pages.

It was shown that using spatial transform obtained by applying the difference to spatial global coordinates and time integral of velocities non linear Navier-Stokes equation transforms into parabolic equations

**Category:** Mathematical Physics

[2] **viXra:1510.0063 [pdf]**
*replaced on 2015-12-19 12:19:26*

**Authors:** Harry Watson

**Comments:** 6 Pages.

Let B denote a ball centered at the origin with radius R=(4pi-1/pi). Gravitational forces from a singularity generate rotation about an axis. Internal rotational forces form a vacuous prolate ellipsoid, with major axis (4pi-1/pi) and minor axes {1/pi, 1/pi}. The ball B ejects a volume (4pi/3)(pi^(-2))(4pi-1/pi). This is the volume of the circumscribed prolate ellipsoid. It is also the volume of an elliptical wedge with curved surface area 4/pi and the elliptical sector with curved surface area 4/pi. It is not unreasonable to suppose that the electron is a ball of unit radius. The volume of the electron is V_e = (4pi/3). The ratio of the volume of ball B to the volume of the electron is given by V_B/V_e = (4pi-1/pi)^3 = 1837.392727.... Let V_w be the volume of the wedge of ejecta.
(V_B-V_w)/(V_e) = (4pi-1/pi)^3-(pi^(-2)(4pi-1/pi) = 1836.15
Look at V_w. V_w/V_e = (pi^(-2))(4pi-1/pi) = 1.24098801$. This ejecta easily supports a charged unit ball, whereas the original ball only had the property of gravitational attraction. At this point we have the basic two stable particles, namely the proton and the electron. We then look at the mass ratio of the proton to the electron.
V_p/V_e = (V_B-V_w)/(V_e) = 1836.15
There are several expressions that yield the same numerical value as the previous equation. First among equals is
(4pi)(4pi-1/pi)(4pi-2/pi) = 1836.15
Moreover,
64pi^3-48pi+8/pi = 1836.15
The above equation is the original estimate.
harry.watson@att.net

**Category:** Mathematical Physics

[1] **viXra:1510.0010 [pdf]**
*submitted on 2015-10-01 18:03:19*

**Authors:** Eun Ji Jang, Jihun Cha, Young Kyu Lee, Won Sang Chung

**Comments:** 12 Pages.

In this paper we extend the so-called dual or mirror image
formalism and Caldirola's- Kanai's formalism for damped harmonic oscillator to the case that both frictional coefficient and time-dependent frequency depend on time explicitly.
As an solvable example, we consider the case that frictional coefficient $ \ga (t) = \frac{ \ga_0}{1 + q t} , (q > 0 )$ and angular frequency function $ w(t) = \frac{ w_0}{ 1 + q t } $. For this choice, we construct the quantum harmonic Hamiltonian and express it in terms of $su(2)$ algebra generators. Using the exact invariant for the Hamiltonian and its unitary transform, we solve the time-dependent Schro\"dinger equation with time-dependent frictional coefficient and time-dependent frequency.

**Category:** Mathematical Physics