Band 75, Heft 12

Head-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ -distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.

Based on Biot’s model for saturated porous media, the governing equation of fluid-saturated porous rectangular plates is presented, in which the compressibility of solid particles and fluid and the viscosity of pore fluid is taken into account. A series solution is given for simply-supported fluid-saturated porous plates. The accuracy of the solution is validated by degenerating the fluid-saturated porous rectangular plates into single-phase solid rectangular plates. As a numerical example, the free vibration characteristic and the dynamic response under harmonic loads are analysed. The influence of surface infiltration conditions, porosity, pore fluid permeability coefficient and loading frequency on the free vibration frequency is discussed.

In this paper, we introduce a novel 3D chaotic oscillator which shows megastability without any external excitation. Some important dynamical properties of the proposed novel system were derived and investigated. Data protection application and its security analysis were realized for electrophysiological signals such as ECG, EEG and EMG on a microcomputer. This paper includes both encryption and data hiding processes for high security. Also a user interface was developed. For the encryption process, random numbers were generated by the megastable chaotic oscillator. These random numbers were tested with NIST-800-22 test which is the most widely accepted statistical test suite. The encrypted electrophysiological signals were analyzed by entropy, differential attacks, histogram, correlation, initial condition sensitivity, etc. The results of the analysis have shown that the proposed two level security method can be used in many fields as mobile. The most important feature of this paper is that both encryption and data hiding processes were implemented for electrophysiological signals. The experimental results verify that the proposed method has high security and is suitable for the protection of vital electrophysiological signals.

Blast waves are produced when there is a sudden deposition of a substantial amount of energy into a confined region. It is an area of pressure moving supersonically outward from the source of the explosion. Immediately after the blast, the fore-end of the blast wave is headed by the shock waves, propagating in the outward direction. As the considered problem is highly nonlinear, to find out its solution is a tough task. However, few techniques are available in literature that may give us an approximate analytic solution. Here, the blast wave problem in magnetogasdynamics involving cylindrical shock waves of moderate strength is considered, and approximate analytic solutions with the help of the power series method (or Sakurai’s approach [1]) are found. The magnetic field is supposed to be directed orthogonally to the motion of the gas particles in an ideal medium with infinite electrical conductivity. The density is assumed to be uniform in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in (a0/U)2${\left({a}_{0}/U\right)}^{2}$, where a 0 and U are the velocities of sound in an undisturbed medium and shock front, respectively. We construct solutions for the first-order approximation in closed form. Numerical computations have been performed to determine the flow-field in an ideal magnetogasdynamics. The numerical results obtained in the absence of magnetic field recover the existing results in the literature. Also, these results are found to be in good agreement with those obtained by the Runge–Kutta method of fourth-order. Further, the flow variables are illustrated through figures behind the shock front under the effect of the magnetic field. The interesting fact about the present work is that the solutions to the problem are obtained in the closed form.

We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics and Connes noncommutative geometry program. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic—together they describe an ‘aikyon’. The Lagrangian of the theory is invariant under global unitary transformations and describes gravity and Yang–Mills fields coupled to fermions. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection. We then motivate why an octonionic space is the natural space in which an aikyon evolves. The group of automorphisms in this space is the exceptional Lie group G 2 which has 14 generators [could they stand for the 12 vector bosons and two degrees of freedom of the graviton?]. The aikyon also resembles a closed string, and it has been suggested in the literature that 10-D string theory can be represented as a 2-D string in the 8-D octonionic space. From the work of Cohl Furey and others it is known that the Dixon algebra made from the four division algebras [real numbers, complex numbers, quaternions and octonions] can possibly describe the symmetries of the standard model. In the present paper we outline how in our work the Dixon algebra arises naturally and could lead to a unification of gravity with the standard model. From this matrix dynamics, local quantum field theory arises as a low energy limit of this Planck scale dynamics of aikyons, and classical general relativity arises as a consequence of spontaneous localisation of a large number of entangled aikyons. We propose that classical curved space–time and Yang–Mills fields arise from an effective gauging which results from the collection of symmetry groups of the spontaneously localised fermions. Our work suggests that we live in an eight-dimensional octonionic universe, four of these dimensions constitute space–time and the other four constitute the octonionic internal directions on which the standard model forces live.

In order to elucidate the quantum ground state structure of nonrelativistic condensates, we explicitly construct the ground state wave function for multiple species of bosons, describing either superconductivity or superfluidity. Since each field Ψ j carries a phase θ j and the Lagrangian is invariant under rotations θ j  →  θ j  +  α j for independent α j , one can investigate the corresponding wave function overlap between a pair of ground states 〈G|G′〉$\langle G\vert {G}^{\prime }\rangle $ differing by these phases. We operate in the infinite volume limit and use a particular prescription to define these states by utilizing the position space kernel and regulating the UV modes. We show that this overlap vanishes for most pairs of rotations, including θ j  →  θ j  +  m j   ϵ , where m j is the mass of each species, while it is unchanged under the transformation θ j  →  θ j  +  q j   ϵ , where q j is the charge of each species. We explain that this is consistent with the distinction between a superfluid, in which there is a nontrivial conserved number, and the superconductor, in which the electric field and conserved charge is screened, while it is compatible with a nonzero order parameter in both cases. Moreover, we find that this bulk ground state wave function overlap directly reflects the Goldstone boson structure of the effective theory and provides a useful diagnostic of its physical phase.

The elastic, thermal and ultrasonic properties of zirconium nanowire (Zr-NW) have been investigated at room temperature. The second and third order elastic constants (SOECs and TOECs) of Zr-NW have been figured out using the Lennard–Jones Potential model. SOECs have been used to find out the Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, Pugh’s ratio, Zener anisotropic factor and ultrasonic velocities. Further these associated parameters of Zr-NW have been utilized for the evaluation of the Grüneisen parameters, thermal conductivity, thermal relaxation time, acoustic coupling constants and ultrasonic attenuation. On the basis of the above analyzed properties of Zr-NW, some characteristics features of the chosen nanowire connected with ultrasonic and thermo-physical parameters have been discussed.

The Michelson liquid-level sensor based on silver coated the end face of the three-core fiber reflection structure has been proposed to measure continuous or discrete liquid level. The Michelson interference structure can be obtained by the combination of the single-mode optical fiber and the three-core optical fiber with the silver film coated on the other end face of it. The inter-mode interference can be obtained by the fiber-core mismatch at the fusion joint. The liquid level can be measured by monitoring the dip wavelength shift of the interference spectrum. The results indicate that the sensitivity of the liquid-level sensor will decrease with the increasing sensing length. The sensing length of 30 mm is selected to investigate the performance of the sensor. The sensitivity of water level is reached as high as 392.83 pm/mm with an excellent linearity of 0.99946. Interestingly, the sensitivity of the sensor increases with the liquid refractive index and the sensitivity of the refractive index for NaCl solution is 4410.74 pm/mm/RIU. The performance of the sensor is very stable in the range of 20–90 °C. The maximum drift for temperature is 0.3001 nm. The sensor can be applied to the measurement of the liquid level in different environments.