Encryption and decryption using a sandwich phase diffuser made by using two speckle patterns and placed in the Fourier plane: Simulation results

In the present paper, we describe the encryption and decryption of two-dimensional images. The encryption is done by employing a sandwich phase diffuser made by using two elongated speckle patterns, and placed in the Fourier plane of a double random phase encoding system. After encryption, the two constituent phase diffusers of such a sandwich diffuser are separated. During decryption, if the conjugate of either of the two elongated phase speckle patterns is used, the image cannot be retrieved. Correct decryption is also not possible if a sandwich diffuser with any of the phase speckle patterns is shifted in position with respect to the other. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugate of the sandwich diffuser, and then the product is further Fourier transformed. It is possible to generate the image only if both the elongated phase speckle patterns are matched point-to-point and then the proper conjugate is made. The use of elongated speckle patterns in constituting a sandwich phase diffuser makes the system less complicated as compared to the use of a sandwich diffuser made with normal speckle patterns, enabling an easy alignment of the random phase diffuser at the time of rejoining the constituent diffusers for making the right key. The ease of alignment is due to the reduction of the requirement of 360° scanning at the time of rejoining these diffusers with little reduction in the security of the system. Simulation results are presented in support of the proposed idea. For optical implementation, the decrypted image may be obtained by generating a phase conjugate wave by the phase conjugation technique, and passing through the same sandwich phase diffuser. To evaluate the reliability of the technique, mean square error (MSE) between the decrypted and original image has been calculated.     

Experimental investigation and thermodynamic calculation of the Bi-Ga-Sn phase equilibria

Binary thermodynamic data, successfully used for phase diagram calculations of binary systems Bi-Ga, Bi-Sn, and Ga-Sn, were used for prediction of phase equilibria in ternary Bi-Ga-Sn system. The thermodynamic functions, such as enthalpy of formation and activity, were calculated using the Redlich-Kister-Muggianu model and compared with experimental data reported in the literature. The liquidus surface, invariant equilibria and three vertical sections with molar ratio Ga:Sn=1, Bi:Sn=1 and Bi:Ga=1 of the Bi-Ga-Sn ternary system were calculated by the CALPHAD method. Alloys, situated along three calculated vertical sections, were investigated by Differential Scanning Calorimetry (DSC). The experimentally determined phase transition temperatures were compared with calculation results and good mutual agreement was noticed.     

Structural and electrical study of Ce-substituted bismuth vanadate

Samples of Ce^IV-substituted bismuth vanadate, formulated as Bi₄Ce_xV_2−xO_{11−(x/2)−δ}; 0≤x≤0.30, were synthesized by solid-state reactions. The phase structure and electrical conductivity were investigated using X-ray powder diffraction, FT-IR, differential thermal analysis and AC impedance spectroscopy. For a low composition range, two phase transitions, α↔β and β↔γ, were exhibited in which the system mimics in most events the parent compound. Impedance analysis evidenced no relationship between the blocking effect of charge carriers and structural changes at ambient temperatures. However, the temperature dependence of conductivity was correlated with the stability region of various phases within the system.     

Phase transition, structural and electrical properties of Pb(Zn1/3Nb2/3)O3-doped Pb(Ni1/3Nb2/3)O3-PbTiO3 ceramics prepared by solid-state reaction method

Phase pure perovskite (1−x−y)Pb(Ni_1/3Nb_2/3)O₃-xPb(Zn_1/3Nb_2/3)O₃-yPbTiO₃ (PNN-PZN-PT) ferroelectric ceramics were prepared by conventional solid-state reaction method via a B-site oxide mixing route. The PNN-PZN-PT ceramics sintered at the optimized condition of 1185 °C for 2 h exhibit high relative density and rather homogenous microstructure. With the increase of PbTiO₃ (PT) content, crystal structure and electrical properties of the synthesized PNN-PZN-PT ceramics exhibit successive phase transformation. A morphotropic phase boundary (MPB) is supposed to form in (0.9−x)PNN-0.1PZN-xPT at a region of x=32-36 mol% confirmed by X-ray diffraction (XRD) measurement and dielectric measurement. The MPB composition can be pictured as providing a “bridge” connecting rhombohedral ferroelectric (FE) phase and tetragonal one since crystal structure of the MPB composition is similar to both the rhombohedral and tetragonal lattices. Dielectric response of the sintered PNN-PZN-PT ceramics also exhibits successive phase-transition character. 0.64PNN-0.1PZN-0.26PT exhibits broad, diffused and frequency dependent dielectric peaks indicating a character of diffused FE-paraelectric (PE) phase transition of relaxor ferroelectrics and 0.40PNN-0.1PZN-0.50PT exhibits narrow, sharp and frequency independent dielectric peaks indicating a character of first-order FE-PE phase transition of normal ferroelectrics. The FE-PE phase transition of 0.56PNN-0.1PZN-0.34PT is nearly first-order with some diffused character, which also exhibits the largest value of piezoelectric constant d₃₃ of 462pC/N.     

Nanocrystalline BaTiO3, doped with Eu and Cr: Fluorescence spectroscopy and spontaneous ordering effects

The results of optical studies of Cr³⁺ and Eu³⁺ ions doped nanocrystalline ferroelectric BaTiO₃ produced by the sol-gel process (particle size 20-40 nm) are reported. The Cr³⁺ impurity ions ²E-⁴A₂ (R-lines) fluorescence spectra in BaTiO₃ revealed significant differences from that reported in literature for the bulk material. At least three types of Cr³⁺ centers were found in the spectra. The temperature dependence of optical second harmonic generation in nanocrystalline BaTiO₃: Eu³⁺ shows a strong hysteresis in C_4v-O_h ferroelectric phase transition region, which was explained by the ordering effects in the system of electric dipole moments of dipole nanocrystals. The temperature dependencies of radiative lifetime of Eu³⁺⁵D₀ excited level reveal some hysteresis too. The possibility of influence of the ordering in the system of BaTiO₃:Eu³⁺ nanocrystals on the effective index of refraction of the medium and thus on the Eu³⁺⁵D₀ radiative lifetime, due to the local field effects is discussed.     

J-matrix method of scattering in one dimension: The nonrelativistic theory

We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.     

Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation

In this paper we present and compare two unconditionally energy stable finite-difference schemes for the phase field crystal equation. The first is a one-step scheme based on a convex splitting of a discrete energy by Wise et al. [S.M. Wise, C. Wang, J.S. Lowengrub, An energy stable and convergent finite-difference scheme for the phase field crystal equation, SIAM J. Numer. Anal., in press]. In this scheme, which is first order in time and second order in space, the discrete energy is non-increasing for any time step. The second scheme we consider is a new, fully second-order two-step algorithm. In the new scheme, the discrete energy is bounded by its initial value for any time step. In both methods, the equations at the implicit time level are nonlinear but represent the gradients of strictly convex functions and are thus uniquely solvable, regardless of time step-size. We solve the nonlinear equations using an efficient nonlinear multigrid method. Numerical simulations are presented and confirm the stability, efficiency and accuracy of the schemes.     

A phase field model for vesicle–substrate adhesion

In this paper, a phase field model is developed for vesicle adhesion involving complex substrate and vesicle geometries. The model takes into account an adhesion potential that depends on the distance of vesicle to the substrate. A variational problem is solved in a 3D computational domain by minimizing the contribution of bending elastic energy and the adhesion energy under the constraints of total surface area and volume, described via a phase function. An adaptive finite element method is used to efficiently compute the numerical solutions of the model. The computational results are validated through comparison of several axisymmetric shapes with the sharp-interface ODE solution. Moreover, we compute shapes for non-axisymmetric situations to support the observation that concave substrates favor adhesion.     

Surface reconstruction of clean bcc-Fe{1 1 0}: A quasi-hexagonal top-layer with periodic height modulation

Hexagonal-pillar shaped pure Fe single crystal whiskers with six {1 1 0} side planes were obtained by means of chemical vapor deposition. Atomically resolved scanning tunneling microscopy images obtained on the {1 1 0} surface showed a quasi-hexagonal atomic array with mesoscopic-range periodic height modulation of about 1/3 of an atomic step. This height modulation was found to be a result of an interference between the quasi-hexagonal top-layer and the sub-surface bcc-Fe{1 1 0} layer. Unit vectors of the mesoscopic-range modulation turned out to be expressed as , where and are the primitive vectors of the two-dimensional atomic array in the top-layer and those in the sub-surface layer, respectively. The two-dimensional density of atoms in the top-layer is slightly higher by 0.46% than that in the sub-surface layer.     

Exploring the phase diagram of strongly interacting matter; news from SPS and RHIC

Two experimental programs are aiming to study nuclear collisions in the energy regime in order to explore an essential part of the phase diagram of strongly interacting matter. The programs are motivated by observations that indicate a phase transition to take place in this energy domain: the onset of deconfinement. The STAR collaboration proposes an energy scan in the Relativistic Heavy Ion Collider (RHIC) at BNL. The ongoing program of the NA61/SHINE experiment consists of a two-dimensional energy-system size scan in nuclear and elementary collisions. The goal of both programs is to study the properties of the onset of deconfinement and to eventually discover the conjectured critical point of strongly interacting matter. A comparison of the strengths and limitations reveals the complementarity of the two programs.