Topological Phase Transition of Non-Hermitian Crosslinked Chain

The contents of topological classification of matter are enriched by non-Hermiticity, such as exceptional points, bulk-edge correspondence, and skin effects. Physically, gain and loss can be introduced by imaginary on-site potentials of lattice Hamiltonians, and the topological phase transition for a cross-linked chain in the presence of such non-Hermiticity is investigated. The topological phase diagram in terms of a winding number is obtained analytically with phase boundaries coinciding with the surfaces of exceptional points. The topologically original edge states with distribution mainly at the joints between domains of different phases are protected even for long chains. The non-Hermitian topological feature can also be reflected by vortex structures in the vector fields of complex eigenenergies, expected values of Pauli matrices, and trajectories of these quantities. This model may be implemented in coupled photonic crystals, fermions trapped in optical lattice, or non-Hermitian electrical-circuit lattices, and the edge states are immune to various kinds of disorders until topological phase transition occurs. This work gives insight into the influence of non-Hermiticity on topological phase of matter.     

Modified Gerchberg–Saxton (G-S) Algorithm and Its Application

The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which n plaintexts can be recovered from n ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.     

Experimental Investigation of the Effect of Purge Flow and Main Flow Interaction in a Low-Speed Turbine Cascade Passage

In order to protect the vulnerable turbine components from extreme high temperature, coolant flow is introduced from the compressor to the disk cavity, inevitably interacting with the main flow. This paper describes an experimental investigation of the interaction between the main flow and the purge flow in a low-speed turbine cascade with three purge flow rates, Cm = 0, Cm = 1%, and Cm = 2%. In order to study the effect of the interaction between the main flow and the purge flow on the secondary flows, a Rortex method developed by Liu Chaoquan is introduced to identify the vortex in the flow field. In the meantime, a method to calculate the mean entropy production rate based on the particle image velocimetry (PIV) result is adopted to investigate the flow loss. The PIV result indicates that the purge flow has a prominent impact on the flow field of the cascade passage, changing the velocity distribution that induces a local blockage area. The results of vortex identification show that the purge flow promotes the generation of the passage vortex near the suction side. In addition, the purge flow makes the passage vortex migrate to the tip wall direction, enlarging the region affected by the secondary flow. The mean entropy production (MEP) result shows that the flow loss is mainly caused by the passage vortex. The coincidence of the high-MEP region and the location of the passage vortex indicates that the purge flow increases the secondary flow loss by affecting the formation and the migration of the passage vortex.     

Maghemite/poly(<Emphasis Type="SmallCaps">d,l</Emphasis>-lactide-<Emphasis Type="Italic">co</Emphasis>-glycolyde) composite nanoplatform for therapeutic applications

A reproducible methodology is described for the synthesis, by following the double emulsion/solvent evaporation technique, of magnetic nanocomposites (average diameter ≈ 135 nm) consisting of maghemite nuclei and a biodegradable poly(d,l-lactide-co-glycolide) matrix. The heterogeneous structure of the nanoparticles can confer them the responsiveness to magnetic gradients, giving both the possibility of their use as a drug delivery system and adequate heating characteristics for a hyperthermia effect. The physical chemistry of the nanocomposites was extensively characterized, this establishing that their surface properties were similar to that of pure poly(d,l-lactide-co-glycolide). From an electrokinetic point of view, zeta potential determinations (as a function of the ionic strength, and pH) pointed out that the nanocomposites were almost indistinguishable from the copolymer. The surface thermodynamic analysis agreed with the electrophoretic one in suggesting that the coverage of the magnetic nuclei was complete, since the hydrophilic nature of maghemite was modified and the nanoparticles turned into hydrophobic, just like the copolymer, when they were embedded into poly(d,l-lactide-co-glycolide). The magnetic behaviours of the composite nanoparticles were also checked. Their heating properties were studied in vitro in a high-frequency alternating gradient of magnetic field: a stable maximum temperature of 47 °C was satisfactorily achieved within 45 min. Blood compatibility of the nanocomposites was also defined in vitro. To our knowledge, this is the first time that such kind of magnetic-sensitive nanoformulation with very promising characteristics (e.g. blood compatibility, magnetic drug targeting capabilities, and hyperthermia) has been developed for therapeutic purposes.     

The electrical conductivity of chloride melts

The interrelationship between electrical conductivity, molar volume and enthalpy of mixing was studied for molten chlorides and their mixtures. The dependence of electrical conductivity and activation energy on the molar volume is different for various groups of salts. The dependence of specific conductivity on molar volume obtained for molten alkali chlorides was found to be similar to other chloride salts. The specific conductivity of binary mixtures that lack strong chemical interactions between the components can also be described by the proposed empirical equation. The enthalpy of mixing should be taken into consideration for these chemical interactions.     

Geometric phase decomposition in the basis of Hermite-Gaussian functions

The work presents geometric phase decomposition for analytical signals using Hermite-Gaussian functions. The decomposition is based on the time-frequency distribution with reassigned and multi-tapered spectrogram resulting in increased phase estimation resolution. Numerical analysis is applied to a number of SU(2) evolutions, such as spin-1/2 particle in a static and rotating magnetic field, as well as polarization rotation of a plane wave in optically active medium. Geometric phase decomposition results are provided also for quantum harmonic oscillator and a radiation field of an electric dipole exited by a short pulse.     

A study on the effect of filling factor for laser action in dielectric random media

In a random system composed of dielectric materials, laser action is expected to occur from the light localization caused by multiple scattering and interference effect. The wavelengths at which the laser oscillation occurs in random media depend on the mean free path of continuous scattering. Since the mean free path of continuous scattering is dependent on the filling factor, it is important to investigate systematically the effect of the filling factor for the laser action. In the present study, we calculate the Poynting vectors of the light emitted from two-dimensional random media consisting of dielectric rods with population inversion modeled by the negative imaginary part of relative permittivity. The spectra of the radiated Poynting vectors from the two-dimensional random media are shown for several different filling factors and for various values of population inversion. We try to find laser generation which occurs at low population inversion and discuss about the threshold of laser action occurring in dielectric structures with different filling factors. We also study the spacial distribution of the electric field amplitude in several frequency regions where light strongly amplifies.     

Statistical Mechanics of a Simplified Bipartite Matching Problem: An Analytical Treatment

We perform an analytical study of a simplified bipartite matching problem in which there exists a constant matching energy, and both heterosexual and homosexual pairings are allowed. We obtain the partition function in a closed analytical form and we calculate the corresponding thermodynamic functions of this model. We conclude that the model is favored at high temperatures, for which the probabilities of heterosexual and homosexual pairs tend to become equal. In the limits of low and high temperatures, the system is extensive, however this property is lost in the general case. There exists a relation between the matching energies for which the system becomes more stable under external (thermal) perturbations. As the difference of energies between the two possible matches increases the system becomes more ordered, while the maximum of entropy is achieved when these energies are equal. In this limit, there is a first order phase transition between two phases with constant entropy.     

Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β≪1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α=〈s ⁴〉−3〈s ²〉²>0, i.e. in the region which we call Gaussian subjugation, where 〈s ^k 〉 denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass −lnβ and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in β.     

Magnetic response of split ring resonator metamaterials: From effective medium dispersion to photonic band gaps

On systematically investigating the electromagnetic response of periodic split-ring resonator (SRR) metamaterials as a function of the size-to-wavelength (a/λ) ratio, we find that the stop bands due to the geometric resonances of the SRR weaken with increasing (a/λ) ratio, and are eventually replaced by stop bands due to Bragg scattering. Our study traces the behaviour of SRR-based metamaterials as the resonance frequency increases and the wavelength of the radiation finally becomes comparable to the size of the unit cell of the metamaterial. In the intermediate stages, the dispersion of the SRR metamaterial can still be described as due to a localized magnetic resonances while Bragg scattering finally becomes the dominant phenomenon as a/λ∼1/2.