Independent Real Parameters Research Articles

Adjustable Phase-Amplitude-Phase Acoustic Metasurface for the Implementation of Arbitrary Impedance Matrices.

Impedance metasurfaces enable accurate regulation of acoustic fields. However, they can hardly supply a flexible response as such perfect operation is accompanied by stringent requirements on the design of unit cells. Actually, an arbitrary lossless and passive target impedance matrix requires the tuning of 3 independent real parameters. The set composed of a reflection phase, a transmission amplitude, and a transmission phase, enables the representation of an arbitrary impedance matrix, possibly possessing singular elements. In this paper, a mechanism of phase-amplitude-phase modulation (PAP modulation) is developed for the generic design of the unit cells of acoustic impedance metasurfaces. Adjustable acoustic impedance metasurfaces are further available under this framework. An impedance unit with 3 mobile parts is designed based on this idea. The assembled metasurface can handle different incidences for acoustic field manipulation at a given frequency. Beam steering and beam splitting are considered as demonstration examples and are verified by numerical simulation and experiment. PAP modulation enriches the design of acoustic impedance metasurfaces and extends the range of application of impedance theory.

Analytic construction of multi-brane solutions in cubic string field theory for any brane number

Abstract We present an analytic construction of multi-brane solutions with any integer brane number in cubic open string field theory (CSFT) on the basis of the ${K\!Bc}$ algebra. Our solution is given in the pure-gauge form $\Psi=U{Q_\textrm{B}} U^{-1}$ by a unitary string field $U$, which we choose to satisfy two requirements. First, the energy density of the solution should reproduce that of the $(N+1)$-branes. Second, the equations of motion (EOM) of the solution should hold against the solution itself. In spite of the pure-gauge form of $\Psi$, these two conditions are non-trivial ones due to the singularity at $K=0$. For the $(N+1)$-brane solution, our $U$ is specified by $[N/2]$ independent real parameters $\alpha_k$. For the 2-brane ($N=1$), the solution is unique and reproduces the known one. We find that $\alpha_k$ satisfying the two conditions indeed exist as far as we have tested for various integer values of $N\ (=2, 3, 4, 5, \ldots)$. Our multi-brane solutions consisting only of the elements of the ${K\!Bc}$ algebra have the problem that the EOM is not satisfied against the Fock states and therefore are not complete ones. However, our construction should be an important step toward understanding the topological nature of CSFT, which has similarities to the Chern–Simons theory in three dimensions.

Rotating Liquid Drops and Delaunay Surfaces

Here we consider the problem of finding the equilibrium configurations of a rotating liquid drop, paying special attention to the cases when the droplet takes the shape of a Delaunay surface. By making use of the canonical forms of the elliptic integrals and the Jacobian elliptic functions we have derived several explicit parameterizations of the Delaunay surfaces. They are expressed relying on two independent real parameters accounting respectively the size and the shape so that all possible Delaunay surfaces are represented in a unified way.

Contact interactions and Kronig–Penney models in Hermitian and symmetric quantum mechanics

The delta function potential is a simple model of zero-range contact interaction in non-relativistic quantum mechanics in one dimension. The Kronig–Penney model is a one-dimensional periodic array of delta functions and provides a simple illustration of energy bands in a crystal. Here we investigate contact interactions that generalize the delta function potential and corresponding generalizations of the Kronig–Penney model within conventional and symmetric quantum mechanics. In conventional Hermitian quantum mechanics we determine the most general contact interaction compatible with self-adjointness and in quantum mechanics we consider interactions that respect symmetry under the transformation where denotes parity and denotes time reversal. In both cases we find that the most general interaction has four independent real parameters and depending on the values of those parameters the contact interaction can support zero, one or two bound states. By contrast the conventional delta function can only support zero or one bound state. In the symmetric case moreover the two bound state energies can be both real or a complex conjugate pair. The transition from real to complex bound state energies corresponds to the spontaneous breaking of symmetry. The scattering states for the symmetric case are also found to exhibit spontaneous breaking of symmetry wherein the eigenvalues of the non-unitary S-matrix depart the unit circle in the complex plane. We also investigate the energy bands when the generalized contact interactions are repeated periodically in space in one dimension. In the Hermitian case we find that the two bound states result in two narrow bands generically separated by a gap. These bands intersect at a single point in the Brillouin zone as the interaction parameters are varied. Near the intersection the bands form a massless Dirac cone. In the symmetric case we find that as the parameters of the contact interaction are varied the two bound state bands undergo a symmetry breaking transition wherein the two band energies go from being real to being a complex conjugate pair. The symmetric Kronig–Penney model provides a simple soluble example of the transition which has the same form as in other models of symmetric crystals.

Texture and cofactor zeros of the neutrino mass matrix

We study Majorana neutrino mass matrices that have two texture zeros, or two cofactor zeros, or one texture zero and one cofactor zero. The two texture/cofactor zero conditions give four constraints, which in conjunction with the five measured oscillation parameters completely determine the nine independent real parameters of the neutrino mass matrix. We also study the implications that future measurements of neutrinoless double beta decay and the Dirac CP phase will have on these cases.

The Infinite Square Well with a Point Interaction: A Discussion on the Different Parameterizations

The construction of Dirac delta type potentials has been achieved with the use of the theory of self adjoint extensions of non-self adjoint formally Hermitian (symmetric) operators. The application of this formalism to investigate the possible self adjoint extensions of the one dimensional kinematic operator $K=-d^2/dx^2$ on the infinite square well potential is quite illustrative and has been given elsewhere. This requires the definition and use of four independent real parameters, which relate the boundary values of the wave functions at the walls. By means of a different approach, that fixes matching conditions at the origin for the wave functions, it is possible to define a perturbation of the type $a\delta(x)+b\delta'(x)$, thus depending on two parameters, on the infinite square well. The objective of this paper is to investigate whether these two approaches are compatible in the sense that perturbations like $a\delta(x)+b\delta'(x)$ can be fixed and determined using the first approach.

The checkerboard family of entangled states of two qutrits

Abstract By modifying the method of Bruß and Peres, we construct two new families of entangled two qutrit states. For all density matrices ρ in these families we have ρ ij = 0 for i + j odd. The first family depends on 27 independent real parameters and includes both PPT and NPT states. The second family consists of PPT entangled states. The number of independent real parameters of this family is ≥ 11

Optimal Polarization Demultiplexing for Coherent Optical Communications Systems

Spectrally-efficient optical communications systems employ polarization division multiplexing (PDM) as a practical solution, in order to double the capacity of a fiber link. Polarization demultiplexing can be performed electronically, using polarization-diversity coherent optical receivers. The primary goal of this paper is the optimal design, using the maximum-likelihood criterion, of polarization-diversity coherent optical receivers for polarization-multiplexed optical signals, in the absence of polarization mode dispersion (PMD). It is shown that simultaneous joint estimation of the symbols, over the two received states of polarization, yields optimal performance, in the absence of phase noise and intermediate frequency offset. In contrast, the commonly used zero-forcing polarization demultiplexer, followed by individual demodulation of the polarization-multiplexed tributaries, exhibits inferior performance, and becomes optimal only if the channel transfer matrix is unitary, e.g., in the absence of polarization dependent loss (PDL), and if the noise components at the polarization diversity branches have equal variances. In this special case, the zero-forcing polarization demultiplexer can be implemented by a 2 ? 2 lattice adaptive filter, which is controlled by only two independent real parameters. These parameters can be computed recursively using the constant modulus algorithm (CMA). We evaluate, by simulation, the performance of the aforementioned zero-forcing polarization demultiplexer in coherent optical communication systems using PDM quadrature phase shift keying (QPSK) signals. We show that it is, by far, superior, in terms of convergence accuracy and speed, compared to conventional CMA-based polarization demultiplexers. Finally, we experimentally test the robustness of the proposed constrained CMA polarization demultiplexer to realistic imperfections of polarization-diversity coherent optical receivers. The PMD and PDL tolerance of the proposed demultiplexer can be used as a benchmark in order to compare the performance of more sophisticated adaptive electronic PMD/PDL equalizers.

A minimal S3-invariant extension of the Standard Model

We present a minimal S3-invariant extension of the Standard Model. We find that in leptonic sector, the exact S3 × Z2 symmetry, which allows 6 real independent parameters, is consistent with experimental data. With exact S3 symmetry, there are 10 real independent parameters and one independent phase, on which the mixing matrix VCKM depends. A set of values of these parameters that are consistent with experimental observations is given.

Deformations and the Karoo aquifers of South Africa

This paper introduces a new three-dimensional poro-elastic model for the flow of groundwater through an aquifer. The main purpose with the model was to investigate to what extent deformations are responsible for the observed physical behaviour of Karoo aquifers in South Africa, which cannot be explained with the conventional porous flow models. This applies in particular to the effect that linear and nonlinear deformations may have on the behaviour of the aquifer. The model not only showed that many of the observations can be explained by the nonlinear deformation of the aquifer, but also that the parameters specific storativity and hydraulic conductivity (and their derivatives storativity and transmissivity) are not independent parameters, as assumed in the conventional literature on groundwater motion. The real independent parameters are the rate at which a borehole in the aquifer is pumped and the mechanical properties of the aquifer. A comparison of the model results and known transmissivities of these aquifers showed that the aquifers are highly anisotropic.

The Flavor Symmetry

Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S_3, we suggest a minimal S_3 invariant extension of the standard model. We find that in the leptonic sector, the exact S_3 x Z_2 symmetry, which allows 6 real independent parameters with two CP-violating phases, is consistent with experimental data and predicts a maximal mixing of the atmospheric neutrinos, and that the third neutrino is the lightest neutrino. With the exact S_3 only, there are 10 real parameters and five phases in the quark sector. A set of values of these parameters that are consistent with experimental observations is given.

Backward and forward scattering of electromagnetic waves from partially aligned axially symmetric particles

The problem of backward and forward scattering of electromagnetic waves from tenuous collections of partially aligned axially symmetric particles is dealt with. Particular attention is paid to symmetry relations: It is demonstrated, by way of symmetry considerations alone, that the ensemble-averaged backward and forward-scattering Mueller matrices contain, in general, five real independent parameters. Analytical expressions for the elements of the Mueller matrices are derived by use of the T-matrix analytical orientation-averaging technique. The resulting formulas are well suited for numerical computation since the maximum order of nested summations is two. A software implementation of this computational scheme is publicly available on the World Wide Web at http://irctr.et.tudelft.nl/~Skaropoulos.

Carbon deposition in Si as a consequence of H and He irradiations: A systematic study

In the present work we have investigated the influence of different parameters that determine the C deposition on a Si target. Among them we have studied the pressure of the irradiation chamber, the implantation fluence, the current density, the target temperature, the energy of the beam, the charge state of the ion, the ion species and the molecular state of the irradiation beam. In order to determine the quantity of C deposited on the Si substrate we have used the Rutherford backscattering/channeling technique together with the resonant C12(α,α)12C reaction. After careful analysis we arrived at the conclusion that the real independent parameters are the pressure of the irradiation chamber, the temperature of the target, the irradiation time and the electronic stopping power of the ion–target combination.

Partially polarized light and multiphoton processes

It was shown that in processes involving absorption or stimulated emission of n photons of a partially polarized wave, polarization must be described by n(n+2) real independent parameters (the nth-order polarization parameters). Description of polarization by means of three parameters, e.g., the Stokes parameters, and the use of the photon density polarization matrix is justified only when one considers one-photon processes or intensity transmission of a polarization filter. The second-order polarization parameters were expressed in terms of directly measurable quantities (intensity correlation functions), and their relation to the Stokes parameters was established. The simple example of unpolarized (natural) light was considered, and the explicit form of the two-photon polarization matrix was derived for that case. It was also shown that the natural light is unpolarized in all orders and that zero Stokes parameters, in particular, do not necessarily mean that the light is unpolarized.

Nine-parameter electrovac metric involving rational functions

An analytically extended nine-parameter family of the electrovac rational function solutions of the Einstein-Maxwell equations generalizing the Chen-Guo-Ernst class of hyperextreme spacetimes is presented. The general four-soliton asymptotically flat solution possessing the equatorial symmetry and involving five independent real parameters is derived in a concise analytical form and its relevance to the equilibrium problem of two extreme particles is discussed.

Experimental signatures of fermiophobic Higgs bosons

The most general Two Higgs Doublet Model potential without explicit CP violation depends on 10 real independent parameters. Excluding spontaneous CP violation results in two 7 parameter models. Although both models give rise to 5 scalar particles and 2 mixing angles, the resulting phenomenology of the scalar sectors is different. If flavour changing neutral currents at tree level are to be avoided, one has, in both cases, four alternative ways of introducing the fermion couplings. In one of these models the mixing angle of the CP even sector can be chosen in such a way that the fermion couplings to the lightest scalar Higgs boson vanishes. At the same time it is possible to suppress the fermion couplings to the charged and pseudo-scalar Higgs bosons by appropriately choosing the mixing angle of the CP odd sector. We investigate the phenomenology of both models in the fermiophobic limit and present the different branching ratios for the decays of the scalar particles. We use the present experimental results from the LEP collider to constrain the models.

Energy-scale dependence of the lepton flavor-mixing matrix

We study an energy-scale dependence of the lepton flavor-mixing matrix in the minimal supersymmetric standard model with the effective dimension-five operators, which give Majorana masses of neutrinos. We analyze the renormalization group equations of the coefficients ( $\kappa_{ij}$ ) of these effective operators under an approximation that neglects terms of order $\kappa^2$ . We find that only $n_\mathrm{g}-1$ (where $n_\mathrm{g}$ is the generation number) real independent parameters in the lepton flavor-mixing matrix depend on the energy scale. In particular, all the phases in $\kappa$ are scale-independent.

Is there a light fermiophobic Higgs boson?

The most general two Higgs doublet model potential without explicit $\mathrm{CP}$ violation depends on 10 real independent parameters. There are two different ways of restricting this potential to 7 independent parameters. This gives rise to two different potentials, ${V}_{(A)}$ and ${V}_{(B)}.$ The phenomenology of the two models is different, because some trilinear and quartic Higgs couplings are different. As an illustration, we calculate the decay width of ${h}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma},$ where precisely due to the different trilinear couplings the loop of the charged Higgs boson gives different contributions. We also discuss the possibility for the existence of a light fermiophobic Higgs boson.

Energy-scale dependence of the lepton flavor-mixing matrix

We study an energy-scale dependence of the lepton-flavor-mixing matrix in the minimal supersymmetric standard model with the effective dimension-five operators which give the masses of neutrinos. We analyze the renormalization group equations of kappa_{ij}s which are coefficients of these effective operators under the approximation to neglect the corrections of O(\kappa^2). As a consequence, we find that all phases in $\kappa$ do not depend on the energy-scale, and that only n_g-1 (n_g: generation number) real independent parameters in the lepton-flavor-mixing matrix depend on the energy-scale.

The general solution of the real graded contractions of

The general solution of the graded contraction equations for a grading of the real compact simple Lie algebra so(N+1) is presented in an explicit way. It turns out to depend on independent real parameters. The structure of the general graded contractions is displayed for the low-dimensional cases, and kinematical algebras are shown to appear straightforwardly. The geometrical (or physical) meaning of the contraction parameters as curvatures is also analysed; in particular, for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous spacetimes.