Symmetry Model Research Articles

Location of hydrogen atoms in hydronium jarosite

Various models for the crystal structure of hydronium jarosite were determined from Rietveld refinements against neutron powder diffraction patterns collected at ambient temperature and also single-crystal X-ray diffraction data. The possibility of a lower symmetry space group for hydronium jarosite that has been suggested by the literature was investigated. It was found the space group is best described as \(R\bar{3}m\), the same for other jarosite minerals. The hydronium oxygen atom was found to occupy the \(\overline{3} m\) site (3a Wyckoff site). Inadequately refined hydronium bond angles and bond distances without the use of restraints are due to thermal motion and disorder of the hydronium hydrogen atoms across numerous orientations. However, the acquired data do not permit a precise determination of these orientations; the main feature up/down disorder of hydronium is clear. Thus, the highest symmetry model with the least disorder necessary to explain all data was chosen: The hydronium hydrogen atoms were modeled to occupy an m (18 h Wyckoff site) with 50 % fractional occupancy, leading to disorder across two orientations. A rigid body description of the hydronium ion rotated by 60° with H–O–H bond angles of 112° and O–H distances of 0.96 Å was optimal. This rigid body refinement suggests that hydrogen bonds between hydronium hydrogen atoms and basal sulfate oxygen atoms are not predominant. Instead, hydrogen bonds are formed between hydronium hydrogen atoms and hydroxyl oxygen atoms. The structure of hydronium alunite is expected to be similar given that alunite supergroup minerals are isostructural.

Leptogenesis in \(A_4\) Flavor Symmetry Model by Renormalization Group Evolution

We study how leptogenesis can be implemented in the seesaw models with \(A_4\) flavor symmetry, which lead to the tri-bimaximalneutrino mixing matrix. By considering renormalzation groupevolution from a high energy scale of flavor symmetry breaking(the GUT scale is assumed) to the low energy scale of relevantphenomena, the off-diagonal terms in a combination of DiracYukawa-coupling matrix can be generated. As aresult, the flavored leptogenesis is successfully realized. Wealso investigate how the effective light neutrino mass \(|\langle m_{ee}\rangle |\) associated with neutrinoless double beta decaycan be predicted byimposing the experimental data on the low energy observables. Wefind a link between the leptogenesis and the neutrinoless doublebeta decay characterized by \(|\langle m_{ee}\rangle|\) through ahigh energy CP phase $\phi$, which is correlated with the lowenergy Majorana CP phases. It is shown that the predictions of \(|\langle m_{ee}\rangle|\) for some fixed parameters of the highenergy physics can be constrained by the current observation ofbaryon asymmetry.

Propagation of Lamb waves in one-dimensional radial phononic crystal plates with periodic corrugations

In this paper, we theoretically investigate the propagation characteristics of Lamb waves in one-dimensional radial phononic crystal plates with periodic corrugations. The dispersion relations, the power transmission spectra, and the displacement fields of the eigenmodes are calculated by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. The axial symmetry model is validated by three-dimensional finite element model in rectangular coordinates. The effects of the geometrical parameters on the band gaps are further explored numerically. Numerical results show that several complete band gaps with a variable bandwidth exist for Lamb waves in the proposed structures. The formation mechanism of opening the acoustic band gaps is attributed to the coupling between the Lamb modes and the corrugation mode. The band gaps are significantly dependent upon the geometrical parameters such as the corrugation height, the corrugation width, and the plate thickness. Significantly, as the increase of corrugation height, band width shifts, new band gaps appear, the bands become flat, and the corrugation mode plays a more prominent role in the opening of Lamb wave band gaps. These properties of Lamb waves in the radial phononic crystal plates can potentially be applied to optimize band gaps, generate filters, and design acoustic devices.

On the stability of multiscale models of dynamical symmetry breaking from holography

We consider two classes of backgrounds of Type IIB supergravity obtained by wrapping D5-branes on a two-cycle inside the conifold. The field theory dual exhibits confinement and, in addition, a region in which the dynamics is walking, at least in the weak sense that the running of the coupling is anomalously slow. We introduce quenched matter in the fundamental, modeled by probe D7-branes which wrap an internal three-dimensional manifold and lie at the equator of the transverse two-sphere. In the space spanned by the remaining internal angle and the radial coordinate, the branes admit two embeddings. The first one is U-shaped: the branes merge at some finite value of the radius. The second one is disconnected and extends along the entire radial direction at fixed angular separation. We interpret these two configurations as corresponding to chiral-symmetry breaking and preserving phases, respectively.We present a simple diagnostic tool to examine the classical stability of the embedding, based on the concavity/convexity conditions for the relevant thermodynamic potentials. We use this criterion to show that U-shaped probes that explore the walking region are unstable, hence providing a dynamical origin for the tachyonic mode found in the literature. Whenever this occurs, the disconnected solution becomes favored energetically. We find that in one of the two classes of backgrounds the U-shaped embedding is always unstable, and thus never realized dynamically. Consequently, these models cannot be used to describe chiral-symmetry breaking. In the second category of solutions, our analysis reveals the presence of a first-order phase transition between chiral-symmetry broken and restored phases. Interestingly, this is in the same class that contains a parametrically light scalar in the spectrum of glueballs of the dual field theory.

Scaling symmetry, renormalization, and time series modeling: The case of financial assets dynamics

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

Generalised CP and A4 family symmetry

We perform a comprehensive study of family symmetry models based on A4 combined with the generalised CP symmetry H CP. We investigate the lepton mixing parameters which can be obtained from the original symmetry A4 ⋊ H CP breaking to different remnant symmetries in the neutrino and charged lepton sectors. We find that only one case is phenomenologically viable, namely $ G_{\mathrm{CP}}^{\nu}\cong Z_2^S\times H_{\mathrm{CP}}^{\nu } $ in the neutrino sector and $ G_{\mathrm{CP}}^l\cong Z_3^T\rtimes H_{\mathrm{CP}}^l $ in the charged lepton sector, leading to the prediction of no CP violation, namely δ CP and the Majorana phases α 21 and α 31 are all equal to either zero or π. We then propose an effective supersymmetric model based on the symmetry A4 ⋊ H CP in which trimaximal lepton mixing is predicted together with either zero CP violation or δ CP ≃ ±π/2 with non-trivial Majorana phases. An ultraviolet completion of the effective model yields a neutrino mass matrix which depends on only three real parameters. As a result of this, all three CP phases and the absolute neutrino mass scale are determined, the atmospheric mixing angle is maximal, and the Dirac CP can either be preserved with δ CP = 0, π or maximally broken with δ CP = ±π/2 and sharp predictions for the Majorana phases and neutrinoless double beta decay.

A dynamic duopoly model with bounded rationality based on constant conjectural variation

In this paper, we construct dynamic models on the basis of constant conjectural variation. Duopolists with dynamic adjustment behavior of bounded rationality have been considered. Numerical simulation is used to illustrate the complexion of models. The existence of equilibrium points and their stability in this nonlinear system are discussed. We study two special cases of symmetry model and Bertrand model with conjectural variation. When the speed of output adjustment changes, a series of complex phenomena including bifurcation, chaos and strange attractors can be observed in our models. We also analyzed the importance of the initial conditions to the system that a tiny variation of the initial value will cause dramatic fluctuations in output.

Bivariate t-distribution type symmetry model for square contingency tables with ordered categories

For the analysis of square contingency tables with the same row and column ordinal classifications, this article pro- poses a new model, which may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate t-distribution with equal marginal variances having any degrees of freedom. The proposed model indicates that the difference between the symmetric two probabilities raised to the power is proportional to the distance from the main diagonal of the table. The model is an extension of the symmetry model. An example is given. The simulation studies based on bivariate t-distribution are given.

Excited states of many-body systems in the fermion dynamical symmetry model with random interactions

In this Brief Report we investigate excited yrast states under random interactions in the framework of the fermion dynamical symmetry model, for the ensemble with spin-0 ground states. Interesting correlations are seen between ${R}_{6}$ and ${R}_{4}$ (where ${R}_{I}\ensuremath{\equiv}{E}_{{I}_{1}^{+}}/{E}_{{2}_{1}^{+}}$) by using the Mallmann plot, for cases with both SP(6) symmetry and SO(8) symmetry.

Effect of hydrogenation on the band gap of graphene nano-flakes

The effects of hydrogenation on the band gap of graphene have been investigated by means of density functional theory method. It is generally considered that the band gap increases with increasing coverage of hydrogen atom on the graphene. However, the present study shows that the band gap decreases first with increasing hydrogen coverage and reaches the lowest value at finite coverage (γ=0.3). Next, the band gap increases to that of insulator with coverage from 0.3 to 1.0. This specific feature of the band gap is reasonably explained by broken symmetry model and the decrease of pi-conjugation. The electronic states of hydrogenated graphene are discussed.

Deviations from tri-bimaximal neutrino mixing using type II seesaw

We study the possibility of generating deviations from tri-bimaximal (TBM) neutrino mixing to explain the non-zero reactor mixing angle within the framework of both type I and type II seesaw mechanisms. The type I seesaw term gives rise to the μ–τ symmetric TBM pattern of neutrino mass matrix as predicted by generic flavor symmetry models like A4 whereas the type II seesaw term gives rise to the required deviations from TBM pattern to explain the non-zero θ13. Considering extremal values of Majorana CP phases such that the neutrino mass eigenvalues have the structure (m1,−m2,m3) and (m1,m2,m3), we numerically fit the type I seesaw term by taking oscillation as well as cosmology data and then compute the predictions for neutrino parameters after the type II seesaw term is introduced. We consider a minimal structure of the type II seesaw term and check whether the predictions for neutrino parameters lie in the 3σ range. We also outline two possible flavor symmetry models to justify the minimal structure of the type II seesaw term considered in the analysis.

Polarization effects in the Higgs boson decay toγZand test ofCPandCPTsymmetries

Polarization characteristics of gamma gamma and gamma Z states in the Higgs boson decays h -> gamma gamma and h -> gamma Z are discussed. Based on effective Lagrangian, describing h gamma gamma and h gamma Z interactions with CP-even and CP-odd parts, we calculate polarization parameters xi_1, xi_2, xi_3. A nonzero value of the photon circular polarization, defined by parameter xi_2, arises due to presence of both parts in effective Lagrangian and its non-Hermiticity. The circular polarization is proportional to the forward-backward asymmetry of fermions in the decay h -> gamma Z -> gamma f bar{f}. Measurement of this observable would allow one to search for deviation from the standard model and possible violation of CPT symmetry. We discuss also a possibility to measure parameters xi_1, xi_3, describing correlation of linear polarizations of photon and Z boson, in the decay h -> gamma* Z -> l+ l- Z via distribution over the azimuthal angle between the decay planes of gamma* -> l+ l- and Z -> f bar{f}. Deviation of the measured value of xi_1 from zero will indicate CP violation in the Higgs sector.

Casting light on BSM physics with SM standard candles

The Standard Model (SM) has had resounding success in describing almost every measurement performed by the ATLAS and CMS experiments. In particular, these experiments have put many beyond the SM models of natural Electroweak Symmetry Breaking into tension with the data. It is therefore remarkable that it is still the LEP experiment, and not the LHC, which often sets the gold standard for understanding the possibility of new color-neutral states at the electroweak (EW) scale. Recently, ATLAS and CMS have started to push beyond LEP in bounding heavy new EW states, but a gap between the exclusions of LEP and the LHC typically remains. In this paper we show that measurements of SM Standard Candles can be repurposed to set entirely complementary constraints on new physics. To demonstrate this, we use WW cross section measurements to set bounds on a set of slepton-based simplified models which fill in the gaps left by LEP and dedicated LHC searches. Having demonstrated the sensitivity of the WW measurement to light sleptons, we also find regions where sleptons can improve the fit of the data compared to the NLO SM WW prediction alone. Remarkably, in those regions the sleptons also provide for the right relic-density of Bino-like Dark Matter and provide an explanation for the longstanding 3 sigma discrepancy in the measurement of (g-2)_\mu.

Comparison of IMD Symmetry and Asymmetry Model in Power Amplifier Based on Multisine Excitation

This paper proposes system level behavior model of a nonlinear power amplifier that exhibit the IMD asymmetry effect based on multisine excitation. For this work, a third order power series coefficients are originatively represented with both the system level circuit features such as a second output intercept point (OIP2), a third output intercept point (OIP3), amplifier gain and its excitation amplitudes. In addition, the memory effect like the asymmetry in lower and upper intermodulation products are distinguished through the analytic description and measurement. The main advantage of the proposed theory is able to analyze the composition of the nonlinear response in power amplifier. This paper also presents the measured results to validate the analytic expressions.

Minimal predictive see-saw model with normal neutrino mass hierarchy

We consider the type I see-saw model with two right-handed neutrinos and a normal neutrino mass hierarchy and impose a zero coupling between the right-handed neutrino mainly responsible for the atmospheric neutrino mass and the electron neutrino. We derive a master formula which relates see-saw input parameters in a one to one correspondence with physical neutrino observables. Using the master formula we search for simple ratios of couplings consistent with current data on neutrino mass and lepton mixing. We discover a minimal predictive example in which the right-handed neutrino mainly responsible for the atmospheric neutrino mass has couplings to (ν e , ν μ , ν τ ) proportional to (0, 1, 1) and the right-handed neutrino mainly responsible for the solar neutrino mass has couplings to (ν e , ν μ , ν τ ) proportional to (1, 1, 3) or (1, 3, 1), with a relative phase η = ∓π/3, providing the link between leptogenesis and CP violation in neutrino oscillation experiments. We show how these patterns of couplings could arise from an A 4 family symmetry model of leptons which predicts all the PMNS parameters in terms of the neutrino mass ratio m 2 /m 3, corresponding to Tri-bimaximal-Cabibbo mixing, accurate to one degree, with the prediction δ ≈ ±π/2.

Double symmetry model and its decompositions in square contingency tables having ordered categories

In this paper, we have employed the non-standard log-linear models to fit the double symmetry models and some of its decompositions to square contingency tables having ordered categories. SAS PROC GENMOD was employed to fit these models although we could similarly have used GENLOG in SPSS or GLM in STATA. A SAS macro generates the factor or scalar variables required to fit these models. Two sets of \(4 \times 4\) unaided distance vision data that have been previously analyzed in (Tahata and Tomizawa, Journal of the Japan Statistical Society 36:91–106, 2006) were employed for verification of results. We also extend the approach to the Danish \(5 \times 5\) Mobility data as well as to the \(3 \times 3\) Danish longitudinal study data of subjective health, firstly reported in (Andersen, The Statistical Analysis of Categorical Data, Springer:Berlin, 1994) and analyzed in (Tahata and Tomizawa, Statistical Methods and Applications 19:307–318, 2010). Results obtained agree with those published in previous literature on the subject. The approaches suggest here eliminate any programming that might be required in order to apply these class of models to square contingency tables.

Minimal see-saw model predicting best fit lepton mixing angles

We discuss a minimal predictive see-saw model in which the right-handed neutrino mainly responsible for the atmospheric neutrino mass has couplings to (νe,νμ,ντ) proportional to (0,1,1) and the right-handed neutrino mainly responsible for the solar neutrino mass has couplings to (νe,νμ,ντ) proportional to (1,4,2), with a relative phase η=−2π/5. We show how these patterns of couplings could arise from an A4 family symmetry model of leptons, together with Z3 and Z5 symmetries which fix η=−2π/5 up to a discrete phase choice. The PMNS matrix is then completely determined by one remaining parameter which is used to fix the neutrino mass ratio m2/m3. The model predicts the lepton mixing angles θ12≈34∘,θ23≈41∘,θ13≈9.5∘, which exactly coincide with the current best fit values for a normal neutrino mass hierarchy, together with the distinctive prediction for the CP violating oscillation phase δ≈106∘.

Molecular structure and barriers to internal rotation of α-naphthalenesulfonyl chloride: a study by gas-phase electron diffraction and quantum chemical calculations

α-Naphthalenesulfonyl chloride, α-NaphSC, was studied by gas-phase electron diffraction (GED) and quantum chemical calculations (HF/6-311 + G**, HF/aug-cc-pVDZ, B3LYP/cc-pVDZ, B3LYP/cc-pVTZ, B3LYP/aug-cc-pVDZ, B3LYP/aug-cc-pVTZ, MP2/cc-pVDZ, and MP2/cc-pVTZ). The calculations predict the existence of two conformers with C1 (I) and Cs (II) symmetries. The most stable conformer I has an enantiomer. The experimental data of α-NaphSC obtained at 370(5) K could be best fitted by a C1 symmetry model indicating that only this form exists in the gas-phase. In this model the Cα–S–Cl plane deviates from the perpendicular orientation relative to the plane of the naphthalene skeleton. Under the applied experimental conditions, the mole fraction of a second less stable conformer II of α-NaphSC predicted by calculations is no more than 1 %. The following geometrical parameters of conformer I were obtained from the experiment (A and °; uncertainties are in parentheses): rh1(C–H) = 1.082(6), rh1(C–C)cp = 1.407(3), rh1(C–S) = 1.764(5), rh1(S–O)av = 1.425(3), rh1(S–Cl) = 2.051(5), ∠C–Cα–C = 122.5(1), ∠Cα–S–Cl = 101.5(10); C9–C1–S–Cl = 71.4(21). The calculated barriers to internal rotation of the sulfonyl chloride group exceed considerably the thermal energy values corresponding to the temperatures of the GED experiments. Natural bond orbitals analysis of the electron density distribution was carried out to explain the peculiarities of the molecular structure of the studied compound and the deviation from the structures of β-NaphSHal molecules and their benzene analogs.

Research on Simulation Technique for Fixed Guide Vanes in Axial Symmetric Models of Spiral Case

The axial symmetric model has been widely used in the research and design of spiral case structure in hydraulic power station due to its convenience, however, instead of a continuous entity, the fixed guide vanes are discretely distributed around the vertical axis of the unit, and there are some different opinions on the simulation techniques for the fixed guide vane in the existing research. Commonly used processing methods for fixed guide vanes in the spiral case axial symmetry model are summarized and two new simulation techniques on the basis of existing research are proposed. Static analyses for a practical spiral case with cushion layer are conducted using 4 axial symmetry models and a 3-D FEM model. The influences of simulation techniques for fixed guide vanes on the stress and their distribution of steel liner, concrete and fixed guide vanes are investigated. The rationality and applicability of each simulation technique for fixed guide vanes are discussed.

Numerical Simulation of Ground Shock Produced by Chemical Explosion in Closed Soil

Empirical formula can be used to get ground shock parameters produced by conventional weapons buried in soil medium. With the development of finite element technology, ground shock parameters can be obtained by numerical simulation. However, sometimes the numerical simulation results were not consistent with the empirical formula results. A two-dimensional axial symmetry model and a three-dimensional model were set up to calculate the ground shock from a fully buried spherical charge, numerical results and empirical formula results were compared and the causes of the calculation error were analyzed.