Room evacuation in the presence of an obstacle

The investigation of human behaviour while trying to escape from a room under panic is an important issue in complex systems research. Several authors have called attention to the fact that placing an obstacle near the exit improves the evacuation time of the room (Helbing et al. (2000, 2005) [2] and [8], Hughes (2003) [6], Johansson and Helbing (2005) [16], Piccoli and Tosin (2009) [5]). We studied this effect in the context of the “social force model” (Helbing et al. (2000) [2]). We show that placing an obstacle does not guarantee, by itself, better chances of survival for all pedestrians. The way they choose to avoid the obstacle is critical for their own performance. We found not only that the faster they try to escape, the slower they get out (“faster is slower” effect), but also, the short cut they might take in order to get to the exit will probably do no better (“clever is not always better” effect).     

Vortex lattices in rotating atomic Bose gases with non-local interactions

We study the groundstates of rotating atomic Bose gases with non-local interactions. We focus on the weak-interaction limit of a model involving s- and d-wave interactions. With increasing d-wave interaction, the mean-field groundstate undergoes a series of transitions between vortex lattices of different symmetries (triangular, square, “stripe” and “bubble” crystal phases). We discuss the stability of these phases to quantum fluctuations. Using exact diagonalization studies, we show that with increasing d-wave interaction, the incompressible Laughlin state at filling factor ν=1/2 is replaced by compressible stripe and bubble states.     

Hidden symmetry of the CKM and neutrino-mapping matrices

We propose that the smallness of the light quark masses is related to the smallness of the T (i.e. CP) violation in hadronic weak interactions. Accordingly, for each of the two quark sectors (“upper” and “lower”) we construct a 3 × 3 mass matrix in a bases of unobserved quark states, such that the “upper” and “lower” basis states correspond exactly via the W^± transitions in the weak interaction. In the zeroth approximation of our formulation, we assume T conservation by making all matrix elements real. In addition, we impose a “hidden symmetry” (invariance under simultaneous translations of all three basis quark states in each sector), which ensures a zero mass eigenstate in each sector.Next, we simultaneously break the hidden symmetry and T invariance by introducing a phase factor e^iχ in the interaction for each sector. The Jarlskog invariant J_CKM, as well as the light quark masses are evaluated in terms of the parameters of the model. Comparing formulas, we find that most unknown factors drop out, resulting in a simple relation with , to leading order in χ and m_s/m_b, with A, λ the Wolfenstein parameters. (Because of the large top quark mass, the contribution from upper quark sector can be neglected.) Setting J_CKM = 3.08 × 10⁻⁵, m_b = 4.7 GeV (1s mass), m_s = 95 MeV, A = 0.818, and λ = 0.227, we find , consistent with the accepted value m_d = 3 − 7 MeV.We make a parallel proposal for the lepton sectors. With the hidden symmetry and in the approximation of T invariance, both the masses of e and ν₁ are zero. The neutrino-mapping matrix V_ν is shown to be of the same Harrison-Perkins-Scott form which is in agreement with experiments. We also examine the correction due to T violation, and evaluate the corresponding Jarlskog invariant J_ν.     

The analytical treatment of magnetic properties of three-layer ferrimagnetic superlattice

The Hamiltonian of the magnetic superlattice with three-layer unit cell was treated within the Boson formalism. The Boson Green’s functions (BGFs) were derived and it was shown that the system for BGFs splits into two sets which lead to the energies with opposite signs, although the energies of elementary excitations are strictly only the positive ones. However, when corresponding energies are used, the correlation functions calculated from both sets are the same. All the physically relevant quantities: total energy of the system, ground state energy, layer magnetization and zero-point (quantum) fluctuations are derived analytically by using both sets, showing that they lead to the same expressions. The Hamiltonian was also diagonalized by the so-called “u-v” transformation of the operators. It is shown that in spite of formal independence of the approaches, there exists a close relationship between BGF and “u-v” transformations.     

Dimer-monomer model on the Sierpinski gasket

We present the numbers of dimer-monomers M_d(n) on the Sierpinski gasket SG_d(n) at stage n with dimension d equal to two, three and four. The upper and lower bounds for the asymptotic growth constant, defined as z_SGd=lim_v→∞lnM_d(n)/v where v is the number of vertices on SG_d(n), are derived in terms of the results at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of z_SGd can be evaluated with more than a hundred significant figures accurate. From the results for d=2,3,4, we conjecture the upper and lower bounds of z_SGd for general dimension. The corresponding results on the generalized Sierpinski gasket SG_d,b(n) with d=2 and b=3,4 are also obtained.     

Magnetic field effect on the pairing state competition in quasi-one-dimensional organic superconductors (TMTSF)2X

We study the effect of the magnetic field on the pairing state competition in organic conductors (TMTSF)₂X by applying random phase approximation to a quasi-one-dimensional extended Hubbard model. We show that the singlet pairing, triplet pairing and the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting states may compete when charge fluctuations coexist with spin fluctuations. This rises a possibility of a consecutive transition from singlet pairing to FFLO state and further to S_z = 1 triplet pairing upon increasing the magnetic field. We also show that the singlet and S_z = 0 triplet components of the gap function in the FFLO state have “d-wave” and “f-wave” forms, respectively, which are strongly mixed.     

Effects of internal viscous damping on the stability of a rotating shaft driven through a universal joint

A rotating flexible shaft, with both external and internal viscous damping, driven through a universal joint is considered. The mathematical model consists of a set of coupled, linear partial differential equations with time-dependent coefficients. Use of Galerkin's technique leads to a set of coupled linear differential equations with time-dependent coefficients. Using these differential equations some effects of internal viscous damping on parametric and flutter instability zones are investigated by the monodromy matrix technique. The flutter zones are also obtained on discarding the time-dependent coefficients in the differential equations which leads to an eigenvalue analysis. A one-term Galerkin approximation aided this analysis. Two different shafts (“automotive” and “lab”) were considered. Increasing internal damping is always stabilizing as regards to parametric instabilities. For flutter type instabilities it was found that increasing internal damping is always stabilizing for rotational speeds v below the first critical speed, v₁. For v>v₁, there is a value of the internal viscous damping coefficient, C_iv, which depends on the rotational speed and torque, above which destabilization occurs.The value of C_iv (“critical value”) at which the unstable zone first enters the practical range of operation was determined. The dependence of C_iv critical on the external damping was investigated. It was found for the automotive case that a four-fold increase in external damping led to an increase of about 20% of the critical value. For the lab model an increase of two orders of magnitude of the external damping led to an increase of critical value of only 10%.For the automotive shaft it was found that this critical value also removed the parametric instabilities out of the practical range. For the lab model it is not always possible to completely stabilize the system by increasing the internal damping. For this model using C_iv critical, parametric instabilities are still found in the practical range of operation.     

Critical velocities and two mechanisms of transition in superfluid liquid He

Two mechanisms of transition of the superfluid liquid ⁴He to quantum turbulence regimes are proposed for the case when the influence of the normal fluid on superfluid flow is suppressed by introducing superleaks at the ends of the capillary. Using dimensional analysis it is found that in the roton mechanism the critical velocity depends on channel size as vc∝d−1/4, matching the experiments. For the second, super-flow mechanism, the analysis of independent parameters relevant for this phenomena leads to critical velocity depending on d as vc∝d−1. It is shown that turbulence for super-flow mechanism arises when a “quantum Reynolds number” exceeds some critical value which is about 10³ for 1D geometry. The dimensional analysis of the equation for critical velocity of superfluid flow without superleaks at the ends of the capillary is also presented.     

The nano-structural properties of hydrogenated a-Si and Si-C thin films alloys by GISAXS and vibrational spectroscopy

Amorphous hydrogenated silicon (a-Si:H) with high hydrogen content (10-40 at.%), and non-stehiometric silicon-carbon (Si_1−xC_x) thin films with a variation of the carbon to silicon ratio up to 0.3, were deposited by using a magnetron sputtering source. The Si_1−xC_x thin films were partially crystallised after deposition by thermal annealing up to 1050 °C.The GISAXS (Grazing Incidence Small Angle X-ray Scattering) spectra of all of the prepared specimens indicate the presence of “particles” in the “bulk” of the films. For the a-Si:H samples, “particles” are most probably voids agglomerates with a variation in size between 3 and 6 nm. The mean value of the size distribution of the “particles” increases while its width slightly decreases with the hydrogen content in the film. This indicates a better structural ordering which is consistent with the results of Raman spectroscopy that show a decrease of the ratio between intensities of transversal acoustic (TA) and transversal optic (TO) phonon peaks, I_TA/I_TO, and a narrowing of the TO peak with increasing hydrogen content. These results are discussed as a consequence of the beneficial influence of hydrogen bombardment during the film growth.For Si_1−xC_x thin films, the “particles” are assumed to be SiC nano-crystals with a size between 2 and 14 nm and they are larger in films with a higher carbon concentration. Inside each of the films, the crystals are larger closer to surface and they grow faster in the direction parallel to the surface than in that which is perpendicular to it.     

Trends in stability, elastic and electronic properties of cubic Rh, Ir, Pd and Pt carbides depending on carbon content: MC versus M4C from first-principles calculations

First principles FLAPW-GGA calculations have been performed to understand the peculiarities of stability, elastic, electronic properties and chemical bonding for cubic carbides of four noble metals M=Rh, Pd, Ir and Pt depending on carbon stoichiometry: MC versus M₄C. Our main findings are as follows: (i) in contrast to mono-carbides MC with positive formation energies E_form>0, carbon-deficient sub-carbides M₄C are stable (E_form<0), thus carbon stoichiometry is one of the major factors determining successful synthesis of these materials, and (ii) as distinct from the majority of other 3d-5d metals (including Pd and Pt examined here), an unusual effect of Rh and Ir “metallization” and the increasing of ductility for these metals owing to the introduction of carbon has been established.     

Micromechanical and thermal behaviour of gel grown pure- and sodium-modified copper tartrate crystals

Results regarding micromechanical characteristics of gel grown pure- and sodium-modified copper tartrate crystals, bearing composition CuC₄H₄O₆·3H₂O, (Cu)_0.77(Na)_0.23C₄H₄O₆·3H₂O and (Cu)_0.65(Na)_0.35C₄H₄O₆·H₂O, as obtained on using indentation induced hardness testing technique are reported. Thermal behaviour of these crystals in the temperature ranging from room temperature (∼25 °C) to about 600 °C is also reported. Pure copper tartrate crystals are found to be thermally more stable than the sodium-modified ones. Dependence of Vickers’ hardness number H_v on load ranging from 0.049 to 2.94 N on two different planes for all the three compositions is analyzed. It is shown that after initial rise in the value of H_v, the same achieves saturation at a load of 0.49 N. Modification of copper tartrate crystal by introducing sodium in its lattice brings about a change in the micromechanical characteristics. The saturation value of H_v decreases with increase in the concentration of sodium ions. The results on (0 0 1) and (1 1 1) planes for both pure and modified copper tartrate crystals suggest hardness anisotropy. Relative difference of hardness between the two planes and yield strength for both pure and modified copper tartrate crystals is worked out. The experimental results are analyzed for applicability of Meyer’s law and Proportional Specimen Resistance Model. It is suggested that the experimental results indicating reverse ISE phenomenon may be explained in terms of the existence of a distorted zone near the crystal-medium interface. The integral method of Coats and Redfern approximation applied to the thermoanalytical data suggests “Random Nucleation Model” for the reaction kinetics of these crystals. Non-isothermal kinetic parameters such as activation energy, frequency factor and order of reaction are calculated.     

Spin-charge gauge compositeness of electron in HTS: Hints from metal-insulator crossover and entropy behavior

We show that the coexistence of Fermi arcs and metal-insulator crossover of the in-plane resistivity can give a hint of a peculiar “gauge compositeness” of the electron in hole-doped high T_c cuprates and a similar hint also comes from the negative intercept at T=0 of the electronic entropy extrapolated from moderate temperatures in the “pseudogap phase”. An implementation of this “compositeness” within the spin-charge gauge approach is outlined and is employed to discuss the above phenomena.     

Systematic analysis of the Fourier transform spectrum of CH3OH between 400 and 950 cm

We have investigated a high-resolution Fourier transform (FT) absorption spectrum of the ¹³CH₃OH isotopomer of methanol from 400 to 950 cm⁻¹ with the “Ritz” program. We present the assignments of 7160 transitions, 3021 of which belong to A-symmetry, and 4139 to E-symmetry. These transitions occur between states labeled by K quantum numbers up to 14, and by torsional quantum numbers n up to 4. The “Ritz” program evaluated the energies of the 4684 involved levels with an accuracy of the order of 10⁻⁴ cm⁻¹. All of the assigned lines correspond to transitions involving torsionally excited levels within the ground small-amplitude vibrational state.     

Structural transition of pentacene monolayer on Ga bilayer: From brick-wall structure to herringbone pattern of molecular dimers

Utilizing the substrate of Ga bilayer grown on Si(1 1 1)-√3 × √3-Ga, we have investigated the structural transition of pentacene monolayer induced by moderate annealing. Short-range ordering has been observed in the monolayer pentacene deposited at room temperature. Annealing the sample at ∼350 K produced ordered pentacene monolayer with the “brick-wall” adsorption pattern. The STM images with sub-molecular resolution revealed that the orbital symmetry of the HOMO is reduced from D_2h to C_2v, due to the substrate-molecule interaction, while the deeper HOMO-1 orbital remains intact. Further annealing at ∼400 K led to the formation of molecular dimers as well as the structural transition from “brick-wall” packing to “herringbone” pattern.     

Spinor with Schrödinger symmetry and non-relativistic supersymmetry

We construct the d-dimensional “half” Schrödinger equation, which is a kind of the root of the Schrödinger equation, from the (d+1)-dimensional free Dirac equation. The solution of the “half” Schrödinger equation also satisfies the usual free Schrödinger equation. We also find that the explicit transformation laws of the Schrödinger and the half Schrödinger fields under the Schrödinger symmetry transformation are derived by starting from the Klein-Gordon equation and the Dirac equation in d+1 dimensions. We derive the 3- and 4-dimensional super-Schrödinger algebra from the superconformal algebra in 4 and 5 dimensions. The algebra is realized by introducing two complex scalar and one (complex) spinor fields and the explicit transformation properties have been found.     

Spin-wave dispersion in ferromagnetic semiconductor superlattices and thin films in the narrow-band limit

Bulk and surface magnetic excitations of the semi-infinite ferromagnetic semiconductor (FMS) superlattices and thin films described by Heisenberg and s-d model are analyzed using the transfer matrix method, developed in our previous work. Results are discussed in the narrow-band limit. The spin-wave frequencies for the semi-infinite narrow-band semiconductors are analyzed in both low- and high-frequency regions. Energies of localized excitations are compared to the bulk and the results of Green function formalism. Depending on the parameters of the system, the surface spin waves appear as “acoustical” and “optical”, and there are only some quantitative difference in the high-frequency region, comparing our method and the Green function method. In the framework of the same methodology, bulk and surface magnetic excitations of more complicated superlattices and thin films made of the FMS superlattices are analyzed in terms of dependence of the system parameters. It is shown that the s-d interaction governs the behavior of the systems. Dependence on bulk and surface parameters is discussed.     

The stable structures of iron pnictides AFeAs (A = alkali and alkaline-earth metals): A first principles study

We have investigated the structural stabilities of iron arsenide compounds A_x(FeAs)_1−x (A = alkali and alkaline-earth metals) by first principles calculations. We find that (i) all of the experimental “122” type structures with composition x=1/3 are stable; (ii) all of the “111” type structures with composition x=1/2 except CsFeAs are stable; (iii) K₃FeAs with composition x=3/4 is stable. The predicted stable KFeAs, RbFeAs, SrFeAs, BaFeAs, K₃FeAs have the As-Fe-As bond angles close to the ideal tetrahedral angles, indicating that they may be superconductors.     

Bandwidth tuning of hybrid liquid-crystal Šolc filters based on an optical cancelling technique

We demonstrate that in addition to their role in tuning the wavelength of an N-stage hybrid liquid-crystal Šolc filter, liquid-crystal cells can also be used to vary the transmission bandwidth of such filter around any of the tuned wavelength. This bandwidth tuning is based on the variation of the number of stages by what we call here an “optical cancelling technique”. This is achieved by varying the birefringence of the liquid-crystal cells whose optical path difference switches between two particular values. We show that for a 10-stage filter and at λ_i = 1.532 μm, the calculated 3-dB bandwidth varies from 2.6 to 11.8 nm when the number of “optically-cancelled” hybrid plates increases from 0 to 8. During the tuning process, the contrast ratio remains equal to that of the equivalent classical Šolc filter.     

Doping effect on the carrier scattering in iron-pnictide superconductors studied by charge transport

In order to reveal the role of “carrier doping” in the iron-based superconductors, we investigated the transport properties of the oxygen-deficient iron-arsenides LnFeAsO_1−y (Ln=La, Ce, Pr and Nd) over a wide doping range. We found that the effect of “doping” in this system is mainly on the carrier scattering rather than carrier density, quite distinct from that in high-T_c cuprates. In the case of La system with lower T_c, the low temperature resistivity is dominated by T² term and fairly large magnetoresistance is observed. On the other hand, in the Nd system with higher T_c, carriers are subject to stronger scattering showing nearly T-linear resistivity and small magnetoresistance. Such strong scattering appears intimately correlated with high-T_c superconductivity in the iron-based system.