Theoretical Analysis of Structures of Ga4N4 Clusters

The structures and energies of a Ga4N4 cluster have been calculated using a full-potential linear-muffin-tin-orbital molecular-dynamics (FP-LMTO MD) method. We obtained twenty-four structures for a Ga4N4 cluster. The most stable structure we obtained is a C8 three-dimensional structure, the energy of which is lower than that of the C2v symmetry structure proposed by Kandalam et al. [J. Phys. Chem. B106 (2002) 1945] The calculated results show that the isomer with an N3 subunit is preferred, supporting the previous result made by Kandalam et al,We found that the most stable structure of Ga4N4 clusters presented semiconductor-like properties through the calculation of the density of states.     

Physical characterisation of 4′-butyl-4-heptyl- bicyclohexyl-4-carbonitrile

We report measurements of birefringence, bend elastic constant, principal dielectric constants and conductivities as functions of temperature in the nematic phase of 4′-butyl-4-heptyl-bicyclohexyl-4-carbonitrile (CCN-47). The compound exhibits a small birefringence and a large negative dielectric anisotropy. Surprisingly, it shows a negative conductivity anisotropy, which probably owes its origin to the structural details of the molecules. The orientational order parameters (S) are estimated from both birefringence and dielectric anisotropy, and they agree well in the entire nematic range. The experimental results are compared with those on CCH7, which has a similar core structure but with a longitudinal dipole moment, in place of the transverse one of CCN-47.     

Refinement of hydrogen positions in Phase II of β-LiNH4SO4

The atomic positions and thermal parameters of the crystal structure for phase II of β-LiNH₄SO₄ are determined from single crystal neutron diffraction data at room temperature to refine N-H bond lengths for ammonium ions. The neutron data are collected using an E5 diffractometer in BENSC (HMI, Berlin, Germany). Atomic positions and thermal parameters are determined by the least-squares method up to R = 0.072 and wR = 0.057. It is shown that an ammonium ion polyhedron is the regular tetrahedron. The text was submitted by the authors in English.     

On the large order behavior of Φ 4 4

We continue the rigorous study of the large order behavior of the perturbation series for the ⁴ model in 4 dimensions started in [1]. In this paper we prove a result announced in [1]. We show that the exact radius of convergence of the Borel transform of the renormalized perturbation series for ₄ ⁴ is greater than or equal to the expected value given by the position of the first renormalon [2]. This result holds for any vector (²)² model withN components, and makes use of the Lipatov bound of [1]. This result is based on a partial resummation of counterterms similar to the one of [3], but in a phase-space analysis of the renormalized series.     

X-ray studies of the smectic B phase of the 4-bromobenzylidene-4′-alkoxyanilines

The results of X-ray studies of the nine members (4?÷?12) of the 4-bromobenzylidene-4′-alkyloxyaniline homologous series (nBBAA) in smectic B (SmB) and smectic A (SmA) phases are presented. Interestingly, no SmC phase was identified. The thickness of smectic layers in the SmA and SmB phases was estimated showing unexpectedly that in SmA it is bigger than in the SmB. For the SmB phase, orthorhombic unit cell parameters were determined as a function of temperature. The obtained data are discussed in relation to rotational dynamics.     

The High-order Squeezing of Orthonormalization Eigenstates of a~4

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Liquid-crystalline properties of 4-alkyl-, 4-alkyloxy and 4-halogene-4′-hydroxyazobenzene alkyloates

Twenty one esters, 4-alkyl-, 4-alkyloxy-, 4-nitro- and 4-halogene-4′-hydroxyazobenzne alkyloates have been synthesised. Basing on the DSC calorimetry and polarizing microscopy liquid- crystalline polymorphism was investigated. Five types of mesophases were identified: nematic, smectics A, C, F and unknown X (probably G).     

μSR studies of YFeMnO4

Muon spin relaxation (SR) studies were carried out on YFeMnO₄. Two interesting phenomena were found in measurements of longitudinal relaxation time spectra atT>T _cusp for a single crystal: (1) difference of the relaxation rates between the directions parallel with and perpendicular to thec-axis, and (2) suppression of local field fluctuations in a longitudinal external field. The spectra atT >T _cusp were reproduced with the function exp[-(₀ t)]. The results are discussed under a picture of the magnetic spin fluctuations of triangular antiferromagnets.     

Perturbative renormalization of massless φ 4 4 with flow equations

Perturbative renormalizability proofs in the Wilson-Polchinski renormalization group framework, based on flow equations, were so far restricted to massive theories. Here we extend them to Euclidean massless φ ₄ ⁴ . As a by-product of the proof we obtain bounds on the singularity of the Green functions at exceptional momenta in terms of the exceptionality of the latter. These bounds seem to be new and are quite sharp.     

Pretransitional dielectric properties of nematogenic 4-cyanophenyl-4′-n-heptylbenzoate

This article presents results of the static and dynamic dielectric studies performed for mesogenic 4-cyanophenyl-4′-n-heptylbenzoate in the isotropic (I) and nematic (N) phases. Pretransitional phenomena are observed in the vicinity of I–N phase transition as an anomalous temperature behavior of both the static and the dynamic dielectric properties of the compound. The temperature dependence of the static permittivity is correlated with the entropy change induced by the probing electric field while an anomalous behavior of the dielectric relaxation directly points out for a subdiffusional Brownian rotation of mesogenic molecules in the vicinity of the phase transition.     

Oriental behaviour of some homologues of 4-n-pentyl-phenylthio-4′-n-alkoxybenzoate doped with dichroic dye

The long-range orientational order of three members of 4-n-pentylphenylthio-4′-n-alkoxybenzoate series doped with a dichroic dye was studied by means of electronic absorption and fluorescence measurements. The order parameters <P₂> and <P₄> as well as the orientational distribution function were determined on the basis of absorption and emission spectra of linearly polarized light recorded as a function of temperature in the nematic, smectic A, and smectic C phases. An influence of the dye molecular structure on the orientational order of the dye/liquid crystal mixture was observed. Moreover, the dependence of the order parameter values on the length of the alkoxy chain in liquid crystal molecules was found. It was shown that the order parameter <P₄>, obtained from fluorescence measurements, can be helpful in recognizing the second-order or weakly first-order transitions between various liquid crystalline phases.     

Covariant Formulation of Electromagnetic 4-Momentum in Terms of 4-Vectors E α and B α

The fundamental difference between the true transformations (TT) and the apparent transformations (AT) is explained. The TT refer to the same quantity, while the AT refer, e.g., to the same measurement in different inertial frames of reference. It is shown that the usual transformations of the three-vectors E and B are - the AT. The covariant electrodynamics with the four-vectors E and B of the electric and magnetic field is constructed. It is also shown that the conventional synchronous definitions of the electromagnetic energy and momentum contain both, the AT of the volume, i.e., the Lorentz contraction, and the AT of E and B, while Rohrlich's expressions contain only the AT of E and B. A manifestly covariant expression for the energy-momentum density tensor and the electromagnetic 4-momentum is constructed using E and B . The 4/3 problem is discussed and it is shown that all previous treatments either contain the AT of the volume, or the AT of E and B, or both of them. In our approach all quantities are four-dimensional spacetime tensors whose transformations are the TT.     

Smectic polymorphism of 4-decyloxybenzylidene- 4′-alkyloxyanilines and their mixtures with polar standards of mesophases

This article describes liquid crystalline properties of the homologous series of 4-decyloxybenzylidene-4′-alkyloxyanilines. Based on the polarization microscopy (POM and TOA methods) and the calorimetric (DSC) measurements a rich polymorphism has been detected. Investigated compounds exhibit nematic, smectic A, smectic C, smectic B, smectic I and G (smectic G) mesophases with their characteristic configurations. The presence of these mesophases was confirmed by the miscibility method, using 4-heptyloxybenxylidene-4′-pentylaniline as a mesophase reference. Nine other smectic standards with different polarity have been applied in order to investigate their influence on the mesophase stability.     

Local existence of the Borel transform in Euclidean φ 4 4

We bound rigorously the large order behaviour of ₄ ⁴ euclidean perturbative quantum field theory, as the simplest example of renormalizable, but non-super-renormalizable theory. The needed methods are developed to take into account the structure of renormalization, which plays a crucial role in the estimates. As a main thorem, it is shown that the Schwinger functions at ordern are bounded byK ⁿ n!, which implies a finite radius of convergence for the Borel transform of the perturbation series.     

Anisotropy Spectra of the Solvent-Sensitive Fluorophore 4-Dimethylamino-4′-Cyanostilbene in the Presence of Light Quenching

We examined the emission wavelength-dependent anisotropies of the solvent-sensitive fluorophore 4-dimethylamino-4-cyanostilbene (DCS) under conditions of light quenching by polarized time-delayed quenching pulses. Illumination on the long-wavelength side of the emission spectrum with time-delayed light pulses resulted in a progressive decrease in the emission anisotropy as the observation wavelength increased toward the stimulating wavelength. The anisotropy changes of DCS were most wavelength dependent when spectral relaxation occurred during the excited-state lifetime. Light quenching of DCS in a low-viscosity solvent revealed no wavelength-dependent anisotropies. Control measurements using a solvent-insensitive fluorophore did not show any wavelength-dependent anisotropy with light quenching. The data for DCS can be explained by a model which allows wavelength-selective quenching of the long-wavelength emission formed by time-dependent spectral relaxation. These results indicate that polarized light quenching can be used to study systems which display multiple emissions and/or time-dependent spectral shifts.     

Phase behavior of four homologous compounds of 4-n-alkyl-4′-isothiocyanatobiphenyl (nBT) under pressure

The phase behavior of four homologous compounds of 4-n-nonyl-, 4-n-decyl-, 4-n-undecyl-, and 4-n-dodecyl-4′-isothiocyanatobiphenyl (9BT, 10BT, 11BT, and 12BT) was reinvestigated to characterize their high-pressure mesophases under pressures up to 150 MPa using a polarizing optical microscope equipped with a high-pressure optical cell and a wide-angle X-ray diffractometer equipped with a high-pressure sample vessel. The pressure-induced mesophases of 9BT and 10BT appearing under pressures above about 60 and 100 MPa, respectively, were identified as nematic (N) and smectic A (SmA) phases, which indicate the reversible Cr–CrE–N–I and Cr–CrE–SmA–I phase transitions under elevated pressure. Both the 11BT and 12BT exhibited the reversible transition of Cr–CrE–SmA–I in the low-pressure regions below about 5 and 23 MPa, respectively. Both the stable CrE phases changed into the monotropic (and metastable) one under higher pressures, which the Cr–SmA–I and I–SmA–CrE–Cr phase transitions on heating and cooling processes were recognized, respectively.     

The critical behavior of φ 1 4

The eigenvalues, eigenfunctions, and Schwinger functions of the ordinary differential operator $$H(\lambda ,m) = \tfrac{1}{2}\{ p^2 + \lambda q^4 + (m^2 - \lambda m^{ - 2} )q^2 \} $$ are studied as λ → ∞. It is shown that the scaling limit of the Schwinger functions equals the scaling limit of a one dimensional Ising model. Critical exponents ofH(λ,m) are shown to equal critical exponents of the Ising model, while critical exponents of the renormalized theory are shown to agree with those of a harmonic oscillator.     

Construction of the Hierarchical φ4-Trajectory

We study the invariant unstable manifold of the trivial renormalization-group fixed point tangent to the ⁴-vertex in the hierarchical approximation. We parametrize it by a running ⁴-coupling with linear step -function. The manifold is studied as a fixed point of the renormalization group composed with a flow of the running coupling. We present a rigorous construction of it beyond perturbation theory by means of a contraction mapping. Starting from a perturbative approximant of order seven, we obtain a convergent representation in dimensions 2 < D < 28/9 with certain restrictions. The perturbative approximant is logarithmically divergent in D = 3 dimensions.     

Investigation of KTiOPO_4 nanocrystals by means of second-harmonic light emission

The finding of nonlinear nanometric-sized probes is of key importance for the development of nonlinear microscopy in physical as well as biological sciences.We isolate nonlinear KTiOPO_4 nanocrystals and study them by second-harmonic generation microscopy(SHGM)and atomic force microscopy(AFM) independently.With both polarization analysis and defocused imaging of the emitted second harmonic field,we extract the Euler angles of the crystalline axes of a single nanocrystal.A balanced coherent optical homodyne detection shows tire coherent nature of the nanocrystal nonlinear emission and allows a phase measurement of the emitted second-harmonic field.These features make the KTiOPO_4 nanocrystal a good candidate for a vectorial probe of electromagnetic near fields.