Theory of spatial dispersion of dielectric and magnetic constants in magnetic uniaxial gyrotropic crystals

The theory of spatial dispersion of dielectric and magnetic constants of magnetic uniaxial crystals based on generalized Maxwell’s equations D = ε?E = (ε + inγ E = ?ns ^× H and B = μ?H = (μ + inδ)H = ns ^× E with spatial dispersion parameters γ and δ is considered. Generalized Fresnel’s and polarization equations for the obtained vectors E, D, H, and B are analyzed for the wave normal direction s ⊥ C (where C is the optic axis of a crystal). The possibility of the existence of a third natural wave in a crystal is proved.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

A Real Quaternion Spherical Ensemble of Random Matrices

One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the anti-sphere with truncations of unitary matrices. This paper focusses on an ensemble corresponding to the sphere: matrices of the form Y=A ^?1 B, where A and B are independent N×N matrices with iid standard Gaussian real quaternion entries. By applying techniques similar to those used for the analogous complex and real spherical ensembles, the eigenvalue joint probability density function and correlation functions are calculated. This completes the exploration of spherical matrices using the traditional Dyson indices β=1,2,4. We find that the eigenvalue density (after stereographic projection onto the sphere) has a depletion of eigenvalues along a ring corresponding to the real axis, with reflective symmetry about this ring. However, in the limit of large matrix dimension, this eigenvalue density approaches that of the corresponding complex ensemble, a density which is uniform on the sphere. This result is in keeping with the spherical law (analogous to the circular law for iid matrices), which states that for matrices having the spherical structure Y=A ^?1 B, where A and B are independent, iid matrices the (stereographically projected) eigenvalue density tends to uniformity on the sphere.     

Model independent bounds on the modulus of the pion form factor on the unitarity cut below the ωπ threshold

We study the structure of local baryon fields using the method of QCD sum rule. We only consider the single baryon fields and calculate their operator product expansions. We find that the octet baryon fields belonging to the chiral representations $[(\mathbf{3},\bar{\mathbf{3}}) \oplus(\bar{\mathbf{3}}, \mathbf{3})]$ and [(8,1)??(1,8)] and the decuplet baryon fields belonging to the chiral representations [(3,6)??(6,3)] lead to the baryon masses which are consistent with the experimental data of ground baryon masses. We also calculate their decay constants, check our normalizations for baryon fields in Chen et?al. (Phys. Rev.?D 81:054002, 2009) and find that they are well-defined.     

Extracting γ and penguin topologies through CP violation in B_{s}^{0}\to J/\psi K_{\mathrm{S}}

The $B_{s}^{0}\to J/\psi K_{\mathrm{S}}$ decay has recently been observed by the CDF collaboration and will be of interest for the LHCb experiment. This channel will offer a new tool to extract the angle γ of the unitarity triangle and to control doubly Cabibbo-suppressed penguin corrections to the determination of sin?2β from the well-known $B_{d}^{0}\to J/\psi K_{\mathrm{S}}$ mode with the help of the U-spin symmetry of strong interactions. While any competitive determination of γ is interesting, the latter aspect is particularly relevant as LHCb will enter a territory of precision which makes the control of doubly Cabibbo-suppressed Standard-Model corrections mandatory. Using the data from CDF and the e ⁺ e ^? B factories as a guideline, we explore the sensitivity for γ and the penguin parameters and point out that the $B_{s}^{0}$ – $\bar{B}_{s}^{0}$ mixing phase φ _s , which is only about ?2° in the Standard Model but may be enhanced through new physics, is a key parameter for these analyses. We find that the mixing-induced CP violation $S(B_{s}^{0}\to J/\psi K_{\mathrm{S}})$ shows an interesting correlation with sin?φ _s , which serves as a target region for the first measurement of this observable at LHCb.     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

A Novel Series Colorimetric and Off–On Fluorescent Chemosensors for Fe3+ Based on Rhodamine B Derivative

A novel series colorimetric and off–on fluorescent chemosensors (2a, 2b, 2c) were designed and synthesized, which showed reversible and highly selective and sensitive recognition toward Fe³⁺ over other examined metal ions. Upon addition of Fe³⁺, sensors (2a, 2b) exhibit remarkably and 2c exhibits moderate enhanced absorbance intensity and color change from colorless to pink in CH₃OH–H₂O(1:1, v/v). The three compounds (2a, 2b, 2c) may therefore be applicable as rhodamine-based turn-on type fluorescent chemosensors.     

Three-dimensional structure of electron transfer components in photosystem II: “2 + 1” ESE of chlorophyll Z and tyrosine D

A“2 + 1” electron spin echo method has been applied to measure the orientation of the distance vectorR from the redox-active tyrosine residue Y_D to chlorophyll Z Chl_Z in a membraneoriented Mn-depleted preparation of photosystem II. The angle betweenR and the normaln to the photosystem II membranes was determined to be 50.0 ±5° with the value of the dipolar interaction parameterD ₀ = 2.0 MHz, the corresponding distance of 29.4 ±0.5 Å, determined in a nonoriented PS II sample.     

Indole-based Fluorescent Sensors for Selective Detection of Hg2+

A series of indole-based fluorescent chemosensors 1–4 were prepared and investigated characteristick features with transition metal ions. Sensors 1 and 2 were selective for Hg²⁺ ion among a series of metal ions in H₂O–DMSO with association constants of 4.60×10⁴ and 5.90×10⁴?M^?1 and detection limits of 140 and 101.6 μM, respectively.

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.     

Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

EPR study of Gd3+ in a ferroelastic BiVO4 single crystal

Electron paramagnetic resonance of the Gd³⁺ ion in a ferroelastic BiVO₄ single crystal with a single domain, grown by the Czochralski method, has been investigated at room temperature using a Q-band spectrometer. The rotation patterns of the resonance fields measured in the crystallographic planes are analyzed using a monoclinic spin Hamiltonian. The principal Z-axis of the second-order zero-field splitting tensorD is found to be along the crystallographicb-axis. Spin Hamiltonian parameters together with the principal axes ofg andD tensors in the monoclinic plane show that the local site symmetry of Gd³⁺ ion in BiVO₄ crystal is monoclinic and that the Gd³⁺ ion substitutes for Bi³⁺ ion.     

Study on the Selectivity of Anion Receptors Based on Similar (thio)urea Fragments

Three new selective anion receptors containing the (thio)urea binding sites were developed, Indole-3-formaldehyde phenyl-semithiocarbazone, Indole-3-formaldehyde nitrophenyl-semithiocarbazone, and Indole-3-formaldehyde nitrophenyl-semicarbazone, nominated as receptors 1, 2 and 3, respectively. Receptor 1 shows high selective recognition for F^? only, while both receptor 2 and receptor 3 containing a p-nitro group show high selective recognition for AcO^?. The high selective recognition of these receptors to anions is further investigated by X-ray crystallography diffraction, UV-vis, fluorescence analyses and ¹H NMR. Furthermore, receptor 2 changes from yellow to orange, and receptor 3 darkens when acetate is added, providing a way of detection by ‘naked-eye’.     

Experimental and numerical modelling of the fluid flow in the continuous casting of steel

This article gives an overview of recent research activities with respect to the mold flow in the continuous casting of steel in presence of DC magnetic fields. The magnetic fields appear to be an attractive tool for controlling the melt flow in a contactless way. Various kinds of magnetic systems are already in operation in industrial steel casting, but the actual impact on the melt flow has not been sufficiently verified by experimental studies. The rapid development of innovative diagnostic techniques in low-melting liquid metals over the last two decades enables new possibilities for systematic flow measurements in liquid metal model experiments. A new research program was initiated at HZDR comprising three experimental facilities providing a LIquid Metal Model for continuous CASTing of steel (LIMMCAST). The facilities operate in a temperature range from room temperature up to 400^°C using the low-melting alloys GaInSn and SnBi, respectively. The experimental program is focused on quantitative flow measurements in the mold, the submerged entry nozzle and the tundish. Local potential probes, Ultrasonic Doppler Velocimetry (UDV) and Contactless Inductive Flow Tomography (CIFT) are employed to measure the melt flow. The behavior of two-phase flows in case of argon injection is investigated by means of the Mutual Inductance Tomography (MIT) and X-ray radioscopy. The experimental results provide a substantial data basis for the validation of related numerical simulations. Numerical calculations were performed with the software package ANSYS-CFX with an implemented RANS-SST turbulence model. The non-isotropic nature of MHD turbulence was taken into account by specific modifications of the turbulence model. First results of the LIMMCAST program reveal important findings such as the peculiar, unexpected phenomenon that the application of a DC magnetic field may excite non-steady, non-isotropic large-scale flow oscillations in the mold. Another important result of our study is that electrical boundary conditions, namely the wall conductivity ratio, have a serious influence on the mold flow while it is exposed to an external magnetic field.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

9, 10-Bis(8-Quinolinoxymethyl)Anthracene—A Fluorescent Sensor for Nanomolar Detection of Cu2+ with Unusual Acid Stability of Cu2+-Complex

In this work, the dipod 9,10-bis(8-quinolinoxymethyl)anthracene (1) and for comparison, monopod 9-(8-quinolinoxymethyl)anthracene (2) have been synthesized. The fluoroionophore 1 in pH 7.1 HEPES buffered CH₃CN:H₂O (4:1 v/v) solution shows quenching only with Cu²⁺ with lowest limit of detection 150 nM, amongst various metal ions. Fluoroionophore 1 could also be applied to sense Co²⁺ with lowest limit of detection 600 nM. By modulating the pH of the solution and concentration of Cu²⁺, 1 shows respective “On-Off-On” and “On-Off” fluorescent switching. The self-assembly of two Cu²⁺ ions and two molecules of fluoroionophore 1 to form closed structure [Cu₂(L)₂]⁴⁺ seems to be responsible for nanomolar sensitivity towards Cu²⁺. The combination of delayed second protonation of 1 (pK_a2?=?2.6) and stepwise protonation of [Cu₂ L ₂]⁴⁺ causes unusual stability of [Cu(LH)₂]⁴⁺ even at pH?<?2.

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

A Schiff-Based Colorimetric Fluorescent Sensor with the Potential for Detection of Fluoride Ions

A simple Schiff-based colorimetric fluorescent receptor 1 was prepared. It exhibits a “turn-on-type” mode with high sensitivity in the presence of F^?. The change in color is very easily observed by the naked eye in the presence of F^?, whereas other anions do not induce such a change. Job plot indicated a 1:2 complexation stoichiometry between receptor 1 and F^?. The association constant for 1-F^? in CH₃CN was determined as 1.32*10⁵ M^?2 by a Hill plot.

A Pulsed EPR and DFT Investigation of the Stabilization of Coordinated Phenoxyl Radicals in a Series of Cobalt Schiff-Base Complexes

We recently demonstrated how the aerobic addition of acetic acid to N,N′-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexane-diamino Co^II, [Co(1)], leads to the formation of an unusual coordinated Co^III-phenoxyl radical. In this work, some of the structural aspects associated with the Schiff-base-derived ligand (1) that are crucial for the acid-mediated formation of the phenoxyl radical are investigated. For comparison with [Co(1)], we therefore studied the influence of acetic acid on two complexes: (1) the N,N′-bis(3,5-di-tert-butylsalicylidene)-1,2-ethane-diamino Co^II complex, [Co(2)], that lacks the cyclohexyl group of [Co(1)], and (2) the N′-disalicylidene-ethylenediamine Co^II salen complex, [Co(3)], that lacks both the tertiary butyl groups and the cyclohexyl groups. It is shown that the cyclohexyl group of [Co(1)] is not involved in the formation or stabilization of the phenoxyl radical, whereas the tertiary butyl groups of [Co(1)] play a crucial role. In addition, the characteristics of the phenoxyl radical, formed after aerobic addition of acetic acid to [Co(2)], are analyzed in detail by pulsed electron paramagnetic resonance, in combination with isotopic labeling. The experimental data are compared to density functional theory computations and to previous data on the acid-mediated phenoxyl radical of [Co(1)].