Nature of electric and magnetic dipoles gleaned from the Poynting theorem and the Lorentz force law of classical electrodynamics

Starting with the most general form of Maxwell's macroscopic equations in which the free charge and free current densities, ρ_free and J_free, as well as the densities of polarization and magnetization, P and M, are arbitrary functions of space and time, we compare and contrast two versions of the Poynting vector, namely, S = μ_o^− 1E × B and S = E × H. Here E is the electric field, H is the magnetic field, B is the magnetic induction, and μ_o is the permeability of free space. We argue that the identification of one or the other of these Poynting vectors with the rate of flow of electromagnetic energy is intimately tied to the nature of magnetic dipoles and the way in which these dipoles exchange energy with the electromagnetic field. In addition, the manifest nature of both electric and magnetic dipoles in their interactions with the electromagnetic field has consequences for the Lorentz law of force. If the conventional identification of magnetic dipoles with Amperian current loops is extended beyond Maxwell's macroscopic equations to the domain where energy, force, torque, momentum, and angular momentum are active participants, it will be shown that “hidden energy” and “hidden momentum” become inescapable consequences of such identification with Amperian current loops. Hidden energy and hidden momentum can be avoided, however, if we adopt S = E × H as the true Poynting vector, and also accept a generalized version of the Lorentz force law. We conclude that the identification of magnetic dipoles with Amperian current loops, while certainly acceptable within the confines of Maxwell's macroscopic equations, is inadequate and leads to complications when considering energy, force, torque, momentum, and angular momentum in electromagnetic systems that involve the interaction of fields and matter.     

The molecular vibration-rotation kinetic-energy operator for general internal coordinates

The molecular kinetic-energy operator for general internal coordinates is formulated in terms of simple generalisations of the matrices A, B, α, and β of Crawford. A new matrix γ of the gradients of the translational and rotational constraints facilitates the calculation of the β matrix. It is shown that the kinetic pseudo-potential U is most conveniently calculated as an atomic sum, and results are given for valence coordinates in various types of molecules.     

Energy, momentum, and force in classical electrodynamics: Application to negative-index media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t) = E(r,t) × H(r,t) / c² emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.     

Magnetic and electronic properties of Cr- and Mn-doped SnO2: ab initio calculations

The ab initio calculations, based on the Korringa–Kohn–Rostoker (KKR) approximation method combined with the coherent potential approximation (CPA), indicated as KKR–CPA, have been used to study the stability of ferromagnetic and ferrimagnetic states, for systems that are SnO₂ doped and co-doped with two transition metals, that is, chromium and manganese. Our results indicate that the ferromagnetic state is more stable than the spin-glass state for the (Sn_1−xCr_xO₂; x = 0.07, 0.09, 0.12 and 0.15)-doped system, while the spin-glass state is more stable than the ferromagnetic state for the (Sn_1−xMn_xO₂; x = 0.02 and 0.05)-doped system. However, the ferromagnetic and/or the ferrimagnetic states are stable for the (Sn_0.98−xMn_0.02Cr_xO₂; x = 0.05, 0.09 and 0.13)-doped system depending on the Cr concentration. Moreover, we estimated the Curie temperature (T_c) for the Cr-doped tin dioxide (SnO₂), and we explained the origin of magnetic behaviour through the total density of states for different doped and co-doped SnO₂ systems.     

Photoinduced electron transfer within a novel synthesized short-chain dyad

The investigations were made by using electrochemical, steady state and time resolved spectroscopic (time correlated single photon counting and laser flash photolysis) techniques on a novel synthesized dyad, 1-(4-chloro-phenyl)-3-(4-methoxy-naphthalen-1-yl)-propenone (MNCA) where the donor 1-methoxy-naphthalene (MNT) is connected with the acceptor p-chloroacetophenone (PCA) by an unsaturated olefinic bond. This dyad possesses mainly extended (E-type) conformation both in the ground and excited state. The unchanged conformational geometry of this dyad even after photoexcitation makes it different from the previously studied benzothiophene-p-chloroacetophenone dyads, though both the donors present are isosteric molecules. In the cases of the latter dyads though E-type isomeric structure dominates in the ground state, considerable amount of Z-type (folded) species are produced in the excited state. It is hinted that the proximity effect of methoxy functionality in donor moiety, may be the reason for the formation of mostly E-isomeric species in the case of the present dyad MNCA system. The observed unchanged values of charge recombination and ion-pair lifetime, estimated from the analysis of transient absorption spectra of the dyad in presence of βCD and without it, confirm the proposition about the maintenance of the extended conformation even upon photoexcitation. From the transient absorption measurements it appears that due to increase of delay times between the exciting and probe pulses, higher triplet T_n of the donor being generated gets involved in PET reactions with the surrounding medium ACN. From the present findings, MNCA in aqueous medium seems to be better candidate to build light energy conversion devices than the previously studied benzothiophene dyads where artificial devices like βCD were used to make elongated geometry. This geometry would help to prevent charge recombination processes within the redox components due to minimal overlapping between them.     

TOWARDS DEEP AND SIMPLE UNDERSTANDING OF THE TRANSCENDENTAL EIGENPROBLEM OF STRUCTURAL VIBRATIONS

When using exact methods for undamped free vibration problems the generalized linear eigenvalue problem (K−ω²M) D=0 of approximate methods, e.g., finite elements, is replaced by the transcendental eigenvalue problem K (ω) D=0. Here ω is the circular frequency; D is the displacement amplitude vector; M and K are the mass and static stiffness matrices; and K (ω) is the dynamic stiffness matrix, with coefficients which include trigonometric and hyperbolic functions involving ω and mass because elements (for example, bars or beams) are analyzed exactly by solving their governing differential equations. The natural frequencies of this transcendental eigenvalue problem are generally found by the Wittrick-Williams algorithm which gives the number of natural frequencies below ω_t, a trial value of ω, as ∑J_m+s{K (ω_t)} wheres {} denotes the readily computed sign count property of K (ω) and the summation is over the clamped-clamped natural frequencies of all elements of the structure. Understanding the alternative solution forms of the transcendental eigenvalue problem is important both to accelerate convergence to natural frequencies, e.g., by plotting ∣K (ω)∣, and to improve the mode calculations, which lack the complete reliability of natural frequencies obtained by using the Wittrick-Williams algorithm. The three solution forms are: ∣K (ω)∣=0; D=0 with ∣K (ω)∣→∞; and ∣K (ω)∣≠0 with D≠0. The literature covers the first two forms thoroughly but the third form has been almost totally ignored. Therefore, it is now examined thoroughly, principally by analytical studies of simple bar structures and also by confirmatory numerical results for a rigidly jointed plane frame. Although structures are unlikely to have exactly the properties giving this form, it needs to be understood, particularly because ill-conditioning can occur for structures approximating those for which it occurs.     

Nonlinear optical absorption and fluorescence of phosphine-substituted bithiophenes in the violet-blue spectral region

The nonlinear optical absorptions of two 5,5′-bis(diphenylphosphino)-2,2′-bithiophene derivatives, Ph₂(X)P(C₄H₂S)₂P(X)Ph₂ (X = O, 1; S, 2), have been investigated by direct transmission measurement with both picosecond and nanosecond laser pulses from 420 nm to 480 nm. Saturated dichloromethane solutions of 1 and 2 exhibit strong nonlinear optical absorptions in this violet-blue spectral region with that of 2 being stronger at all wavelengths. In the picosecond regime, at 420 nm, the transmittance rapidly falls to 50% when the incident fluence is 0.22 J/cm² for 1 and 0.11 J/cm² for 2. Two-photon absorption appears to be the primary mechanism for this nonlinear absorption. The two-photon absorption coefficients β for 1 (2.1 cm/GW) and 2 (4.4 cm/GM) were obtained by fitting the measurement of transmittance as the function of incident beam intensity at 420 nm. These β values are comparable with some of the best results obtained for organic materials in the green, red and infrared spectral region. Both compounds also show fluorescence with an emission peak at 390 nm for 1 and 400 nm for 2. The fluorescence of 1 is considerably stronger than is that of 2. The combination of the wide band gap and strong fluorescence emission of 1 makes it a promising candidate as a host material for blue organic light emitting diodes.     

Whence the Minkowski momentum?

Electromagnetic waves carry the Abraham momentum, whose density is given by p_EM = S(r,t) / c². Here S(r,t) = E(r,t) × H(r,t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n₂ + iκ₂, submerged in a transparent dielectric of refractive index n₁, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n₁, n₂, κ₂, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n₁ is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.     

Organic radical molecular solids based on [(TCNQ)n] (n=1 or 2): Syntheses, crystal structures, magnetic properties and DFT analyses

Four molecular solids consisting of the 7,7,8,8-tetracyanoquinodimethane (TCNQ) radical and benzylpyridinium or benzylquinolinium derivatives with molar ratios of 1:1 (1-3) and 2:1 (4) have been prepared and characterized. In the crystals of 1 and 3, TCNQ⁻ monoanions and the corresponding cations form segregated stacks, which are regular in 1 but irregular in 3. Instead of segregated stacks, TCNQ⁻ monoanions in 2 form isolated π-dimers. In the crystals of 4, two crystallographic independent TCNQ species possess almost equal fractional negative charge (ca. −0.5). Two types of TCNQ species form a tetrad, these tetrads make a TCNQ stack with the pattern …BAAB…BAAB… along the crystallographic a-b direction. The magnetisms for 1-4 can be simply explained by the formation of singlet spin state. A broken symmetry approach in a density functional theory framework at the ub3lyp/6-31 g level was used to calculate the magnetic exchange constants in 1-4. The results qualitatively demonstrate the observed magnetic properties.     

Viscous mhd solutions with no transfer of energy through the spectrum

Exact space periodic solutions to the viscous magnetohydrodynamics equations with arbitrary vector periods p₁, p₂, p₃ are derived. A complete classification of the p_j-periodic MHD solutions with pairwise noninteracting Fourier modes is obtained. The solutions have no transfer of energy through the spectrum and are smooth for all values of the time variable t ≥ 0.     

Active suppression of narrowband noises in 3D sound fields

This paper presents a simple multiple-input-multiple-output (MIMO) controller for active suppression of narrowband noise in 3D sound fields. The controller only depends on a complex matrix H(jω₀) instead of an n × n transfer matrix to model the secondary paths. Unlike other available ANCs that obtain the controller transfer functions by adaptation, the proposed one solves its controller transfer matrix directly from H(jω₀); and tolerates some degrees of errors in H(jω₀). If necessary, the proposed system may be made adaptive to trace the drifting secondary path. Online identification of a matrix H(jω₀) is easier than that of a transfer matrix with many coefficient matrices. The estimate would be more accurate for H(jω₀) if other conditions remain the same. The proposed scheme can be modified to suppress narrowband noises with multiple bands by a moderate increase in complexity.     

Structure and thermal behaviors of organic crystals based on substituted 1,3,4-thiadiazoles

The crystalline structure of some compounds containing the 1,3,4-thiadiazole moiety, (1) 5-ethyl-2-amino-1,3,4- thiadiazole (EATZ), (2) 5-benzylsulfany-2-amino-1,3,4-thiadiazole (BSATZ) and (3) 2,5-bis-benzylsulfanyl-1,3,4-thiadiazole (BBSTZ) were determined. Both EATZ and BBSTZ show orthorhombic structures with space group Pbca and BSATZ a monoclinic system with space group C2/c. The lattice parameters: a=0.72280 (14), b=1.0811 (2), c=1.6210 (3) nm for 1, a=2.5282 (5), b=0.59083 (12), c=1.5390 (3) nm for 2 and a=0.87530 (18), b=1.0365 (2), c=3.6098 (7) nm for 3. To compare the intra- and intermolecular interactions in thiadiazole containing organic crystals, thermal analysis studies on each crystal is performed using DSC and TG in N₂ atmosphere to describe the thermal behaviors. Based on the results, the changing regularity of melting point and decomposition temperature of these compounds is educed     

Photoluminescent properties of heteroleptic cyclometalated platinum(II) complexes bearing 1,3-bis(3,4-dibutoxyphenyl)propane-1,3-dionate as an ancillary ligand

A new series of heteroleptic cyclometalated platinum(II) complexes Pt-1a-f was synthesized, employing 2-arylpyridine (or 1-arylisoquinoline) (HC^∧N-1) and 1,3-bis(3,4-dibutoxyphenyl)propane-1,3-dione (HO^∧O-1) for cyclometalation and as ancillary ligands, respectively, and photoluminescent properties were investigated. Focusing on red-shifted phosphorescence, C^∧N ligands containing π-extended aromatics and electron-rich heterocycles were examined. All obtained complexes exhibited photoluminescence at ambient temperature, and the emission maxima ranged from green (λ_PL=518 nm) to far red (λ_PL=708 nm). The large Stokes shifts of more than 100 nm and sub-microsecond or microsecond emission lifetimes revealed that these complexes are phosphorescent emissive. The quantum yield of Pt-1 ranged from 0.02 to 0.59 at ambient temperature and decreased as the emission maximum was red-shifted. In comparison with the reference platinum(II) complexes, Pt-2 bearing an aliphatic ancillary ligand, such as 2,2,6,6-tetramethylheptane-3,5-dionate (O^∧O-2), the ligand O^∧O-1 did not significantly affect the photoluminescence emission maxima, indicating that the energy gap between the singlet ground state and the triplet level was predominantly dependent on the C^∧N ligand.     

Supramolecular selectivity of [60]-fullerene among equivalently photoactive porphyrins

The photophysical investigation of different para-substituted tetraphenylporphyrins (TP), viz., meso-tetra(4′-hydroxyphenyl)-21H-23H-porphyrin(1),meso-tetrakis(4′-hex-5-enyloxyphenyl)-21H-23H-porphyrin(2), meso-tetrakis(4′-oct-7-enyloxyphenyl)-21H-23H-porphyrin(3) and meso-tetrakis(4′-undecyloxyphenyl)-21H-23H-porphyrin (4) revealed that except for quantum yield (φ) the para-substitution has little effect on any other photophysical properties like lifetime, excitation, emission wavelength, etc. The host-guest type interactions of these tetraarylporphyrins (TP 1-4), with [60]-fullerene (F) have been studied with ¹H NMR and fluorescence spectrometric techniques in carbon tetrachloride medium. Fluorescence studies revealed that the Q band of the TPs was sufficiently quenched upon addition of F. All the fullerene/porphyrin systems were found to produce stable complexes with 1:1 stoichiometry. Binding constants (K) of all the fullerene/porphyrin complexes have been determined by fluorescence quenching method. The association constant values for 1/F have been determined from plots of the Stern-Volmer equation (103.713×10⁴) and the Benesi-Hildebrand equation (110.440×10⁴). It has been observed that the insertion of long chain oxo-alkenyl/alkyl group in the para position of TPs in 2, 3 and 4 diminished the K values for F by two, four and even ten times with respect to that of 1. The observed trend in variation of the binding constants was supported by a gradual variation in the shift of ¹H NMR signal when measurements were carried out in CDCl₃.     

Isomerization and fluorescence characteristics of sterically hindered azobenzene derivatives

We report synthesis and isomerization behaviors of sterically hindered azobenzene derivatives (1 and 2) with decyloxy and hydroxy groups, respectively, and their fluorescence enhancement under UV light irradiation characterized by means of absorption and fluorescence spectroscopy measurements. Upon irradiation of as-prepared solution (1) with UV light (∼200 mJ/cm²) a cis-rich photostationary state was reached. Obviously different from 2 showing very fast thermal cis-to-trans isomerization within 2 min, slow cis-to-trans thermal back isomerization of 1 with a long alkyl chain at ambient temperature was observed on the time scale of weeks. In contrast to no striking changes in absorption and fluorescence spectra of compound 2, the azobenzene 1 showed green fluorescence upon prolonged irradiation with UV light (about 3-8 J/cm² exposure doses), although both the initial trans-rich and cis-rich states of azobenzene molecules were not fluorescent in solution. The stability of fluorescence efficiency caused by drying and redissolving processes was examined.     

A statistical method for characterizing the noise in nonlinearly reconstructed images from undersampled MR data: The POCS example

The projection-onto-convex-sets (POCS) algorithm is a powerful tool for reconstructing high-resolution images from undersampled k-space data. It is a nonlinear iterative method that attempts to estimate values for missing data. The convergence of the algorithm and its other deterministic properties are well established, but relatively little is known about how noise in the source data influences noise in the final reconstructed image. In this paper, we present an experimental treatment of the statistical properties in POCS and investigate 12 stochastic models for its noise distribution beside its nonlinear point spread functions. Statistical results show that as the ratio of the missing k-space data increases, the noise distribution in POCS images is no longer Rayleigh as with conventional linear Fourier reconstruction. Instead, the probability density function for the noise is well approximated by a lognormal distribution. For small missing data ratios, however, the noise remains Rayleigh distributed. Preliminary results show that in the presence of noise, POCS images are often dominated by POCS-enhanced noise rather than POCS-induced artifacts. Implicit in this work is the presentation of a general statistical method that can be used to assess the noise properties in other nonlinear reconstruction algorithms.     

Synthesis of 2,3-dimorpholino-6-aminoquinoxaline derivatives and application to a new intramolecular fluorescent probe

Two fluorescent monomers having a quinoxaline skeleton, N-(2,3-dimorpholinoquinoxalin-6-yl)acrylamide (QxA) and N-(1-(2,3-dimorpholinoquinoxalin-6-ylamino)prop-2-yl)methacrylamide (QxAlaMA), were synthesized. Thermo-responsive copolymers of N-isopropylacrylamide (NIPAM) and a small amount of a fluorescent monomer were synthesized and their fluorescence properties investigated. The fluorescent monomers showed intense solvatochromism in their fluorescence. The wavelength at the maximum fluorescence intensity of the QxAlaMA-labeled PNIPAM dramatically blue-shifted and the fluorescence intensity of the QxA-labeled PNIPAM significantly increased around the transition temperature. It was found that these fluorescent dyes can sense and report the thermo-responsive behavior of the PNIPAM in water. Both QxAlaMA and QxA were demonstrated to be applicable to new intramolecular fluorescent probes.     

Eu(III) and Tb(III) luminescent lanthanide systems derived from DTPA-bisamide and DTTA-based ligands incorporating bipyridine antenna

Four new polycarboxylate ligands H₃Lⁿ have been synthesized by the attachment of two or one 2,2′-bipyridine subunits onto a diethylenetriamine pentacarboxylic acid (DTPA-bisamide derivatives: H₃L¹, H₃L²) or a diethylenetriamine tricarboxylic acid (DTTA derivatives: H₃L³, H₃L⁴) core. The neutral Eu^III and Tb^III complexes of these chelates have been prepared and studied from their UV-vis and luminescence data. The main photophysical characteristics of these complexes, i.e. the absorption and luminescence spectra, the metal-centred lifetimes and the overall luminescence yields (Φ) were measured in buffered aqueous solutions. In addition the role played by non-radiative paths (vibrational energy transfer involving coordinated water molecules, involvement of ligand-to-metal charge-transfer excited states, or metal→ligand back-transfer) was investigated. In all complexes, we found that the bidentate bipyridine chromophore is not coordinated to the lanthanide ion, allowing one (LnL¹, LnL²) or two (LnL³, LnL⁴) water molecules to penetrate the first coordination sphere of the metal. Although the bipyridine chromophore behaves as remote (from the binding site) light-harvesting unit for the lanthanide ion in these systems, a sizeable sensitization of the Eu- and Tb-centred luminescence can be effective (LnL², LnL³, Φ=16-19% in aerated D₂O solutions). Our photophysical investigations show that overall non-radiative deactivation is not dependant of thermally activated non-radiative channels but the efficiency of the ligand→Ln intramolecular energy transfer has to be taken into account to explain the obtained results.     

Surface-enhanced Raman scattering studies on bombesin, its selected fragments and related peptides adsorbed at the silver colloidal surface

SERS studies presented in this work on BN^8-14, [d-Phe⁶,β-Ala¹¹,Phe¹³,Nle¹⁴]BN^6-14, [d-Tyr⁶,β-Ala¹¹,Phe¹³,Nle¹⁴]BN^6-14, BN and its modified analogues, as well as NMB, NMC, and PG-L show that these molecules at pH 8.3 bind to a colloidal silver surface mainly through Trp⁸ and Met¹⁴ residues. Trp⁸ adsorbs at the surface almost perpendicularly. Met¹⁴ appears on the surface mainly as a P_C-G conformer. His¹², as is evident from the spectra, practically does not take part in the adsorption process. Substitution of l-leucine at the 13 position of amino acid sequence with l-phenylalanine does not change substantially the pattern of the adsorption mechanism; however, substitution of phenylalanine at the 12 position (instead of l-histidine) causes changes in the SERS spectra that show that Phe¹² takes parallel orientation to the surface upon adsorption of [d-Phe¹²]BN, while in the case of [Tyr⁴,d-Phe¹²]BN this residue is perpendicular to the surface and influences the orientation of the bound Trp⁸. On the other hand, substitution of Asn with Tyr in the 6 position in nonapeptide fragment causes changes in the adsorption mechanism. In this case, the discussed fragment binds to the silver colloidal surface by Tyr⁶, Trp⁸, and Met¹⁴. The SERS spectrum of NMC is very similar to that of BN; although it differs by the binding orientation of the amide bond towards the surface. Appearance of Phe¹³ in NMB and PG-L causes that this residue competes successfully with Trp⁸ forcing it to take tilted orientation. As seen from the enhancement of the characteristic Phe vibrations this moiety in NMB and PG-L adsorbs on the silver surface in a tilted fashion. This arrangements cause that the 8-14 peptide chain in all these studied compounds takes almost a parallel orientation to the surface while the 1-5 fragment of the peptide chain is removed from the silver surface vicinity.     

Relative power loss of misalignment based on electro-optical printed circuit board

In this paper, the power loss values between 45° total internal reflecting waveguide mirror (TIRWM) and the polymer optical waveguide layer are obtained by vector finite element method. There are some misalignments during an actual fabrication of electro-optical printed circuit board (EOPCB). And, b, a, c correspond to the error value of alignment in the x-axis, y-axis and z-axis direction, respectively. Another, four effective refractive indices of the 45° TIRWM and polymer optical waveguide layer are calculated, separately. And, n_eff1 = 1.425211 is uniquely chosen. Next, these relative power errors Δ are calculated, when a, b, c separately change. Moreover, these error values are plotted into some curved surface figures. By these figures, it is easy to find the relationship between a, b, c and Δ. Furthermore, it is beneficial for us to avoid the region of larger power loss during an actual fabrication of EOPCB.