The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E ^a and B ^a , as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms.     

The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations: The New Lorentz Invariant Field Equations

In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B, respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebraic objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebraic objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors E_Hv and B_Hv and the abstract tensors, the 4-vectors E^a and B^a. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D bf E and B and their ST.     

Maxwell’s demon and the management of ignorance in stochastic thermodynamics

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.     

Spin-1/2 Maxwell Fields

Requiring covariance of Maxwell's equations without a priori imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, ²–A ², E ²–B ²+2i EB–(₀ +A)². The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein–Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein–Gordon mass, and thus one complex Klein–Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass.     

“True Transformations Relativity” and Electrodynamics

Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach, which we call the true transformations (TT) relativity. In this approach a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor (when no basis has been introduced) or equivalently by a coordinate-based geometric quantity comprising both components and a basis (when some basis has been introduced). This invariant approach is compared with the usual covariant approach, which mainly deals with the basis components of tensors in a specific, i.e., Einstein's coordinatization of the chosen inertial frame of reference. The third approach is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rather quantities from 3+1 space and time, e.g., the synchronously determined spatial length. This formulation is called the apparent transformations (AT) relativity. It is shown that the principal difference between these approaches arises from the difference in the concept of sameness of a physical quantity for different observers. This difference is investigated considering the spacetime length in the TT relativity and spatial and temporal distances in the AT relativity. It is also found that the usual transformations of the three-vectors (3-vectors) of the electric and magnetic fields E and B are the AT. Furthermore it is proved that the Maxwell equations with the electromagnetic field tensor F^ab and the usual Maxwell equations with E and B are not equivalent, and that the Maxwell equations with E and B do not remain unchanged in form when the Lorentz transformations of the ordinary derivative operators and the AT of E and B are used. The Maxwell equations with F^ab are written in terms of the 4-vectors of the electric E^a and magnetic B^a fields. The covariant Majorana electromagnetic field 4-vector ^a is constructed by means of 4-vectors E^a and B^a and the covariant Majorana formulation of electrodynamics is presented. A Dirac like relativistic wave equation for the free photon is obtained.     

Magnetic resonance imaging of rigid polymers at elevated temperatures with SPRITE

Magnetic resonance imaging has rarely been applied to rigid polymeric materials, due primarily to the strong dipolar coupling and short signal lifetimes inherent in these materials. SPRITE (single point ramped imaging withT ₁ enhancement) (B. J. Balcom, R. P. MacGregor, S. D. Beyea, D. P. Green, R. L. Armstrong, T. W. Bremner: J. Magn. Reson. A123, 131–134, 1996) is particularly well suited to imaging solid materials. With SPRITE, the only requirement is thatT ₂^* be long enough so that the signal can be phase-encoded. The minimum phase encoding time is limited by the maximum gradient strength available and by the instrument deadtime. At present this is usually tens of microseconds and will only improve with refinements in technology. We have used the SPRITE sequence in conjunction with raising the sample temperature to obtain images of rigid polymers that have largely frustrated conventional imaging methods. This approach provides a straightforward and reliable method for imaging a class of samples that, up until now, have been very difficult to image.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

Self-consistent equilibria in a cylindrical reversed-field pinch

Summary A previous investigation by one of us, concerning the self-consistent equilibria of a two-region (plasma+gas) cylindrical Tokamak, is extended to the similar equilibria of a Reversed-Field Pinch, where a significant current density is driven by a dynamo electric field due to turbulence. The previous model has been generalized under the following basic assumptions:a) to the lowest order, the turbulent dynamo electric fieldE ^t is expressed as a homogeneous function of degree 1 of the magnetic fieldB, sayE ^t =α·B, with α being a 2nd-rank tensor, homogeneous of degree 0 inB, and generally depending on the plasma state;b)E ^t does not appear in the plasma power balance, as if it were produced by a Maxwell demon able to extract the needed power from the plasma internal energy. In particular we show that, in the simplest case when both α and the plasma resistivity η are isotropic and constant, the magnetic field turns out force-free with constant abnormality αμ₀/η for vanishing axial electric fieldE _z . This case has also been solved analytically, for whateverE _z , under circular, besides cylindrical, symmetry.     

Absolute line intensities in the ν1 + 3ν3 band of 12C2H2 by laser photoacoustic spectroscopy and Fourier transform spectroscopy

Line intensities and self-broadening coefficients in the ν₁ + 3ν₃ band of ¹²C₂H₂ near 0.8 μm at room temperature were measured by means of both laser photoacoustic and Fourier transform spectroscopy. An experimental protocol has been developed to obtain absolute intensities from the photoacoustic measurements. Namely, the spectrometer was calibrated using water vapour line intensities available in Hitran 1996 [L. S. Rothman et al. (1998) J. quant. Spectrosc. Radiat. Transfer, 60, 665–710]. These photoacoustic line intensities were found to be on average 5% higher than corresponding measurements performed using Fourier transform spectroscopy, the accuracy of the latter being estimated to better than 4%. The accuracy of the photoacoustic intensities is discussed. Previous results from the literature [F. Herregodts, D. Hurtmans, J. Vander Auwera, and M. Herman (1999) J. chem. Phys., 111, 7954—7960] are revised.     

Two new integrable couplings of the soliton hierarchies with self-consistent sources

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with sl(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.     

A quasi-classical trajectory study of the Cl + H<Subscript>2</Subscript> (D<Subscript>2</Subscript>) reaction on a new BW3 potential energy surface

Molecular reaction dynamics of Cl + H₂ (D₂) has been studied on the latest analytical potential energy surface called BW3 using the Monte Carlo quasi-classical trajectory method. Excitation functions, differential cross sections and angular distributions of HCl and DCl products have been calculated. The excitation functions of the Cl (²P_3/2) + n-H₂ and Cl(²P_3/2) + n-D₂ reactions are also studied. The results are compared with those of quasi-classical trajectory [M. Alagia et al.: Phys. Chem. Chem. Phys. 2 (2000); F. J. Aoiz et al.: J. Phys. Chem. 100 (1996)], quantum mechanical (QM) calculations [F. J. Aoiz et al.:J. Chem. Phys. 115 (2001)] and experimental data [S. H. Lee et al.: J. Chem. Phys. 110 (1999); F. Dong et al.: J. Chem. Phys. 115 (2001)]. Discussions are given to some new results.     

The dipole moment distribution on water is improved by using large flexibility and large bending angle

A highly flexible model of water with fixed charges is used to study properties of water. The bending angle of an isolated molecule is 125^○ that was chosen to match the experimental dipole moment. The geometry of water in the liquid phase is made closer to that of the rigid SPC/E model by decreasing the bending angle spring constant, k _Θ. The new model, called SPCE-FHΘ, is a modified version of the recently proposed SPCE-FH [J. Alejandre, G.A. Chapela, F. Bresme and J.-P. Hansen, J. Chem. Phys. 130, 174505 (2009)] to simulate ionic solutions which includes short ranged interactions on the hydrogen atoms. By increasing angle flexibility it is possible to obtain, in the liquid phase at ambient conditions, bending angles ?Θ(HOH)? ～ 109^○, dipole moment ?μ? ～ 2.5 D and dielectric constant ?ε? ～ 80. The dipole moment distribution at room temperature goes from 1.5 to 3.5 D due to large fluctuations in bending angle and has the same trend found in ab initio simulations of liquid water. The dipole moment profile at the interface of water varies from 1.9 D in the vapour phase to 2.5 D in the liquid region at 400 K. The SPCE-FHΘ gives dipole moment, dielectric constant, coexisting densities and surface tension along the liquid–vapour coexistence line closer to the experimental values than those obtained for the SPC/E force field.     

The individual success of musicians, like that of physicists, follows a stretched exponential distribution

Over the last five years or so, a number of studies have focussed on the distribution of `success' in physics and other sciences; in these studies, `success' is measured by the number of times a paper, or an author, is cited. The distribution of citations of individual papers approximates to a power-law [S. Redner, Eur. Phys. J. B 4, 131 (1998)], while lifetime total citations of the 1120 most-cited physicists follows a stretched exponential [J. Laherrère, D. Sornette, Eur. Phys. J. B 2, 525 (1998)]. Here, I examine the distribution of success in popular music, a field of creativity that has social structures very different from those of physics, and which is generally held to be controlled primarily by fashion. For this study, the lifetime total success of bands was measured by the total number of weeks they were in the weekly `top 75' list of best-selling recordings. Like the lifetime success of physicists reported by Laherrere and Sornette, the success of the 6107 bands that appeared in the UK `top 75' from 1950 until 2000 follows a stretched exponential of the form P(x)dx = c(x ^{c - 1}/x ₀ ^c)exp[- (x/x ₀)^c]dx; for the music data, c = 0.5 and x ₀ = 9.37. Received 23 October 2001 Published online 25 June 2002     

A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field which represents a map S ³×RS ² and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies A·Bd³ r=n, n being an integer and an action constant, which necessarily appears in the theory, because of reasons of dimensionality.     

A refined potential energy surface and the rovibrational states for the electronic ground state of ozone

A potential energy surface for the electronic ground state of ozone has been optimized by using a variational procedure with the exact vibrational Hamiltonian in bond length-bond angle coordinates. In the optimization, the ab initio force field of Borowski, P., Andersson, K., Malmquist, P.-A., and Roos, B. O., 1992, J. chem. Phys., 97, 5568 is taken as the starting point, and the recent observed vibrational band origins up to 4900 cm^-1 reported by Floud, J.-M., Barbe, A., Camy-Peyret, C., and Plateaux, J. J., 1996, J. molec. Spectrosc., 177, 34 are involved. The root mean square error of this fit for the 39 observed vibrational energy levels is 0.83 cm^-1. In order to test the refined potential, the rovibrational energy levels up to J = 15 are calculated and compared with the observed values.     

Demonstration of the approximation of eliminating atomic excited populations in an atomben cavity system

Using the master equation approach to a V-type three-level atom inside a high-finesse single-mode cavity in the strong coupling condition, we demonstrate the approximation of eliminating populations of atomic excited states, which is widely used in the field of the atom-cavity systems [Hechenblaikner G, Gangl M, Horak P and Ritsch H 1998 Phys. Rev. A 58 3030]; Liu L W, Tan T and Xu Y 2008 J. Mod. Opt. 56 968; Cho J, Angelakis D G and Bose S 2008 Phys. Rev. A 78 062338. This is reflected in the deviation of the population δ, of which the value is 10^-3～10^-2. We further find the deviation of the dipole force and demonstrate that the deviation of atomic population will not notably affect the dipole force of the atom in the strong coupling condition. A relevant experimental case is also presented.     

Monte Carlo simulation of three-dimensional dilute Ising model

A multispin coding program for site-diluted Ising models on large simple cubic lattices is described in detail. The spontaneous magnetization is computed as a function of temperature, and the critical temperature as a function of concentration is found to agree well with the data of Marro et al.⁽⁴⁾ and Landau⁽³⁾ for smaller systems.The first successful epsilon expansion seems to be by D. E. Khmelnitskii,ZhETF 68:1960 (1975), English translationSov. Phys. JETP 41:981 (1975); for numerical estimates see K. E. Newman and E. K. Riedel,Phys. Rev. H25:264 (1982), for experiments see R. J. Birgenau, R. A. Cowley, G. Shirane and H. Yoshizawa,J. Stat. Phys. 34:817 (1984).     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.     

Stereochemical Assignment of Tertiary Hydroxyl Group in Diterpene Furan Glycosides by Pyridine Induced Shifts, 13C- and 2D-NMR Spectroscopy

The stereochemistry of the tertiary hydroxyl group in diterpene furan glycosides viz. cordifolisides D (1) and cordifoliside E (2) has been assigned on the basis of pyridine solvent induced shifts (PIS) in the ¹H and ¹³C NMR spectra. The methyl and the methylene groups occupying positions vicinal, 1,3-diaxial and geminal to the tertiary hydroxyl group were deshielded to different extent depending on the dihedral angle. The stereochemical assignments are well supported by ¹³C-γ shifts and 2D Overhauser spectroscopy.     

Quantum Singularity in Quasiregular Spacetimes, as Indicated by Klein-Gordon, Maxwell and Dirac Fields

Klein-Gordon, Maxwell and Dirac fields are studied in quasiregular spacetimes, those space-times containing a classical quasiregular singularity, the mildest true classical singularity [G. F. R. Ellis and B. G. Schmidt, Gen. Rel. Grav. 8, 915 (1977)]. A class of static quasiregular spacetimes possessing disclinations and dislocations [R. A. Puntigam and H. H. Soleng, Class. Quantum Grav. 14, 1129 (1997)] is shown to have field operators which are not essentially self-adjoint. This class of spacetimes includes an idealized cosmic string, i.e. a four-dimensional spacetime with a conical singularity [L. H. Ford and A. Vilenkin, J. Phys. A: Math. Gen. 14, 2353 (1981)] and a Gal'tsov/Letelier/Tod spacetime featuring a screw dislocation [K. P. Tod, Class. Quantum Grav. 11, 1331 (1994); D. V. Gal'tsov and P. S. Letelier, Phys. Rev. D 47, 4273 (1993)]. The definition of G. T. Horowitz and D. Marolf [Phys. Rev. D52, 5670, (1995)] for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. The definition is extended here, in the case of quasiregular spacetimes, to include Maxwell and Dirac fields. It is shown that the class of static quasiregular spacetimes under consideration is quantum-mechanically singular independent of the type of field.