Electrodynamics Under a Possible Alternative to the Lorentz Transformation

A generalization of the classical electrodynamics for systems in absolute motion in presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S is given by H = a(H – v × D) and E = a(E + v × B), where a is a matrix whose elements depend of the absolute velocity of the system. c) The constitutive relations in the moving frame S are given by D = E, B = H and J = E. It is found that Maxwell's equations, which are transformed to the moving frame, take a new form depending on the absolute velocity of the system. Moreover, differing from classical electrodynamics, it is proven that the electrodynamics proposed explains satisfactorily the Wilson effect.     

Trouton–Noble Paradox Revisited

An apparent paradox is obtained in all previous treatments of the Trouton–Noble experiment; there is a three-dimensional (3D) torque T in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque T′ in S′, the rest frame of the capacitor. Different explanations are offered for the existence of another 3D torque, which is equal in magnitude but of opposite direction giving that the total 3D torque is zero. In this paper, it is considered that 4D geometric quantities and not the usual 3D quantities are well-defined both theoretically and experimentally in the 4D spacetime. In analogy with the decomposition of the electromagnetic field F (bivector) into two 1-vectors E and B we introduce decomposition of the 4D torque N (bivector) into 1-vectors N _s , N _t . It is shown that in the frame of “fiducial” observers, in which the observers who measure N _s and N _t are at rest, and in the standard basis, only the spatial components and remain, which can be associated with components of two 3D torques T and T _t . In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in complete agreement with the principle of relativity and with the Trouton–Noble experiment without the introduction of any additional torque.     

On the maximum in the differential cross sections of the F + H2 reaction in the region of small scattering angles

By means of quantum mechanical simulation of the reaction F + H₂(v = 0; j = 0, 1, 2) → H + HF(v′, j′) on the Stark-Werner ground state potential energy surface at collision energies of 1.84, 2.74, and 3.42 kcal/mol, we have analyzed interference of the “partial waves” corresponding to different values of the total angular momentum J. As the vibrational quantum number v′ of the HF(v′, j′) product increases, the interference for the HF forward scattering becomes noticeably more constructive. This is probably the reason for the maximum in the angular distributions of the HF(v′= 3) molecules at small scattering angles that was discovered experimentally by D.M. Neumark, A.M. Wodtke, G.N. Robinson, C.C. Hayden, and Y.T. Lee, J. Chem. Phys. 82 (7), 3045 (1985) at the same collision energies. We have also determined the intervals of J values most effective for forward scattering of the HF(v′, j′) molecules.     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.     

Intermolecular interaction in plant oils from refractive and density measurements

Refractive indices n and density ρ of three plant oils (Anise, Nigelle, and Juniper berries) have been measured in the temperature range of 10–60°C. The model of the effective electric field E′ acting on a molecule in the material, E′ = E + x4πP, with the unlimited value of the coefficient of polarization input x has been applied to the analysis of the results obtained. The value x of the oils studied have been found to be in the range of 0.193–0.269, which is smaller than a similar value for water (x _water > 0.3), known as a strong polar liquid.     

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.     

Propagation of a transient electromagnetic disturbance in an inhomogeneous, collisional, Magnetized plasma

Summary The time response of an anisotropic, inhomogeneous magnetized plasma to a time-dependent externally applied electric field is studied. The plasma is considered as a conducting medium embedded in a static magnetic fieldB _o, with finite and constant parallel conductivity σ_∥ and normal conductivity σ_⊥ exponentially varying; a constant ion polarization conductivity (σ_pol) normal toB ₀ is also included. The driving termE ₀ is assumed to be normal to the ambient magnetic field, with a space dependence only in the (E ₀, B₀)-plane (two-dimensional case). The problem is treated as an initial (in time) and boundary (in space) value problem, and an analytic solution is obtained for the time response of the system to a unit step of electric field; the solution for any other driving field is then given via a convolution integral. This model can be used in particular to study the propagation through the ionosphere of ULF waves generated by the motion of an artificially created ion cloud in the upperF region. Moreover, the mathematical technique is rather general, so it may be used also for different plasma models.

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Riassunto Si presenta lo studio della risposta temporale (transitorio) di un plasma magnetizzato, anisotropo e inomogeneo ad un campo elettrico esterno impresso. Il plasma è trattato come un mezzo conduttore, immerso in un campo magnetico staticoB ₀, la cui conducibilità elettrica parallela al campo magnetico σ_∥ è costante, mentre la conducibilità normale σ_⊥ varia esponenzialmente nello spazio; si considera inoltre una conducibilità dovuta alla polarizzazione degli ioni (σ_pol) costante e normale aB ₀. Il campo impressoE ₀ è assunto normale al campo magnetico ambiente con dipendenza spaziale solo nel piano (E ₀, B₀) (caso bidimensionale). In queste ipotesi si perviene ad un problema ai valori iniziali e al contorno, e si deriva una soluzione analitica per la risposta transitoria del sistema ad un gradino di campo elettrico impresso; la soluzione per una qualsiasi funzione di campo applicato è data come integrale di convoluzione con la risposta al gradino. Questo modello può essere usato, in particolare, per studiare la propagazione attraverso la ionosfera di un'onda ULF generata dal moto di una nuvola ionica creata artificialmente nella parte superiore della regioneF. Un ulteriore interesse deriva dal fatto che, essendo la tecnica matematica utilizzata molto generale, questa può essere applicata pure a differenti modelli di plasma.

     

Dynamics of magnetic insulation failure and self-organization of an electron flow in a magnetron diode

The dynamics of back cathode bombardment (BCB) instability in a magnetron diode (a coaxial diode in a magnetic field, B ≡ B _0z ≡ B ₀) is numerically simulated. The quasi-stationary regime of electron leakage across the high magnetic field (B ₀/B _cr > 1.1, where B _cr is the insulation critical field) is realized. An electron beam in the electrode gap is split into a series of bunches in the azimuthal direction and generates the electric field component E _θ(r, θ, t), which accelerates some of the electrons. Having gained an extra energy, these electrons bombard the cathode, causing secondary electron emission. The rest of the electrons lose kinetic energy and move toward the anode. Instability is sustained if the primary emission from the cathode is low and the secondary emission coefficient k _se=I _se/I _{e, BCB} is greater than unity. The results of numerical simulation are shown to agree well with experimental data. A physical model of back-bombardment instability is suggested. Collective oscillations of charged flows take place in the gap with crossed electric and magnetic fields (E × B field) when the electrons and E × B field exchange momentum and energy. The self-generation and self-organization of flows are due to secondary electron emission from the cathode.     

Nature of conduction via impurities in uncompensated silicon

The static conductivity σ(E) and photoconductivity (PC) at radiation frequencies ħω=10 and 15 meV in Si doped with shallow impurities (density N=10¹⁶−6×10¹⁶ cm⁻³, ionization energy ε₁≃45 meV) with compensation K=10⁻⁴−10⁻⁵ in electric fields E=10–250 V/cm are measured at liquid-helium temperatures T. Special measures are taken to prevent the high-frequency part of the background radiation (ħω>16 meV) from striking the sample. It is found that the conductivity σ(E) is due to carrier motion along the D ⁻ band, which is filled with carriers under the influence of the field E. In fields E<E _q (E _q ≃100–200 V/cm) the carrier motion consists of hops along localized D ⁻ states in a 10–15 meV energy band below the bottom of the free band (energy ε=ε₁); for E>E _q carriers drift along localized D ⁻ states with energy ε∞ε₁−10 meV. An explanation is proposed for the threshold behavior of the field dependence of the photo-and static conductivities. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 232–236 (25 August 1997)     

Force constants from intensity analysis of molecules CH3Cl and CD3Cl

The secular equation (GF - Eλ)L = 0 contains more force constants than can be calculated from the equations formulated using the frequencies. For a 3 × 3 matrix, there are 6 force constants but only 3 frequencies. Attempts were made by others to estimate all the 6 constants to satisfy the frequencies and Coriolis constants and rotation distortion constants. However, many attempts are not made in these estimations to satisfy the intensities. A full complement of equations is derived to evaluate all the force constants combining the intensity equationsI =L’A withLL’ =G and evaluated the force constants ofA ₁ species of CH₃Cl and CD₃Cl. A simple analysis of a 2 × 2 matrix shows thatF ₁₂/F ₂₂=G ₁₂ ⁻¹ /G ₂₂ ⁻¹ as reported earlier.     

Multiple ionization of argon in coincidence with projectile ions in 60–120 MeV Si q+-Ar collisions

A projectile ion-recoil ion coincidence technique has been employed to study the multiple ionization and the charge transfer processes in collisions of 60–120 MeV Si ^q+ (q = 4−14) ions with neutral argon atoms. The relative contribution of different ionization channels, namely; direct ionization, electron capture and electron loss leading to the production of slow moving multiply charged argon recoil ions have been investigated. The data reported on the present collision system result from a direct measurement in the considered impact energy for the first time. The total ionization cross-sections for the recoil ions are shown to scale as q ^1.7/E _p ^0.5 , where E _p is the energy in MeV of the projectile and q its charge state. The recoil fractions for the cases of total- and direct ionizations are found to decrease with increasing recoil charge state j. The total ionization fractions of the recoils are seen to depend on q and to show the presence of a ‘shell-effect’ of the target. Further, the fractions are found to vary as 1/j ² upto j = 8+. The average recoil charge state 〈j〉 increases slowly with q and with the number of lost or captured electrons from or into the projectile respectively. The projectile charge changing cross-sections σ _qq′ are found to decrease with increasing q for loss ionization and to increase with q for direct-and capture ionization processes respectively. The physics behind various scaling rules that are found to follow our data for different ionization processes is reviewed and discussed.     

TDPAC studies of the intercalation compound Li x TiS2 in the region 0≤x≤1

The electrochemical intercalation of Li⁺ into hafnium-doped TiS₂ was studied using time-differential perturbed angular correlations (TDPAC). The¹⁸¹Ta nuclear quadrupole interaction was monitored as a function of the charge transfer,n _F. For low uptakes, 0≤n _F≤0.03, a two-phase region was found with an empty host interaction, characterized byV _q=458(4) MHz, η=0.19(3) and δ-0.083(5), and a second interaction corresponding to lithiated material withv _q=597(5) MHz, η=0.13(4) and δ=0.061(5). No evidence was found for intermediate phases.     

Motion of vortex lines and mutual friction in superfluid4He nearT λ

The motion of a single vortex line in superfluid⁴He nearT is studied within modelF. The linear response of the vortex-line velocityv _L to a homogeneous counterflowv _s –v _n is calculated up to lowest order of renormalized perturbation theory. The critical temperature dependence is taken into account via the renormalizationgroup theory. Non-asymptotic critical effects are found to be important. The results are generalized to describe collective vortex motion and mutual friction in rotating superfluid⁴He. The phenomenological mutual-friction coefficientsB andB of Hall and Vinen are determined without adjustment of parameters. ForB quantitative agreement with experiments nearT is found whereas forB the agreement is only semiquantiative.     

Dynamic shielding of a charge in a metal

A discussion of the shielding of a charged particle in a current-carrying conductor is given that is based on the linearized Thomas-Fermi approximation. An expression for the force on a particle of charge q is obtained from which the value of the electric field E_c in the conductor may be found:

$\text{E}{}_{\mathrm{c}}\text{=}\text{lim}\text{q→0}\text{F}{}_{\mathrm{q}}\text{/q}$

It is shown that the force on the particle has the form $\text{F}{}_{\mathrm{q}}\text{= q}\text{E}{}_0\text{× (1 + γ(}\text{q}\text{e}\text{) + …}$ to second order in the charge q, where E₀ is the electric field at large distances from q, e is the charge of the carrier, and γ is a material-dependent constant. The shielding correction has the character of a “wind-force,” and the electric field in the conductor is given by Ec = E₀.     

Damping of zero sound in Luttinger liquids

We calculate the damping γ_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k² / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ_q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k_F ≪F (where k_F = m v_F is the Fermi wave-vector) we find to leading order γ_q ∝| q |³ /(v_F m²). On the other hand, for F ≪| q| /k_F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q²/m. We also show that zero sound damping leads to a finite maximum proportional to |k - k_F | ^{-2 + 2 η} of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_0.3MoO₃. We comment on other recent calculations of γ_q.     

Thermal boundary layer for non-Newtonian fluid

Summary Analytical and numerical solutions for the momentum and thermal boundary layer equations of a non-Newtonian power law fluid are presented. The flow is assumed to be under the influence of an external magnetic fieldB (x) applied perpendicular to the surface and an electric fieldE(x) perpendicular toB(x) and the direction of the longitudinal velocity in the boundary layer. For the power law fluid it is assumed that the shear stress is proportional to then-th power of the velocity gradient andn is called the flow index. The variations of the velocity fieldf′, the temperature field θ, the shear stress on the surfaceτ _W , the displacement thicknessδ ₁ and the momentum thicknessδ ₂ with the magnetic-field parameter γ, the flow indexn, the heat transfer indexS and the Prandtl number Pr are studied. It is found that, if the outer flow velocityU(x) (potential flow) is proportional to the arc lengthx raised to a powerm, then the similarity solution for the thermal boundary layer equation is possible only whenm=1/3, which represents flow past a wedge of included angle π/2. It is established that the temperature of the wedge increases with the increase of γ, Pr,S and the decrease ofn. In general the magnetic field can be used as a heater for the surface of the wedge.     

Interaction force between incompatible star-polymers in dilute solution

We consider a low-density assembly of spherical colloids, such that each is clothed by L end-grafted chemically incompatible polymer chains either of types A or B. These are assumed to be dissolved in a good common solvent. We assume that colloids are of small size to be considered as star-polymers. Two adjacent star-polymers A and B interact through a force F originating from both excluded-volume effects and chemical mismatch between unlike monomers. Using a method developed by Witten and Pincus (Macromolecules 19, 2509 (1986)) in the context of star-polymers of the same chemical nature, we determine exactly the force F as a function of the center-to-center distance h. We find that this force is the sum of two contributions F _e and F _s. The former, that results from the excluded volume, decays as F _e∼A _L h ^-1, with the L -dependent universal amplitude A _L∼L ^3/2. While the second, which comes from the chemical mismatch, decays more slowly as F _s∼χB _L h ^{-1 - τ}, where τ is a critical exponent whose value is found to be τ 0.40, and χ is the standard Flory interaction parameter. We find that the corresponding L-dependent universal amplitude is B _L∼L ^{3 + τ /2}. Theses forces are comparable near the cores of two adjacent star-polymers, i.e. for h∼h _c∼a (a is the monomer size). Finally, for two star-polymers of the same chemical nature (A or B), the force F that simply results from excluded-volume effects coincides exactly with F _e, and then the known result is recovered. Received 2 October 2000 and Received in final form 24 January 2001     

Numerical investigation of the theta pinch in intrinsic indiumantimonide

The electron-hole plasma in intrinsic InSb at 300 K can be compressed by electric and magnetic fields. In the theta-pinch configuration one applies, by a capacitor discharge over a one-winding coil around the sample, a magnetic field (0, 0,B _z), which induces an electric field (0,E _φ, 0); both fields cause the ambipolar motion (v _r, 0, 0) of the plasma. We describe the electron-hole plasma by means of a magnetohydrodynamical two-fluid model. The resulting system of differential equations is solved numerically under the assumptions of scalar hydrodynamic pressure and field-independent mobilities. The influence of the plasma properties on the theta pinch is studied as well as the dependence on the experimental conditions like radius of the sample, maximum value and risetime of the magnetic field.     

EPR of trivalent iron ions in a LiCaAlF6 crystal

The orientational dependences of the EPR spectra of Fe³⁺-doped LiCaAlF₆ single crystals (space group P31c, Z=2), grown at the Laboratory of Magnetic Radio Spectroscopy at Kazan’ State University, have been investigated in detail. The spectrum is described by a trigonal spin Hamiltonian with the following parameters: B ₂₀=40.072×10⁻⁴ cm⁻¹, B ₄₀=−5.799×10⁻⁴ cm⁻¹, B ₄₃=−4.281×10⁻⁴ cm⁻¹, A _s=24.33±1, A _p=6.13±1, g _∥=g _⊥=2.00217±0.0003. A theoretical calculation of the hyperfine structure parameters shows that they are described quite well when allowance is made for the overlapping of the wave functions of the paramagnetic center and the ligands (F⁻). Fiz. Tverd. Tela (St. Petersburg) 39, 488–490 (March 1997)     

Redistribution of excess space charge in structures based on single-crystal strontium titanate

A band mechanism for transport in single-crystal strontium titanate (STO) is used as a basis for estimating the parameters characterizing the localization and redistribution of space charge in STO for T<100 K. A comparison of the experimental and calculated temperature dependences of the charge carrier concentration yield an estimate for the location of the Fermi level in STO at T=4.2 K with E _F-E _v∼10 meV. The phenomena at metal/STO and YBCO/STO contacts are discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 349–352 (February 1997)