Front Form Research Articles

Experimental analysis of reservoir release wave routing in upland boulder bed rivers

AbstractReservoir release wave routing during 33 controlled reservoir releases, along 15 upland boulder bed river channel reaches, on five different regulated rivers were monitored to assess the importance of river channel roughness and reservoir release magnitude on reservoir release wave speeds. Wave speeds varied between 0.52 and 3.01 m s−1. Reservoir release wave translation, steepening, and attenuation occurred. With high channel roughness values reservoir release wave arrival speed is retarded in comparison to peak stage and wave steepening occurs, but with a reduction in channel roughness reservoir release wave front arrival is accelerated producing attentuation. The threshold between reservoir release wave front attenuation and steepening occurs at a pre‐release discharge/channel width of approximately 0.1, an index of channel roughness.The paper also demonstrates, via comparison of observed and calculated reservoir release wave speeds on the River Washburn, Yorkshire, the difficulty of accurately predicting flood wave movement in upland boulder bed channels using existing prediction equations. The calculated values, however, revealed systematic error with pre‐release discharge and reservoir release magnitude. Apparently the equations fail to account for the effects of high channel roughness together with pressure gradient forces, induced by rapid rates of stage change on the rising limb of reservoir releases. In order to accurately predict reservoir release wave movement in regulated rivers, this paper demonstrates that hydraulic studies need to be undertaken and pre‐release discharges prescribed to determine desired reservoir release wave routing behaviour. Manipulation of the reservoir release pattern at the dam alone, cannot dictate reservoir release wave front form downstream or wave speed.

Wigner Rotations and Precession of Polarization

An easy and direct derivation of Thomas precession is obtained from infinitesimal Wigner rotations arising in unitary representations of the Poincare group. For spin > 1/2, multipole parameters are studied from this point of view. The canonical 3-component definition of polarization arising naturally in this context is compared with formalisms which start form a pseudo 4-vector and an antisymmetric tensor respectively. The full Thomas equations, including Larmor precession, is derived using time derivatives of finite Wigner rotations. Exact solutions, with arbitrary initial conditions, are presented for constant magnetic fields and for orthogonal constant electric and magnetic fields. For a class of plane wave external fields exact solutions are obtained for the Dirac equation generalized by the inclusion of anomalous magnetic moment (Pauli) and electric dipole moment terms. Using the front form of dynamics, well-adapted to this context and coinciding with proper time dynamics, expectation values are calculated. The polarization pseudo 4-vector thus obtained is shown to satisfy the BMT equation, which is equivalent to the Thomas equation. This shows that the validity of the classical precession equations is not necessarily restricted to slowly varying external fields. These solutions can also be of interest in the study of spin 1/2 particles in laser fields and in the study of electric dipole moments.

Front form of relativistic Lagrangian dynamics in two-dimensional space-time and its connection with the Hamiltonian description

A Lagrangian relativistic theory is formulated in two-dimensional space-time in the front form of dynamics; the connection between it and predictive mechanics, the Hamiltonian description, and the theory of Fokker action integrals is established. Relations are found in a closed form without the use of formal expansions. The existence of mathematical restrictions on the values of the two-particle interaction Lagrangians is established.

Front form and point form formulation of predictive relativistic mechanics. Noninteraction theorems

The front form and the point form of dynamics are studied in the framework of predictive relativistic mechanics. The noninteraction theorem is proved when a Poincaré-invariant Hamiltonian formulation with canonical position coordinates is required.

Group theoretical methods in optics

Scalar Fourier optics is concerned with the passage of paraxial light beams through ideal optical systems. It is well known that the action of the latter on the former can be given in the framework of the two- and four-dimensional real symplectic groups. It is shown here that, based on an analysis of the Poincare symmetry of the complete Maxwell equations in the front form, a natural representation for paraxial Maxwell beams emerges, which moreover shows the way to a generalization of scalar to vector Fourier optics preserving the group structure of ideal optical systems. Properties of generalized rays, and the usefulness of some pseudo-orthogonal groups in the treatment of Gaussian Schell-model beams, are also brought out.

Instant and Front Form realizations for N relativistic particles

Instant and Front Form realizations of the Poincaré group are presented for two and N relativistic point particles. A physical interpretation in terms of world lines is given due to some explicit prescriptions for defining position coordinates in physical phase space.

Paraxial-wave optics and relativistic front description. II. The vector theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincar\'e group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincar\'e group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Paraxial-wave optics and relativistic front description. I. The scalar theory

The scalar wave equation is analyzed in the relativistic front form, appropriate for paraxial-wave optics. The group-theoretical basis for this treatment is uncovered. The formal similarity of the propagation of paraxial beams through optical systems to the quantum mechanics of particles in two dimensions subject to harmonic impulses, and the role of the metaplectic group of Bacry and Cadilhac, are both traced back to the structure of the Poincar\'e group. Light rays are defined in this context as in statistical-wave optics, and the laws for their free propagation as well as transmission through lenses are derived.

Relativistic two-nucleon calculations on the light front

The relativistic theory for few-nucleon systems developed by Giockle and Muller is transformed into the light front formalism. For a model of scalar particles exchanging scalar mesons the 10 generators of the Poincare group are derived in pure particle space up to lowest order in the coupling. Because of the impossibility of a complete partial-wave decomposition on the light front, only bound states can be calculated numerically. This is done for the two-body system. The results differ from those at an instant because of the omission of higher-order terms.

Origin of constraints in relativistic classical Hamiltonian dynamics

We investigate the null-plane or the front form of relativistic classical Hamiltonian dynamics as proposed by Dirac and developed by Leutwyler and Stern. For systems of two spinless particles we show that the algebra of Poincar\'e generators is equivalent to describing dynamics in terms of two covariant constraint equations, the Poisson bracket of the two constraints being weakly zero. The latter condition is solved for certain simple forms of constraints.

Reduction Formula and Non-Leptonic Decays in Light Front Formalism

Light-like front formalism!),Zl has been developed with relation to the fundamental problems about constituents of the hadrons. In this letter we show a reduction formula for a decay process a~8 + n- in the light­ like charge formalism and its advantages, in comparison with the reduction formula based on the conventional space-like defini­ tion of charge in the soft-meson limit3l •4l Let us denote a four-vector as shown in the position and momentum vectors,

Impact parameter and infinite-momentum frame kinematics

A group-theoretical interpretation of the impact parameter within the framework of the Poincare group is given. To this end timelike representations of the Poincare group are reduced with respect to the subgroup of transverse Galilei boosts and light front translations. It is shown that the eigenvalues of operatorsB1=(N1+M2)/(p0−p3),B2=(N2−M1)/(p0−p3), can be interpreted as a relativistic generalization of the impact parameter. One- and two-particle impact-parameter states are introduced and it is shown that the expansion of the scattering amplitude in terms of these states reduces to the usual impact-parameter expansion. It is demonstrated that the quantitiesB1,B2 recover the familiar definition of the impact parameter in the front form of classical mechanics too.

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.

Hamiltonian dynamics of fields in front form

We propose a new approach for constructing the Hamiltonian dynamics for a coupled Dirac field Ψ( x), quantized on the light-front t+ z = 0, in which the momentum representation of fields is used to obtain the anti-commutator for Ψ( x) and its momentum conjugate π( x). Aside from the usual definition of π( x), the Hamiltonian, the anti-commutators and the Hamiltonian equations of motion, we need a subsidiary condition for Ψ( x) to make the front-form dynamics consistent and valid in any inertial frame. By treating all components of Ψ( x) in the same manner and retaining the subsidiary condition, we make the theory simple and elegant. In contrast to the infinite-momentum-frame approach, there is no non-covariant term in the Hamiltonian and the propagator in our approach. The resultant Feynman rules make the equivalence of the scattering matrices between the front-form dynamics and the conventional dynamics become apparent. The difference between the two forms of dynamics is also discussed.

Temperaturegradient plates for growth of microorganisms.

Landman, Otto E. (Fort Detrick, Frederick, Md.), Howard T. Bausum, and Thomas S. Matney. Temperature-gradient plates for growth of microorganisms. J. Bacteriol. 83:463-469. 1962.-Different temperature-gradient plates have been devised for the study of microbial growth on solid media through continuous temperature ranges or in liquid media at finely graded temperatures. All plates are made of heavy-gauge aluminum; heat supplied at one end is dissipated along the length of the metal so that a gradient is produced. The shape and range of the gradient depends on the amount of heat supplied, the insulation, the ambient temperature, and other factors. Differences of 0.2 C in temperature sensitivity between bacterial strains can be detected. The plates are simple to construct and operate. The dimensions of the aluminum, the mode of temperature measurement, and the method of heating may all be modified without diminishing the basic utility of the device.A sharp growth front develops at the maximal temperature of growth of bacteria. In most strains, all bacteria below the front form colonies and all bacteria above the front are killed, except for a few temperature-resistant mutants.