Full Vacuum Research Articles

Global Results for the Rarita-Schwinger Equations and Einstein Vacuum Equations

We prove global existence and uniqueness of solutions to the Rarita-Schwinger evolution equations compatible with the constraints. We use a gauge fixing for the Rarita-Schwinger equations for helicity 3/2 fields in curved space that leads to a straightforward Hilbert space framework for their study. We explain how these results might be applied to the global analysis of the full Einstein vacuum equations and provide a complete analysis as a basis for such applications. These and a programme for developing a scattering/inverse scattering transform for the full Einstein equations are discussed. 1991 Mathematics Subject Classification: 83C60, 35Q75, 83C05, 35L45.

Empty matter and the full physical vacuum

Experiments with elementary particles have shown that much of matter is made up of empty space, but this vacuum is not really empty. The uncertainty principle allows the temporary existence of virtual particles, and these have been shown experimentally to have measurable effects.

Coupling constant and quark-loop expansion for corrections to the valence approximation

For full QCD vacuum expectation values we construct an expansion in quark loop count and in powers of a coupling constant. The leading term in this expansion is the valence (quenched) approximation vacuum expectation value. Higher terms give corrections to the valence approximation. A test of the expansion is presented for moderately heavy quarks on a small lattice. We consider briefly an application of the expansion to quarkonium-glueball mixing.

Résultats globaux pour les équations de Rarita—Schwinger en espace-temps d'Einstein asymptotiquement plats

We study the Rarita-Schwinger equations on globally hyperbolic asymptotically flat vacuum space-times. We use a gauge fixing that guarantees the positive definiteness of the conserved quantity at each time. This leads to a straightforward Hilbert space framework in which we solve the global Cauchy problem. Applications to the analysis of the full Einstein vacuum equations are briefly discussed.

Bioventing in Shallow Tundra Overlying Permafrost

The purpose of this research was to investigate the feasibility of suction bioventing for treatment of contaminated tundra soil. Two laboratory-scale venting reactors were prepared with tundra from Arctic Alaska and operated, one for 32 d and the other for 52 d. For each rectangular reactor, suction was applied to a central well screened at mid-depth, while opposite ends of the reactor were screened to serve as air intake zones. The volume of liquid and gas recovered from the suction well was quantified daily. Numbers for heterotrophic organisms, pH, and dissolved organic carbon were quantified in the recovered liquid. The suction pump held a full vacuum (i.e., 101 kPa vac) for the duration of both experiments, indicating continuous obstruction of pneumatic and hydraulic conductivity. In both reactors, the soil in the proximity of the suction well separated from the bulk of the soil, precluding hydraulic communication. Furthermore, the soil nearest the well screen compacted, forming a barrier to appreciable pneumatic conductivity. At the end of operation, the soil was removed and sampled for moisture content, pH, and numbers of heterotrophic organisms at various locations. The results of this study showed that for suction bioventing to be successful in tundra, consolidation of the soil around the well screen must be prevented, as it will cause well isolation and limit both pneumatic and hydraulic conductivities.

Improving stochastic estimator techniques for disconnected diagrams

Disconnected diagrams are expected to be sensitive to the inclusion of dynamical fermions. We present a feasibility study for the observation of such effects on the nucleonic matrix elements of the axial vector current, using SESAM full QCD vacuum configurations with Wilson fermions on 16 3 × 32 lattices, at β = 5.6. Starting from the standard methods developed by the Kentucky and Tsukuba groups, we investigate the improvement from various refinements thereof.

Influence of the full vertex and vacuum polarization on the fermion propagator in (2+1)-dimensional QED.

We investigate the influence of the full vacuum polarization and vertex function on the fermion propagator, using the coupled Dyson-Schwinger equations for the photon and fermion propagator. We show that, within a range of vertex functions, the general behavior of the fermion propagator does not depend on the exact details of the vertex, both in the massless and in the massive phase. Independent of the precise vertex function, there is a critical number of fermion flavors for dynamical mass generation in (2 + 1)-dimensional QED. A consistent treatment of the vacuum polarization is essential for these results.

Effect of Reaction Time on Poly(ethylene terephthalate) Properties

Byproducts are formed at various times or positions within the PET process. During esterification, the conversion rate of terephthalic acid and ethylene glycol is the highest, and the largest changes are observed in prepolymer carboxyl end group and diethylene glycol concentration. During the polycondensation stage, under full vacuum, when the reaction temperature is highest, molecular weight increases at the fastest rate. Color changes dramatically during this period. The product becomes grayer and greener as a result of the reduction of the Sb 3+ polycondensation catalyst to antimony metal and more yellow because of the formation of colored, high molecular weight byproducts via polymer degradation reactions. A previously unidentified byproduct, trans-4,4'-dicarboxystilbene, formed in this stage, is fluorescent and could contribute to the fluorescence of PET. This compound is also significant because it indicates that the redox chemistry which produces high molecular weight byproducts during polycondensation may result in the reduction of Sb 3+ to Sb 0 .

Nontrivial vacua from equal time to the light cone.

Kinematic arguments suggest that the perturbative vacuum may be an eigenstate of the full Hamiltonian for light-cone-quantized field theories. Nevertheless, properties such as spontaneous symmetry breaking can be accommodated in this approach, by applying a quantization which interpolates between equal-time and light-cone quantization and in which the quantization surface may approach the light cone as a limit. In several simple two-dimensional models presented here, including the Gross-Neveu and Schwinger models, the difference between the full and perturbative vacuum vanishes in this limit. Nonzero vacuum expectation values, however, are preserved by singularities in the fields near ${k}_{\ensuremath{-}}=0$. Furthermore, this procedure provides a simple treatment for massless fields and nontrivial tests of Lorentz invariance, and may be applied to models, such as that of Gross and Neveu, for which conventional light-cone quantization is difficult to implement. Finally, the connection between long distances and short times suggests that vacuum effects may be incorporated in an effective Hamiltonian.

Radiation-induced electrical discharges in complex structures

Polyethylene terephthalate (PET) foils were exposed to 25-keV electron beams of 3 nA/cm/sup 2/, which has been known to charge the PET surface to -15 kV or more and to produce rapid pulse discharges sufficient to lower the magnitude of the surface potential significantly. The major experimental finding is that the pulse discharges often propagate to nearby mutually biased electrodes and can create a full vacuum breakdown between stainless steel electrodes, rarely if biased at as little as 100 V, but often if biased at 300 V. The phenomena appear to be associated with the pulsed creation of dense plasma from the discharging dielectric, and the pulsed volume of gas evolved is equivalent to roughly 0.1 to 0.4 mm/sup 3/ at 1 atm for nominally 50-cm/sup 2/ samples. The plasma could evolve to interconnect more than two electrodes. Additionally, PET pulse rates were strongly dependent upon the proximity of sharp edges, either metallic or dielectric. >

Sizing of vacuum relief valves for atmospheric distillation columns

Abstract A distillation column operating under pressurized conditions may not be designed for full vacuum. A vacuum relief valve on such column must, therefore, be sized to prevent negative pressures in the shell under the worst case scenario, i.e. when the feed, bottoms, distillate and reboiler steam are cut off, but the condenser still operates. The valve can be sized considering that the inflowing air (or other gas) first accumulates in the condenser, which is the vacuum source, and blankets the heat exchange area stopping the condensation. A conservative estimate of the amount of air required to blanket the condenser is given by the condenser volume. The rate at which this inflow must occur can be found from a transient total energy balance around the column, as described below. This method has been applied for valve sizing in real columns and results in reasonable valve sizes. To the best of our knowledge, no other method for carrying out this calculation is available in the open literature.

A connection between the Einstein and Yang-Mills equations

It is our purpose here to show an unusual relationship between the Einstein equations and the Yang-Mills equations. We give a correspondence between solutions of the self-dual Einstein vacuum equations and the self-dual Yang-Mills equations with a special choice of gauge group. The extension of the argument to the full Yang-Mills equations yields Einstein's unifield equations. We try to incorporate the full Einstein vacuum equations, but the approach is incomplete. We first consider Yang-Mills theory for an arbitrary Lie-algebra with the condition that the connection 1-form and curvature are constant on Minkowski space. This leads to a set of algebraic equations on the connection components. We then specialize the Lie-algebra to be the (infinite dimensional) Lie-algebra of a group of diffeomorphisms of some manifold. The algebraic equations then become differential equations for four vector fields on the manifold on which the diffeomorphisms act. In the self-dual case, if we choose the connection components from the Lie-algebra of the volume preserving 4-dimensional diffeomorphism group, the resulting equations are the same as those obtained by Ashtekar, Jacobsen and Smolin, in their remarkable simplification of the self-dual Einstein vacuum equations. (An alternative derivation of the same equations begins with the self-dual Yang-Mills connection now depending only on the time, then choosing the Lie algebra as that of the volume preserving 3-dimensional diffeomorphisms.) When the reduced full Yang-Mills equations are used in the same context, we get Einstein's equations for his unified theory based on absolute parallelism. To incorporate the full Einsteinvacuum equations we use as the Lie group the semi-direct product of the diffeomorphism group of a 4-dimensional manifold with the group of frame rotations of anSO(1, 3) bundle over the 4-manifold. This last approach, however, yields equations more general than the vacuum equations.

QCD potentials with dynamical quarks at finite temperatures

We investigate the potential between a static quark-antiquark pair in the full QCD vacuum. The dynamical quark sea is considered both by Kogut-Susskind and Wilson fermions. Two temperatures T below and above the phase transition T c are studied. The behavior of the interquark potential in the full quantum field is driven by the explicitly broken Z 3 symmetry in the fermionic action for T< T c and by an additional spontaneous Z 3 symmetry breaking for T< T c .

A kinetic model for the vacuum refining of inductively stirred copper melts

An experimental investigation into the removal of impurities (bismuth, lead, arsenic, and antimony) from baths of molten copper (blister, anode and cathode type copper) under vacuum was carried out. A pilot scale vacuum induction melting facility was used for these tests. The effects of (1) vacuum levels of 8.0 to 40.0 Pascals, (2) melt temperatures of 1150 to 1350 °C, (3) melt surface area to volume ratios of 6 to 10 m−1, (4) a water cooled condenser placed within a distance of two centimeters above the melt surface, and finally, (5) different levels of dissolved oxygen and/or sulfur contained in the melt, were studied. Kinetic data were obtained for evaluating the potential of a full scale vacuum melting facility. A mathematical model was also developed for the proper interpretation of the experimental results and for making projections for lower pressure and higher temperature levels. The rate of removal of bismuth and lead increased as the chamber pressure was lowered and the melt temperature increased, while removal of arsenic and antimony was negligible. Neither the melt surface area to volume ratio nor the distance of the condenser to melt surface had any significant effects on the rate constants governing the rate of removal of impurities. The rate of elimination of bismuth and lead over the range of 1150 to 1350 °C and 40.0 to 8.0 Pa followed first order kinetics. Removal rates were largely controlled by mass transport in the gas phase.

The Maxwell, Yang-Mills and Einstein equations and closed path parallel propagation

Two linear partial differential equations (and several non-linear generalizations) for a function H, defined on the unit sphere, will be described and their relationship to gauge fields discussed. The two equations are ∂H + ∂ A = 0 and ∂H + [H, A] + ∂ A = 0 , where the differential operators ∂ and ∂ are given by either ∂ A= −sinθ ∂ ∂θ + i sinθ ∂ ∂φ ( A/sinθ) , ∂ H= −sinθ ∂ ∂θ + i sinθ ∂ ∂φ ( H/sinθ) , or (using complex stereographic coordinates (ζ, ζ ) given by ζ = e iφ cot θ/2) ∂ A = 2P 2 ∂ ∂ζ ( A/P) , ∂ H = 2P 2 ∂ ∂ζ ( H/P) with P = 1 2 (1 + ζ ζ) . The function A is to be considered as (essentially) an arbitrary function of three variables u, θ, φ (or u, ζ, ζ ) where u is a particular given function of (θ, φ) and four parameters x a , ( a = 0, 1, 2, 3), i.e. A has the form A ( u(θ, φ, x a ), θ, φ). In eq. (1), H and A are scalar valued while in eq. (2) they are matrix (or Lie algebra) valued. The claim now is that eq. (1) is equivalent to the vacuum Maxwell equations and eq. (2) is equivalent to the anti-self-dual Yang-Mills equations. The x a , which only appear as parameters in the equation, represent the Minkowski space-time points. In both equations the function H( x a , θ, φ) has a simple geometric interpretation as an infinitesimal holonomy operator (or parallel propagator) associated with a particular family of paths, while the function A ( u, φ, θ) is the free characteristic data for the respective fields. In both cases the fields F ab and vector potential γ a are easily determined from knowledge of H. Eqs. (1) and (2) have been generalized to the following cases; 1. a) the full vacuum Yang-Mills equations on Minkowski space; 2. b) the Maxwell and Yang-Mills equations on a given asymptotically flat space-time; 3. c) the asymptotically flat vacuum solutions of the Einstein equations, with the self or anti-self-dual fields as a simple special case. Only in the maxwell and self-dual Yang-Mills case are the equations linear. In each of the succeeding cases the interactions between H and its complex conjugate H gets more complicated. Moreover the equations become integro-differential equations which is a manifestation of the non-Huygens nature of the propagation.

An analytic algorithm for decoupling and integrating systems of nonlinear partial differential equations

Abstract An analytic method is presented which by taking advantage of integrability conditions decides if a system of equations, in which the functions and their partial derivatives have only positive integer exponents, allows solutions and leads to new equations of lower order. The method is especially striking if the equations are overdetermined and can be implemented on a computer. An application to the full vacuum field equations of general relativity in the presence of a Killing vector leads to the known formulation with potentials.

Laboratory-scale controlled-atmosphere chamber for use with premium coal samples

The recent availability of premium coal samples makes it desirable to have the capability for working with these materials, in one’s own laboratory, in an atmosphere which can be controlled. A controlled-atmosphere chamber, large enough to allow for processing samples yet small enough to fit easily in an ordinary laboratory, has been designed and fabricated. The overall cost of this controlled-atmosphere chamber was competitive with commercially available systems. The major advantages of this specific system include: convenient size and reversible design for use in a limited work space; incorporation of a full vacuum antechamber that minimizes loss of the working chamber purified atmosphere; and a recirculating system with a bypass valve arrangement allowing separate or combined operation of oxygen and moisture removal systems. The design features were combined to create a unique apparatus capable of both the specific use for which it was intended and general controlled-atmosphere chamber applications. Compatible modular-design work chambers could have been purchased from commercial vendors; however, it still would have been necessary to custom fabricate both the antechamber and recirculation system to meet the requirements of the anticipated experimental work.

The electric field of a pulsar magnetosphere

Numerical solutions are found for the electric field of a simplified model of a radio pulsar's magnetosphere. The magnetic field assumed is that of a rotating point dipole with modulation in radius and azimuth chosen to emulate the effect of the field line sweepback expected in a full magnetospheric solution. This choice allowed an analytic solution for the noncorotation potential which was used in verifying the numerical results. The magnetic and rotation axes were assumed to be orthogonal Nonneutral beams of particles were injected along the polar field at radii r = 0.1 R/sub L/, where R/sub L/ is the light cylinder distance. The properties of these beams were chosen according to an existing theory of low-altitude particle acceleration. Nonpolar field lines were modeled as regions of corotation. Pair creation is neglected, as is appropriate for objects of sufficiently weak field and also as is appropriate for studies of the stability of a magnetosphere with respect to pair creation. Specific results are obtained for rotation period P = 0.5 and magnetic moment ..mu.. = 5 x 10/sup 29/ cgs. Our results show that the maximum noncorotation potential reached is 20%--35% of the full vacuum potential drop which can occur overmore » the polar caps when the neighboring closed zone is a good conductor. This percentage increases a the assumed radius of the last closed field line is decreased below R/sub L/. The ratio Vertical BarEVertical Bar/Vertical BarBVertical Bar was calculated to see where acceleration across B can occur, as this is an important mechanism for the formation of return currents in more realistic pulsar models.« less

Evaluation of the colliding beam accelerator first string full cell vacuum system

The CBA (colliding beam accelerator, formerly know as ISABELLE) full cell magnet system consisting of six superconducting dipole magnets and two superconducting quadrupole magnets requires two separate vacuum systems. One, known as beam vacuum, operates below 3×10−11 Torr and the other, known as insulating vacuum, operates at less than 10−7 Torr to isolate cryocircuits from atmosphere and from the UHV beam tubes. The UHV bore tube is isolated from the 4.0 K magnet by 36 layers of superinsulation and insulating vacuum. Heat load measurements on the bore tube have been completed and found to agree with data obtained in smaller controlled experiments. Measurements of helium, accumulated on cryogenic pumped charcoal panels over many weeks, have verified sensitive helium mass spectrometer leak detection methods for vacuum integrity, proving sound design of the welded complex. The full cell was assembled and operated under conditions that would exist in the completed machine. Pressures below 2×10−11 Torr beam vacuum requirement and below 1×10−7 Torr insulating vacuum, were routinely achieved during all phases of the full cell operation and support systems testing.

Synchrotron Radiation Lead Shielding of the Vacuum Chambers for LEP

The high linear power density and the energetic photon spectrum in LEP impose a complete radiation shield around the vacuum chamber. The absorption and scattering of the photons in the vacuum chamber has been studied with the use of the Monte Carlo shower program EGS in view of defining the lead shielding required for acceptable dose levels. To avoid the excessive production of ozone or of corrosive products in the air surrounding the vacuum chamber it is proposed to apply the lead shield directly onto the aluminium profile. In this way the cooling circuits of the vacuum chamber can cool the lead shield which will later be necessary at increased LEP energies. Different methods of bonding the lead to the aluminium have been studied and have resulted in a cladding process using a tin-lead solder joint. This method has been applied to aluminium tubes of up to 12 m length and to full size prototype vacuum chambers.