Topological bootstrap theory of hadrons

A topological framework is constructed for anS-matrix bootstrap theory of particles. Each component of anS-matrix topological expansion is associated with a pair of intersecting “quantum” and “classical” surfaces whose complexity exhibits an entropy property. The bounded classical surface embeds graphs that carry the direct observables — energymomentum, spin and electric charge. The closed quantum surface carries a triangulation whose orientations represent internal quantum numbers — which turn out to be baryon number, lepton number and flavor. A form of “color” automatically appears. All strong-interaction components of the expansion are generated through “Landau connected sums” from “zeroentropy” surface pairs — which are self generating. Elementary particles correspond to triangulated areas on the quantum surface; consistency at zero entropy determines allowed hadrondisks on quantum spheres together with the associated quantum numbers. Elementary topological hadrons turn out to include mesons, baryons and baryoniums, with quarks appearing as “peripheral triangles” (along the perimenters of hadron disks) whose attachments correspond to a total of 8 flavors as well as spin. Individual quarks do not carry momentum and cannot be hadrons; quark confinement is automatic. Also appearing within hadron disks are “core triangles” that carry baryon number and electric charge but no flavor or spin. Hadron disks have quantum numbers that accord with the lowestmass physically-observed mesons and baryons. The relation of topological theory to QCD is discussed.     

Essential restriction on the symmetry of a unified theory for the case of massive gluons

In unified gauge theories with massive “color” gluons, the physical requirement of maintaining “color” SU(3) as a global classification symmetry is shown to lead to the following restrictions: (i) the local unifying symmetry group must be of the form G_flavor?G_color; (ii) quarks are to be integer charged; (iii) the number of flavors is an integral multiple of the number of “colors”.     

Maximum “focusing” of surface phonons

“Focusing” of surface phonons is studied in detail. Three types of surface phonon “focusing” are found. The asymptotic dependence of the amplitude u of surface wave on the distance r from a point source is obtained for every “focusing” type. The type of maximum “focusing” where $\text{u((r)～ O(r}{}^{\mathrm{<mtext>?1</mtext><mtext>4</mtext>}}\text{)}$ holds is picked out. The “focusing” type is shown to be changed as elastic anisotropy is altered.     

Asymptotic Behavior of Beta-Integers

Beta-integers (“β-integers”) are those numbers which are the counterparts of integers when real numbers are expressed in an irrational base β > 1. In quasicrystalline studies, β-integers supersede the “crystallographic” ordinary integers. When the number β is a Parry number, the corresponding β-integers realize only a finite number of distances between consecutive elements and are in this sense the most comparable to ordinary integers. In this paper, we point out the similarity of β-integers and ordinary integers in the asymptotic sense, in particular for a subclass of Parry numbers – Pisot numbers for which their Parry and minimal polynomial coincide.     

MHD effects on the channel flow of a fractional viscous fluid through a porous medium: An application of the Caputo-Fabrizio time-fractional derivative

This research article considers the exact solutions and theoretical aspects of the channel flow of a fractional viscous fluid which is electrically conducting and flowing through a porous medium. Joint Laplace and Fourier transform techniques are used to solve the momentum equation. The Caputo-Fabrizio time fractional derivative is used in the constitutive equations. Exact solutions for an arbitrary velocity are obtained, and then in the limiting cases over a bottom plate three types of flow are considered: that is, the impulsive, accelerating and oscillating motion of the fluid. The case where the flow of the fractional fluid is unaffected by the side walls, is correspondingly taken into account. For oscillating flow the solutions are separated into steady and transient parts for both sine and cosine oscillations. Moreover these solutions are captured graphically, and the effect of the Reynolds number “Re”, fractional parameter “α”, effective permeability “K_eff” and the time “t”, on the fluid's motion are observed.     

A k-distribution-based radiation code and its computational optimization for an atmospheric general circulation model

The gas absorption process scheme in the broadband radiative transfer code “mstrn8”, which is used to calculate atmospheric radiative transfer efficiently in a general circulation model, is improved. Three major improvements are made. The first is an update of the database of line absorption parameters and the continuum absorption model. The second is a change to the definition of the selection rule for gas absorption used to choose which absorption bands to include. The last is an upgrade of the optimization method used to decrease the number of quadrature points used for numerical integration in the correlated k-distribution approach, thereby realizing higher computational efficiency without losing accuracy. The new radiation package termed “mstrnX” computes radiation fluxes and heating rates with errors less than 0.6 W/m² and 0.3 K/day, respectively, through the troposphere and the lower stratosphere for any standard AFGL atmospheres. A serious cold bias problem of an atmospheric general circulation model using the ancestor code “mstrn8” is almost solved by the upgrade to “mstrnX”.     

Quantum creation of multidimensional universes

A non zero probability amplitude for the appearance of a multidimensional universe of (1+d) dimensions is found. This can happen either in a “symmetric phase”, in which all dimensions are in an exponential expansion, or else in a “broken phase”, withd ₁ dimensions inflating exponentially andd ₂ forming a sphere of constant radius. The value of these amplitude for different total number of dimensions is discussed, and so physical consequences for Kaluza-Klein cosmologies are drawn.     

Temperature evolution of the hysteresis in the current-voltage characteristic of a polycrystalline high-temperature superconductor with 1-2-3 structure

The temperature evolution of the current-voltage (I-U) characteristic of a contact of the break-junction type with direct conduction is investigated on a polycrystalline HTSC of the Y-Ba-Cu-O system. The experimental I-U characteristics possessing a hysteresis are correctly described in the framework of the Kümmel-Nicolsky theory for an S-N-S contact (S stands for a superconductor; N, for a normal metal) in which the Andreev reflection of quasiparticles from the N-S interface is considered. It is shown that the shape of the I-U curve, as well as the existence of a hysteresis, is determined by the ratio of the number of “long” and “short” intergranular boundaries in the polycrystal under investigation. The coincidence of the calculated and experimental I-U curves made it possible to estimate the effective length of “natural” intergranular boundaries in polycrystalline HTSC materials. The estimate is obtained from the experimental temperature dependence of the critical current in the sample under investigation.     

Nonequilibrium statistical mechanics in the general theory of relativity I. A general formalism

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The object here is the development of a tractable theory for self-gravitating systems. It is argued that the “state” of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. by mapping the true physics onto a fictitious “background” spacetime, which may be chosen to satisfy some “average” field equations, one then obtains a useful covariant notion of “evolution” in response to a fluctuating “gravitational force.” For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as “localized” in space and time, one obtains a tractable kinetic equation which reduces, in the newtonian limit, to the standard Landau equation.     

Ectoplasm has no topology

In a new approach to the theory of integration over Wess-Zumino supermanifolds, we suggest that a fundamental principle is their consistency with an “Ethereal Conjecture” that asserts the topology of the supermanifold must be generated essentially from its bosonic submanifold. This naturally leads to a theory of “ectoplasmic” integration based on super p-forms. One consequence of this approach is that the derivation of “density projection operators” becomes trivial in a number of supergravity theories.     

A transport-phase-transition as a solution of a simplified extended Peierls-Boltzmann equation

We investigate a simple example of a “transport-phase-transition” in a phonon system (linear chain) including a localized mode. For increasing (decreasing) energy flux there is a critical value Φ_cu(Φ_cl) for which the local excitation “jumps” from the “thermodynamic” to a nonthermodynamic branch (or vice versa). Noteworthy is the “hysteresis” and the fact that only an additional relaxation path creates stability.     

Theoretische Untersuchungen über die Lage des Zwischengitteratoms in Kupfer

The different stable atomic configurations, formation energies and changes in volume of the crystal for an interstitial in copper are calculated with the help of the electronic digital computer Z 22 using a general method developed byTewordt. For the interaction between a pair of ions the Born-Mayer potentialV ₁, given byHuntington, and the Morse potentialV _M, given byGirifalco-Weizer, are employed. Two equilibrium configurations for an interstitial are found. In the stable configuration“A” the interstitial and one next neighboured atom are symmetrically located relative to one of the elementary cube faces along a cubic axis passing through the cube center. In the stable configuration“B” the interstitial and one next neighboured atom are symmetrically located relative to a cube corner along a {111}-axis. The interstitial is found not to reside at the center of an elementary cube. Neglecting electronic contributions to the relaxation of the lattice due to the redistribution of the electrons the calculations showed that the interstitial moved along a cubic axis about 0.4a/2 away from the elementary cube center into a stable configuration“A”. Moreover the crowdion is found to be unstable. It is shown that the crowdion decays into an interstitial lying in a next neighboured configuration“A”. The configuration“B” is separated from surrounding“A” and unstable “body-centered” and “crowdion” configurations by energy barriers. The number of atoms around the mobile interstitial treated as movable discrete particles is about 150 for the configuration“A” and about 50 for the configuration“B”. Using the Born-Mayer potentialV ₁ the changes in volume of the crystal arising from the interstitial are found to be 1.126 atomic volumes for the configuration“A” and 1.432 atomic volumes for the configuration“B”. The contributions to the formation energy of an interstitial arising from the potentialV ₁ turn out to be 3.548 eV for the configuration“A” and 4.098 eV for the configuration“B”. The results of the theoretical calculations are discussed in connection with recent radiation damage experiments performed at low temperatures on copper.     

Six bits for nine colored quarks

The hypercomplex number system of the Dirac equation is used to generalizeSU(2) to the covering group ofSO(4). The basic representations in this number language suggest a parton model of 6 “bits” and 6 “antibits”; one with spin 0, two with spin 1/2, and three with spin 1. The relationship of this to the special relativity group is also considered.     

Statistical evaluation of the accuracy of external sound level predictions arising from models

Methods of predicting the sound level resulting from a source in a complex environment, such as an urban area, have been extensively studied in recent years. A number of methods, often based on some form of modelling, have proved useful for this purpose. However, comparatively little theoretical study of the relative or absolute accuracies of these methods has been performed. In this paper, a number of modelling strategies, utilizing different amounts of information about the environment, are studied and their absolute accuracies determined. It is found that, in general, the most suitable method will be one in which the paths of sound “rays” are explicitly traced up to their mth reflection, and treated by an “averaging” process after this. The value of m will depend on the accuracy required, and could be 0, but will rarely be greater than 3, as a strong law of diminishing returns is operative for large values of m.     

A study of Fe-doped Bi-Sr-Ca-Cu superconductors

We have substituted 1.5% of Fe for Cu in several “2212” and “2223” Bi-Sr-Ca-Cu superconductors. All of the samples show a reduction ofT _c about 13 K due to the Fe impurities. Mössbauer measurements at room temperature reveal the structural characteristics such as stacking faults and intergrowth of different phases in these Bi-based compounds on the microscopic scale. The susceptibility ofT _c to Fe-doping in the Bi-“2212” or “2223” system is comparable to that of the “123” system but much smaller than that of the “214” system. The interplanar correlation existing in the “123” and the Bi-“2212” and “2223” systems seems to play an important role in sustaining the high temperature superconductivity and weakening the detrimental effect of impurity elements on superconductivity in these two systems.     

Streuung von Licht an rauhen Oberflächen bei der Anregung von Oberflächenplasmonen

The electromagnetic theory, which explains the scattering of light from a rough surface of a metal foil by means of normale surface currents, is extended to the case of arbitrary directions of this currents. This allows to calculate the scattered intensity ofp ands polarised light in all directions. It is shown that the excitation of surface plasmons (“radiative” and “non radiative”) can produce a characteristic maximum in the scattered light. Detailed calculations for silver foils deposited on a quartz hemisphere are presented and compared with experiments. Furthermore the theory is applied to calculate the decrease in the reflection at frequences near the surface plasma frequenceΩ _s .     

Transverse relaxation of cesium vapour in a “strong” resonance radio frequency field

The fast adiabatic passage method was used to conduct measurements of the transverse relaxation times within hyperfine states of the ground state of cesium. The results of the experiment confirm the relations presented by Bouchiat for “weak” fields in spite of the fact that the field used, H₀ = 0.40 Oe is not a “weak” field. This apparent controversy is easily removed when one considers that in the presence of a rf field, atoms “see” an effective field which turns out to be a “weak” field.     

Molecular dynamics simulation of compression of single-layer graphene

The compression of a single-layer graphene sheet in the “zigzag” and “armchair” directions has been investigated using the molecular dynamics method. The distributions of the xy and yx stress components are calculated for atomic chains forming the graphene sheet. A graphene sheet stands significant compressive stresses in the “zigzag” direction and retains its integrity even at a strain of ～0.35. At the same time, the stresses which accompany the compressive deformation of single-layer graphene in the “armchair” direction are more than an order in magnitude lower than corresponding characteristics for the “zigzag” direction. A compressive strain of ～0.35 in the “armchair” direction fractures the graphene sheet into two parts.     

Fredholm–Lagrangian–Grassmannian and the Maslov index

This is a review article on the topology of the space, so called, Fredholm–Lagrangian–Grassmannian and the quantity “Maslov index” for paths in this space based on the standard theory of functional analysis. Our standing point is to define the Maslov index for arbitrary paths in terms of the fundamental spectral property of the Fredholm operators as an intersection number with the “Maslov cycle”. This argument was first recognized by J. Phillips and was used to define the “Spectral flow” not only for loops but also for arbitrary paths of selfadjoint Fredholm operators. We make the arguments as elementary as possible.