Showing papers by "Cornell University published in 1971"

Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture

Abstract: The Kadanoff theory of scaling near the critical point for an Ising ferromagnet is cast in differential form. The resulting differential equations are an example of the differential equations of the renormalization group. It is shown that the Widom-Kadanoff scaling laws arise naturally from these differential equations if the coefficients in the equations are analytic at the critical point. A generalization of the Kadanoff scaling picture involving an "irrelevant" variable is considered; in this case the scaling laws result from the renormalization-group equations only if the solution of the equations goes asymptotically to a fixed point.

Thermal Conductivity and Specific Heat of Noncrystalline Solids

Abstract: The thermal conductivity of vitreous Si${\mathrm{O}}_{2}$, Se, and silica- and germania-based glasses has been measured between 0.05 and 100 \ifmmode^\circ\else\textdegree\fi{}K. Comparison with earlier work on noncrystalline solids shows that they all have the same conductivity within a factor of 5 over the entire temperature range investigated, with the same characteristic plateau around 10 \ifmmode^\circ\else\textdegree\fi{}K, and that their conductivity varies as ${T}^{n}$, $n\ensuremath{\sim}1.8$, below $T=1$\ifmmode^\circ\else\textdegree\fi{}K. Furthermore, the average phonon mean free path is large by comparison with the phonon wavelength, about ${10}^{\ensuremath{-}4}$ cm at 2 \ifmmode^\circ\else\textdegree\fi{}K and decreasing as ${T}^{\ensuremath{-}4}$ at larger $T$, suggesting a Rayleigh-type scattering mechanism. Such a mean free path can be quantitatively explained by approximating the glassy structure with that of a crystal in which every atom is displaced from its lattice site. Then every atom scatters like an interstitial atom, or---even simpler---like one that is missing at its regular lattice site, with a scattering cross section determined by the missing mass (isotopic defect). The specific heat of amorphous Si${\mathrm{O}}_{2}$, Ge${\mathrm{O}}_{2}$, and Se has been found to vary as $AT+B{T}^{3}$ between 0.1 and 1 \ifmmode^\circ\else\textdegree\fi{}K, with $A=10$ erg/g \ifmmode^\circ\else\textdegree\fi{}${\mathrm{K}}^{2}$ within a factor of 2. This departure from the Debye specific heat may be characteristic of the glassy state, as all earlier measurements of other glasses [polystyrene, glycerol, Lucite (PMMA)] indicate a similar anomaly. Its origin is not clear. Impurities or surface effects through adsorbed gases are unlikely because of the many samples and experimental techniques used in different laboratories. We have tried to attribute the anomaly to low-lying electronic states, motional states of ions, trapped atoms or large groups of atoms, or one-dimensional vibrations within a three-dimensional solid, so far without success. At the present time, the only independent evidence for these excitations appears to be in the low-temperature thermal conductivity at $Tl1$ \ifmmode^\circ\else\textdegree\fi{}K described above.

Conjoint Measurement for Quantifying Judgmental Data

Abstract: Conjoint measurement is a new development in mathematical psychology that can be used to measure the joint effects of a set of independent variables on the ordering of a dependent variable. In this...

Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior

Abstract: A generalization of the Ising model is solved, qualitatively, for its critical behavior. In the generalization the spin ${S}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}}$ at a lattice site $\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$ can take on any value from $\ensuremath{-}\ensuremath{\infty} \mathrm{to} \ensuremath{\infty}$. The interaction contains a quartic term in order not to be pure Gaussian. The interaction is investigated by making a change of variable ${S}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}}=\ensuremath{\Sigma}{m}^{}{\ensuremath{\psi}}_{m}(\mathrm{n}){S}_{m}^{\ensuremath{'}}$, where the functions ${\ensuremath{\psi}}_{m}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}})$ are localized wavepacket functions. There are a set of orthogonal wave-packet functions for each order-of-magnitude range of the momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$. An effective interaction is defined by integrating out the wave-packet variables with momentum of order 1, leaving unintegrated the variables with momentum 0.5. Then the variables with momentum between 0.25 and 0.5 are integrated, etc. The integrals are computed qualitatively. The result is to give a recursion formula for a sequence of effective Landau-Ginsberg-type interactions. Solution of the recursion formula gives the following exponents: $\ensuremath{\eta}=0$, $\ensuremath{\gamma}=1.22$, $\ensuremath{ u}=0.61$ for three dimensions. In five dimensions or higher one gets $\ensuremath{\eta}=0$, $\ensuremath{\gamma}=1$, and $\ensuremath{ u}=\frac{1}{2}$, as in the Gaussian model (at least for a small quartic term). Small corrections neglected in the analysis may make changes (probably small) in the exponents for three dimensions.

A proposed staging for children with neuroblastoma. Children's cancer study group A

Abstract: A clinical staging of patients with neuroblastoma is proposed. Such staging is desirable to aid in estimating the prognosis and to be able to evaluate the efficacy of differing therapeutic regimens by analyzing results obtained in comparable groups of patients. That the suggested staging is practical is illustrated by the ease with which 100 children with neuroblastoma, entered in previous studies by Children's Cancer Study Group A, were staged using the criteria described. Short-term survival data of this small sample demonstrated, in addition, that the proposed staging appears to be of help in estimating the prognosis. Also proposed is a list of investigations which aid in accurate staging.

The steiner problem in graphs

Abstract: An algorithm for solving the Steiner problem on a finite undirected graph is presented. This algorithm computes the set of graph arcs of minimum total length needed to connect a specified set of k graph nodes. If the entire graph contains n nodes, the algorithm requires time proportional to n3/2 + n2 (2k-1 - k - 1) + n(3k-1 - 2k + 3)/2. The time requirement above includes the term n3/2, which can be eliminated if the set of shortest paths connecting each pair of nodes in the graph is available.

Fundamentals of earthquake engineering

Abstract: Keywords: Tremblement de terre ; Danger naturel Reference Record created on 2004-09-07, modified on 2016-08-08

A Linear Alternative to Quadratic and Semivariance Programming for Farm Planning under Uncertainty

Abstract: Quadratic decision criteria for farm planning are theoretically appealing but difficult to handle computationally. This paper reviews the advantages of the quadratic approach and develops a linear alternative which, while retaining most of the desired features of the quadratic models, can be readily solved on conventional linear programming codes with the parametric option.

Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation

Abstract: In this paper we give two derivative-free computational algorithms for nonlinear least squares approximation. The algorithms are finite difference analogues of the Levenberg-Marquardt and Gauss methods. Local convergence theorems for the algorithms are proven. In the special case when the residuals are zero at the minimum, we show that certain computationally simple choices of the parameters lead to quadratic convergence. Numerical examples are included.

Renormalization Group and Strong Interactions

Abstract: The renormalization-group method of Gell-Mann and Low is applied to field theories of strong interactions. It is assumed that renormalization-group equations exist for strong interactions which involve one or several momentum-dependent coupling constants. The further assumption that these coupling constants approach fixed values as the momentum goes to infinity is discussed in detail. However, an alternative is suggested, namely, that these coupling constants approach a limit cycle in the limit of large momenta. Some results of this paper are: (1) The e+−e− annihilation experiments above 1-GeV energy may distinguish a fixed point from a limit cycle or other asymptotic behavior. (2) If electrodynamics or weak interactions become strong above some large momentum Λ, then the renormalization group can be used (in principle) to determine the renormalized coupling constants of strong interactions, except for U(3)×U(3) symmetry-breaking parameters. (3) Mass terms in the Lagrangian of strong, weak, and electromagnetic interactions must break a symmetry of the combined interactions with zero mass. (4) The ΔI=12 rule in nonleptonic weak interactions can be understood assuming only that a renormalization group exists for strong interactions.

Detoxication Enzymes in the Guts of Caterpillars: An Evolutionary Answer to Plant Defenses?

Abstract: Higher activity of midgut microsomal oxidase enzymes in polyphagous than in monophagous species indicates that the natural function of these enzymes is to detoxify natural insecticides present in the larval food plants. Differing strategies of adaptation to plant defenses may partly account for the great diversity of insect herbivores.

Stereochemistry of hemes and other metalloporphyrins.

Abstract: Metalloporphyrins, most notably the iron porphyrins, observe clearly defined, internally consistent, structural principles that promise to be fully applicable to the hemes in the several families of the hemoproteins.

Serological demonstration of h-y (male) antigen on mouse sperm.

Abstract: WE have recently overcome certain technical difficulties in applying the cytotoxicity test to mouse spermatozoa and have been able to show directly that H-2 antigens are expressed on these cells1, thus confirming less direct evidence leading to the same conclusion2. We have since applied the cytotoxicity test to sperm with antisera directed against a number of other systems of mouse alloantigens, TL3, θ4, Ly-A5 and Ly-B5, but none of these has given a positive reaction with sperm. This is not surprising because these are all “differentiation antigens”6 expressed primarily on lymphoid cells. Another antigenic system which distinguishes one mouse from another is H-Y. The H-Y antigen is carried by male cells only and is responsible for the rejection of male tissues by females of the same inbred strain7.

Sex attractant of the codling moth: characterization with electroantennogram technique.

Abstract: trans-8, trans-10-Dodecadien-1-ol is a sex attractant of the codling moth, Laspeyresia pomonella. Antennal responses (electroantennograms) to a series of monounsaturated compounds were used in determining the location and configuration of the two double bonds. The synthetic compound is very attractive to male codling moths in the field.

Thermal convection with large viscosity variations

Abstract: The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated. Solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength. The effects of a temperature-dependent and a depth-dependent viscosity were each studied; calculations were also carried out using a temperature- and depth-dependent viscosity model appropriate to the earth's mantle.

Bounds for a class of linear functionals with applications to Hermite interpolation

Abstract: A general estimation theorem is given for a class of linear functionals on Sobolev spaces. The functionals considered are those which annihilate certain classes of polynomials. An interpolation scheme of Hermite type is defined inN-dimensions and the accuracy in approximation is bounded by means of the above mentioned theorem. In one and two dimensions our schemes reduce to the usual ones, however our estimates in two dimensions are new in that they involve only the pure partial derivatives.

Transneuronal Transfer of Radioactivity in the Central Nervous System

Abstract: After injection of tritiated amino acid into the mouse eye, radioactivity appeared in the contralateral visual cortex, indicating that some material had been transferred from optic axons to lateral geniculate neurons. The radioactivity in the cortex was about 2 percent of that arriving in the geniculate, and most of it was contained in material that appeared to be protein.

Another look at “cultural fairness”1

Abstract: Four definitions of “cultural fairness” are examined and found to be not only mutually contradictory (for reasons which are explained), but all based on the false view that optimum treatment of cultural factors in test construction or test selection can be reduced to completely mechanical procedures. If a conflict arises between the two goals of maximizing a test's validity and minimizing the test's discrimination against certain cultural groups, then a subjective, policy-level decision must be made concerning the relative importance of the two goals. The terms in which this judgment should be made are described, and methods are described for entering the result of this judgment into mechanical procedures for constructing a “culturally optimum” test. Such a test will not necessarily fit any of the four definitions of “cultural fairness.”

Two-Photon Mechanism of Particle Production by High-Energy Colliding Beams

Abstract: We report on the calculation of the cross sections for the production of positive-charge-conjugation states such as ${\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}$, ${e}^{+}{e}^{\ensuremath{-}}$, ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ by a two-photon mechanism in ${e}^{\ensuremath{-}}{e}^{+}$ and ${e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ collisions. We give the precise relationship of the process $e+e\ensuremath{\rightarrow}e+e+X (X \mathrm{is}\mathrm{any} C=+ \mathrm{state})$ to the corresponding two-photon annihilation process $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}X$, as well as a careful derivation of the equivalent-photon approximation. In the case of the ${\ensuremath{\pi}}^{0}$ production, we have found that, for the beam energy $E$ in the 1-3 GeV range, the exact total cross section is 20-30% larger than the one calculated previously in the equivalent-photon approximation. However, the introduction of form factors cuts down the exact total cross section, reducing it to within 10% of the equivalent-photon-approximation result. For $\ensuremath{\eta}$ production the agreement is even better. Thus it appears that the use of the equivalent-photon approximation is justified in most cases. We discuss detailed angular distributions in this approximation for the case of ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ production. One important problem which cannot be adequately studied in the equivalent-photon approximation is the degree of noncoplanarity of the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ (and the ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$) pair. We have studied this problem using the exact formula and found that, for $E=1$ GeV, typically 40-50% of pion pairs will be produced with the noncoplanarity angle greater than 12\ifmmode^\circ\else\textdegree\fi{}. We discuss the general structure of the $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}$ amplitude as well as a simple model incorporating the $\ensuremath{\sigma}$ meson. We also give a rough estimate of multihadron production cross sections.

Interband Absorption and the Optical Properties of Polyvalent Metals

Abstract: Excitation of electrons between parallel or near-parallel one-electron bands in simple polyvalent metals constitutes a major source of the observed optical absorption. Much of the effect can be accounted for in a straightforward calculation of both real and imaginary parts of the conductivity, which does not require the constant-matrix-element assumption. In many cases, the magnitude and rounding of the absorption edges (singular in the absence of scattering) are quite sensitive to the phenomenological relaxation times (and hence to temperature) and to surface scattering. The sum rule for the (transverse) optical conductivity is related to the Fourier components of the weak periodic potential, and an expression is derived for the optical mass. The theory has been applied to study the optical properties of Al.

Markov Random Fields and Gibbs Ensembles

Abstract: (1971). Markov Random Fields and Gibbs Ensembles. The American Mathematical Monthly: Vol. 78, No. 2, pp. 142-154.