The fractal dimension $D$ of a mesoporous silica gel was determined by three independent approaches: (1) adsorption methods based on (a) tiling of the surface with molecules of different cross-sectional area and (b) analysis of the change in measured surface area as a function of the size of the silica particles; (2) analysis of one-step dipolar energy transfer between adsorbed rhodamine B and malachite green; (3) measurements of power-law small-angle x-ray scattering. All three techniques indicate that the surface is extremely rough and irregular, with a fractal dimension $D$ nearly equal to 3.

We report the results of an experimental study of the fracture stress, $S$ and the Young's modulus, $E$, of a two-dimensional solid (network) which has undergone random dilution to the point where the solid becomes geometrically disconnected. In the scaling region, $E\sim {(p-p_c)}^f$ with $f=3.1\mathrm{}\pm 0.1$ and $S\sim {(p-p_c)}^F$ with $F=1.7\mathrm{}\pm 0.1$. We find that appropriately modified formulations of the Griffith relation can account for the fracture stress in the entire range of bond dilution.

We report the observation of a $T^2$ temperature dependence of the magnetic field penetration depth in U${\mathrm{Be}}_{13}$ at low temperatures. We show that this behavior is consistent with an anisotropic gap function for an axial $P$-wave state. Our results further show that the Landau parameter $F_{\mathrm{l}}^s$ appears to be small.

Raman measurements are reported of collective modes (plasmons) and single-particle excitations in modulation-doped $\mathrm{Ga}\frac{\mathrm{As}}{{\mathrm{Al}}_x}{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum-well systems as a function of the wave-vector component $k_{\parallel }$ parallel to the electron layers. Samples with five layers show discrete layer-plasmon modes manifesting the coupling of the electrons in different layers by Coulomb interaction. The Raman spectra due to single-particle excitations are narrow bands peaking at $\overline{h}{k}_{\parallel }{v}_{\mathrm{F}}^{2\mathrm{D}}$ characteristic for the response of a 2D electron gas.

We discuss a Monte Carlo algorithm to study properties of dilute magnetic alloys; the method can treat a small number of magnetic impurities interacting with the conduction electrons in a metal. Results for the susceptibility of a single Anderson impurity in the symmetric case show the expected universal behavior at low temperatures. Some results for two Anderson impurities are also discussed.

The dynamic critical behavior in a $d=3\mathrm{}$ random-field Ising-model system is studied with ac susceptibility $\chi \left(\omega \right)$ techniques on ${\mathrm{Fe}}_{0.46}$${\mathrm{Zn}}_{0.54}$${\mathrm{F}}_2$. Extraordinary critical slowing down is seen in the $\omega$ dependence of ${\chi }^{\prime }\left(\omega \right)$ at very low frequencies. In the range 2 Hz to 8.5 kHz, the peak value ${\left[{\chi }_c^{\prime }\right(\omega \left)\right]}_p$ decreases and the width $t^{*}\left(\omega \right)$ increases with increasing $\omega$. A conventional dynamicscaling interpretation with $t^{*}\left(\omega \right)\sim {\omega }^{\frac{1}{z\nu }}$ gives ${\left[{\chi }_c^{\prime }\right(\omega \left)\right]}_p\sim \left|\ln \omega \right|$ and yields $z\nu \simeq 14$. An equally good fit is obtained with $t^{*}\left(\omega \right)\sim {\left|\ln \omega \right|}^{-1\mathrm{}}$ and ${\left[{\chi }_c^{\prime }\right(\omega \left)\right]}_p\sim \ln \left|\ln \omega \right|$, consistent with an activated dynamic scaling.

The relaxation of the electric polarization is investigated in the charge-density-wave compound ${\mathrm{K}}_{0.3}$Mo${\mathrm{O}}_3$. Direct measurements of discharge current in the time interval of ${10}^{-5\mathrm{}}$ to ${10}^3$ s reveal a stretched exponential law for the time decay of polarization: $P=P_0\exp [-{\left\{\frac{t}{\tau }\mathrm{}\right(T\left)\right\}}^{1-n}]$, where both the initial polarization, $P_0$, and the exponent ($1-n=0.7$) are temperature independent. The time scale of the process indicates temperature activation with an activation energy equal to the single-particle Peierls gap. The glassy relaxation of randomly pinned charge-density waves is compared with recent theories and experiments on spin-glasses.

The optical nonlinearity ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ of excitons localized by disorder or impurity has a large value as a consequence of the double multiplication of the giant oscillator strength due to exciton localization because the ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ process involves the double repetition of the excitonic transition. The importance of the exciton correlation in the coherent nonlinear optical process is pointed out for the first time. The sign of ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ relative to ${\chi }^{\mathrm{}\left(1\right)\mathrm{}}$ gives important information about the character of the exciton correlation.

We present a microscopic theory of electronic scattering in graphite intercalation compounds. The properties of the carrier Bloch states result in anomalous tunneling through staging dislocations. The contribution to the residual resistivity due to the Daumas-Hérold domain walls is calculated with use of Thomas-Fermi potentials in the Boltzmann equation. Typical domain sizes and wall arrangements produce large residual-resistivity values, so that accurate measurements can provide a bulk probe of the domain size. We also predict highly unusual low-$T$ transport for some domain configurations.

Molecular membranes in aqueous solutions interact via van der Waals, hydration, and electrostatic forces. In addition, thermal fluctuations of the membranes generate long-range effective repulsion. A systematic theory of the interplay among these interactions reveals a continuous phase transition from a state where the membranes are bound together to a state where they are completely separated. In three dimensions, this unbinding transition is driven by fluctuations. Quantitative correlations with data for lipid bilayers suggest that it can be observed experimentally.

A recent result concerning the assignment of well-defined values to certain noncommuting observables in quantum ensembles which have been both preselected and post-selected appears to show that quantum mechanics is "contextual." Extending the argument to the case of measurements on two separated spin-½ systems suggests that quantum mechanics is nonlocal. The significance of these phenomena is evaluated, and it is shown that they have no bearing on the question of contextuality or nonlocality.

We establish the mapping of the master equation for classical motion in random media to a quantum system, describing the motion of a quantum particle in a random potential. Invoking dynamic scaling, the mapping connects the time-dependent mean square displacement of classical motion with the density of states in terms of the classical correlation length. These connections are illustrated for a model with exactly solvable diffusion properties, confirming dynamic scaling. The numerical results for the quantum counterpart reveal energy-dependent localization in terms of the real part of the Lyapunov exponent, which is proportional to the inverse localization length.

An experiment carried out by Kreuzer in 1968 can be interpreted as setting an upper limit on the strength of any intermediate-range coupling to baryon number. The upper limit is one-half the strength obtained by Fischbach et al. in their reanalysis of the Eötvös experiment. The two results are consistent within 2 standard deviations if what Kreuzer calls an "upper bound" is a $1\sigma$ limit.

It is shown that Eötvös-type torsion-balance experiments performed in the vicinity of a large cliff may be used as sensitive tests for the recently postulated existence of a medium-range hypercharge force. The residual nonzero effect found in the original Eötvös results could be mainly due to terrain irregularities and thus be larger than, but still correlated to, the effects expected from the Earth's rotation and the hypercharge hypothesis.

Other experiments testing the suggested new vectorial interaction of subgravitational strength and the possible theoretical interpretations of this interaction are discussed.

The counterterms constructed by Green and Schwarz in the field-theory limit of superstrings are put into a form of Calabi-Yau compactification. Dimension-six operators are explicitly extracted. The modifications of the gauge kinetic terms and of the Kähler potential are obtained. Axion couplings and some $\mathrm{CP}$-nonconserving interactions are given.

Angular momentum distributions for the dominant decay channels of ${}_{}{}^{156}{}_{}{}^{}\mathrm{Er}$ compound nuclei have been studied with the Darmstadt-Heidelberg "crystal ball" detector in nearly mass-symmetric (${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$+${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$) and asymmetric (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$) entrance channels. Strong differences in the $\alpha n$ yield and $\frac{2_n}{3_n}$ cross-section ratios are observed at the same excitation energy (47 MeV) and spin in ${}_{}{}^{156}{}_{}{}^{}\mathrm{Er}$. This effect indicates that there is memory of the entrance channel during the particle-evaporation stage of the compound-nucleus decay. The dominant exit channels do not exhibit high-angular-momentum components.

Nuclei of ${}_{}{}^{218}{}_{}{}^{}\mathrm{Ra}$ were produced in the reaction ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}({}_{}{}^{13}{}_{}{}^{}\mathrm{C},3n)$. After being separated from the beam by a velocity filter, they were implanted in a Si(Au) surface-barrier detector and their $\alpha$-particle decays were observed in the same detector. From these $\alpha$-decay events the half-life of ${}_{}{}^{218}{}_{}{}^{}\mathrm{Ra}$ was measured to be 25.6 ± 1.1 μs, almost a factor of 2 greater than the previously reported value of 14 ± 2 μs. The resultant $\alpha$ width fits well into the overall picture of $\alpha$-decay-rate systematics and weakens one piece of evidence quoted for the existence of $\alpha$ clusters in heavy elements.

The reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(e,e^{\prime }p)$ in the dip region ($\omega =200\mathrm{} \mathrm{MeV}, \mathrm{q}=400\mathrm{} \mathrm{Mev}c$) has been measured in parallel kinematics for missing energies up to 160 MeV. A coincidence yield considerably larger than that expected for a one-body reaction process is observed, though the one-body contribution from $p$- and $s$-shell knockout is also present. A uniform continuum strength extends from beyond the $p$ shell to the highest measured missing energies. This continuum strength is the dominant contribution to the ($e,e^{\prime }p$) reaction process in the dip region.

Antiprotonic x-ray spectra of ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$, and ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$ have been measured with Ge detectors. The $E2\mathrm{}$ nuclear-resonance effect was observed for the first time in $\overline{p}$ atoms, yielding information on the "hidden" $n=5\mathrm{}$, $l=4\mathrm{}$ level of the $\overline{p}$-molybdenum atom. Strong interaction widths and shifts affecting the 7 → 6 transition were determined and the effective $\overline{p}$-nucleon scattering length was deduced. A unique strong-coupling effect was established in $\overline{p}-{}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$.