Showing papers on "Saturation (graph theory) published in 1993"

Gyrokinetic simulation of ion temperature gradient driven turbulence in 3D toroidal geometry.

Abstract: Results from a fully nonlinear three dimensional toroidal electrostatic gyrokinetic simulation of the ion temperature gradient instability are presented. The model has fully gyro-averaged ion dynamics, including trapped particles, and adiabatic electrons. Simulations of large tokamak plasma volumes are made possible due to recent advances in {delta}f methods and massively parallel computing. Linearly, a coherent ballooning eigenmode is observed, where the mode is radially elongated. In the turbulent steady-state, the spectrum peaks around k{theta} {rho}{sub s} {approximately} 0.1 with the ballooning structure reduced, but still prevalent.

Self-consistent signal-to-noise analysis of the statistical behavior of analog neural networks and enhancement of the storage capacity.

Abstract: Based on the self-consistent signal-to-noise analysis (SCSNA) capable of dealing with analog neural networks with a wide class of transfer functions, enhancement of the storage capacity of associative memory and the related statistical properties of neural networks are studied for random memory patterns. Two types of transfer functions with the threshold parameter \ensuremath{\theta} are considered, which are derived from the sigmoidal one to represent the output of three-state neurons. Neural networks having a monotonically increasing transfer function ${\mathit{F}}^{\mathrm{M}}$, ${\mathit{F}}^{\mathrm{M}}$(u)=sgnu (\ensuremath{\Vert}u\ensuremath{\Vert}g\ensuremath{\theta}), ${\mathit{F}}^{\mathrm{M}}$(u)=0 (\ensuremath{\Vert}u\ensuremath{\Vert}\ensuremath{\le}\ensuremath{\theta}), are shown to make it impossible for the spin-glass state to coexist with retrieval states in a certain parameter region of \ensuremath{\theta} and \ensuremath{\alpha} (loading rate of memory patterns), implying the reduction of the number of spurious states. The behavior of the storage capacity with changing \ensuremath{\theta} is qualitatively the same as that of the Ising spin neural networks with varying temperature. On the other hand, the nonmonotonic transfer function ${\mathit{F}}^{\mathrm{NM}}$, ${\mathit{F}}^{\mathrm{NM}}$(u)=sgnu (\ensuremath{\Vert}u\ensuremath{\Vert}), ${\mathit{F}}^{\mathrm{NM}}$(u)=0 (\ensuremath{\Vert}u\ensuremath{\Vert}\ensuremath{\ge}\ensuremath{\theta}) gives rise to remarkable features in several respects.First, it yields a large enhancement of the storage capacity compared with the Amit-Gutfreund-Sompolinsky (AGS) value: with decreasing \ensuremath{\theta} from \ensuremath{\theta}=\ensuremath{\infty}, the storage capacity ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$ of such a network is increased from the AGS value (\ensuremath{\approxeq}0.14) to attain its maximum value of \ensuremath{\approxeq}0.42 at \ensuremath{\theta}\ensuremath{\simeq}0.7 and afterwards is decreased to vanish at \ensuremath{\theta}=0. Whereas for \ensuremath{\theta}\ensuremath{\gtrsim}1 the storage capacity ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$ coincides with the value ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ifmmode \tilde{}\else \~{}\fi{} determined by the SCSNA as the upper bound of \ensuremath{\alpha} ensuring the existence of retrieval solutions, for \ensuremath{\theta}\ensuremath{\lesssim}1 the ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$ is shown to differ from the ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ifmmode \tilde{}\else \~{}\fi{} with the result that the retrieval solutions claimed by the SCSNA are unstable for ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ifmmode \tilde{}\else \~{}\fi{}. Second, in the case of \ensuremath{\theta}1 the network can exhibit a new type of phase which appears as a result of a phase transition with respect to the non-Gaussian distribution of the local fields of neurons: the standard type of retrieval state with r\ensuremath{ e}0 (i.e., finite width of the local field distribution), which is implied by the order-parameter equations of the SCSNA, disappears at a certain critical loading rate ${\mathrm{\ensuremath{\alpha}}}_{0}$, and for \ensuremath{\alpha}\ensuremath{\le}${\mathrm{\ensuremath{\alpha}}}_{0}$ a qualitatively different type of retrieval state comes into existence in which the width of the local field distribution vanishes (i.e., r=${0}^{+}$). As a consequence, memory retrieval without errors becomes possible even in the saturation limit \ensuremath{\alpha}\ensuremath{ e}0. Results of the computer simulations on the statistical properties of the novel phase with \ensuremath{\alpha}\ensuremath{\le}${\mathrm{\ensuremath{\alpha}}}_{0}$ are shown to be in satisfactory agreement with the theoretical results. The effect of introducing self-couplings on the storage capacity is also analyzed for the two types of networks. It is conspicuous for the networks with ${\mathit{F}}^{\mathrm{NM}}$, where the self-couplings increase the stability of the retrieval solutions of the SCSNA with small values of \ensuremath{\theta}, leading to a remarkable enhancement of the storage capacity.

Richtmyer-Meshkov experiments on the Nova laser at high compression.

Abstract: We investigate the shock induced Richtmyer-Meshkov instability at high compression using the Nova laser. The instability and shock characteristics are measured radiographically in planar two-fluid targets with Atwood number 0. The growth of imposed interfacial perturbations \ensuremath{\eta}=${\mathrm{\ensuremath{\eta}}}_{0}$ sinkx agrees with linear theory if the pre- and postshock initial amplitudes are averaged. When k\ensuremath{\eta}\ensuremath{\sim}2, the fundamental mode saturates and harmonics emerge producing a slowly developing bubble and spike.

Electric-field-induced change of the order parameter in a nematic liquid crystal.

Abstract: We measure optically the increase of quadrupolar order \ensuremath{\Delta}S, induced by a stabilizing electric field E, in the nematic liquid crystal 4'-n-pentyl-4-cyanobiphenyl with large positive dielectric anisotropy ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$\ensuremath{\sim}10. \ensuremath{\Delta}S shows a linear and a quadratic dependence on E. Both effects are comparable for the largest field E\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}${10}^{5}$ V/cm. The linear variation is interpreted as originating from the quenching of macroscopic orientational fluctuations, while the quadratic contribution is a superposition of the microscopic Kerr effect and of a saturation term due to the macroscopic effect.

Observation of a saturation in the time scale for multifragment emission in symmetric heavy-ion collisions.

Abstract: We have measured two-fragment reduced-velocity correlation functions of the intermediate mass fragments (IMF: 3\ensuremath{\le}Z\ensuremath{\le}7) produced in multifragment final states for the Kr+Nb system (E/A=35, 45, 55, 65, and 75 MeV). From the measured correlation functions we extract mean IMF emission lifetimes (\ensuremath{\tau}) which are observed to decrease from \ensuremath{\tau}\ensuremath{\approxeq}400 fm/c at E/A=35 MeV to \ensuremath{\tau}\ensuremath{\approxeq}125 fm/c at E/A=55 MeV. For beam energies in excess of E/A=55 MeV, no further decrease in \ensuremath{\tau} is observed, indicating a possible saturation of the mean emission lifetime for IMF produced in multifragment exit channels.

Multilayer adsorption of xenon, krypton, and argon on graphite: An ellipsometric study.

Abstract: We present ellipsometric measurements of multilayer adsorption of xenon, krypton, and argon on highly oriented pyrolytic graphite along numerous isotherms spanning the coverage range from completion of the first layer to about twelve layers and the temperature range from below the melting of the top layer to above the bulk adsorbate melting point ${\mathit{T}}_{\mathit{m}}$. The three adsorbates have very similar phase diagrams, and all show reentrant first-order layering. The top layer of three-layer and thicker films disorders at 0.81${\mathit{T}}_{\mathit{m}--}$0.83${\mathit{T}}_{\mathit{m}}$. For films thicker than three layers, first-order layer condensation reappears at shifted coverages and chemical potentials in the range 0.83${\mathit{T}}_{\mathit{m}--}$0.87${\mathit{T}}_{\mathit{m}}$ to 0.92${\mathit{T}}_{\mathit{m}--}$0.94${\mathit{T}}_{\mathit{m}}$. The solid adsorbate films reach a limiting thickness of about 12 layers at saturation, but the limiting thickness increases rapidly just below ${\mathit{T}}_{\mathit{m}}$ and reaches the equivalent of about 24 layers in the liquid region. We discuss implications of these results for roughening and melting of the adsorbate (111) surfaces. Chemical potentials for layer condensation are compared to a simple Frankel-Halsey-Hill theory.

Structure of the Si{100} surface in the clean (2×1), (2×1)-H monohydride, (1×1)-H dihydride, and c(4×4)-H phases

Abstract: The structure of the Si{100} surface in the clean (2\ifmmode\times\else\texttimes\fi{}1), (2\ifmmode\times\else\texttimes\fi{}1)-H monohydride, (1\ifmmode\times\else\texttimes\fi{}1)-H dihydride, and c(4\ifmmode\times\else\texttimes\fi{}4)-H phases has been studied by time-of-flight scattering and recoiling spectrometry. The hydrogenated phases were formed by saturation exposure to atomic hydrogen at room temperature for (1\ifmmode\times\else\texttimes\fi{}1), \ensuremath{\approxeq}400 \ifmmode^\circ\else\textdegree\fi{}C for (2\ifmmode\times\else\texttimes\fi{}1), and \ensuremath{\approxeq}620 \ifmmode^\circ\else\textdegree\fi{}C for c(4\ifmmode\times\else\texttimes\fi{}4). Time-of-flight spectra of scattered and recoiled neutrals plus ions were collected as a function of crystal azimuthal angle and primary-beam incident angle to the surface. Structural analyses of the phases were obtained from the azimuthal anisotropy of the recoiled silicon-atom flux from 4 keV ${\mathrm{Ar}}^{+}$ primary ions and from the critical incident angles for 4-keV ${\mathrm{Ne}}^{+}$ primary ions scattering along selected azimuths. Analysis of shadowing and blocking effects in these scattering and recoiling events, using calibrated shadow cones, is used in the structure determinations. The data provide a direct determination of the interatomic spacings in the outermost silicon layer of the four surface phases investigated.

Soft-mode studies in KTa 0.93 Nb 0.07 O 3 with use of the time-resolved third-order optical susceptibility χ 3

Abstract: Determinations of the third-order optical susceptibility have been used to investigate the dynamical properties of the ${\mathit{A}}_{1}$(TO) soft-polariton mode in ${\mathrm{KTa}}_{0.93}$${\mathrm{Nb}}_{0.07}$${\mathrm{O}}_{3}$ as a function of temperature. Saturation of the soft-polariton frequency as T\ensuremath{\rightarrow}${\mathit{T}}_{\mathit{c}}$ indicates an interaction with the relaxation mode and evidence is found for the presence of low-frequency excitations that significantly increase the observed damping rate. Also, with the use of the polariton dispersion and self-energy formulas, frequency and damping are compared to the TO Raman-active phonon parameters.

Semileptonic $\pi$ and $K$ Decays and the Chiral Anomaly at One-loop

Abstract: We calculate the $O(p^6)$ corrections to the anomalous form factors appearing in $\pi^+$, $K^+ \to e^+ u \gamma,\ \mu^+ u\gamma$ and $K_{l4}$ decays in Chiral Perturbation Theory. The relevant dimension $6$ terms of the lagrangian are evaluated assuming their saturation by the vector meson contribution.

Absorption saturation of intersubband optical transitions in GaAs/AlxGa1-xAs multiple quantum wells.

Abstract: The optical-absorption saturation of intersubband transition within the conduction band of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum wells (MQW's) has been investigated The MQW sample grown by molecular-beam epitaxy consists of 50 periods of 70-\AA{}-wide GaAs wells and 178-\AA{}-wide ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As barriers with x=025 The absorption is peaked at 949 \ensuremath{\mu}m The infrared radiation from a tunable transversely excited atmosphere ${\mathrm{CO}}_{2}$ laser was to induce the transition between the lower subbands The saturation intensity obtained is ${\mathit{I}}_{\mathit{s}}$=067 MW/${\mathrm{cm}}^{2}$ Using our theoretical expression for saturation intensity, we have calculated ${\mathit{I}}_{\mathit{s}}$=052 MW/${\mathrm{cm}}^{2}$

Hyperfine spectra of the radioactive isotopes Kr 81 and Kr 85

Abstract: Isotope shifts and hyperfine constants are reported for the radioactive isotopes ${\mathrm{Kr}}^{81}$ and ${\mathrm{Kr}}^{85}$ and the stable isotope ${\mathrm{Kr}}^{83}$. The previously unreported nuclear moments of ${\mathrm{Kr}}^{81}$ were determined to be ${\mathrm{\ensuremath{\mu}}}_{\mathrm{I}}$=-0.909(4) nuclear magneton and Q=+0.630(13) b from the hyperfine constants. This work increases the number of transitions for which ${\mathrm{Kr}}^{85}$ hyperfine constants and isotope shifts have been measured from 1 to 4. The hyperfine anomaly for krypton reported in the previous measurement of ${\mathrm{Kr}}^{85}$ hyperfine constants [H. Gerhardt et al., Hyperfine Interact. 9, 175 (1981)] is not supported by this work. The isotope shifts and hyperfine constants of ${\mathrm{Kr}}^{83}$ measured in this work are in excellent agreement with previous work. Saturation spectroscopy was used to study transitions from krypton's metastable ${1\mathrm{s}}_{5}$ state to the ${2\mathrm{p}}_{9}$, ${2\mathrm{p}}_{7}$, and ${2\mathrm{p}}_{6}$ states. In saturation spectra, different line shapes were observed for the even- and odd-mass krypton isotopes. This even- versus odd-line-mass shape difference can be explained using the large cross section that has been reported for collisional transfer of the ${1\mathrm{s}}_{5}$ state excitation between krypton atoms. Two-color two-photon laser-induced fluorescence was used to measure the hyperfine spectra of the ${1\mathrm{s}}_{5}$-${4\mathrm{d}}_{4}^{\ensuremath{'}}$ transition using the ${2\mathrm{p}}_{9}$ state as the intermediate state. This technique proved to be more sensitive than saturation spectroscopy.

Radiation Stability of WWER-440 Vessel Materials

Abstract: The main results of a complex investigation of radiation embrittlement of WWER-440 reactor vessel (RV) materials, carried out in the former USSR are presented The object of the investigation was surveillance specimen (SS) evaluation of RV materials It has been found that at an irradiation temperature of 270 C neither the base metal (steel 15 Kh2MFA) nor weld metal exhibits saturation of radiation embrittlement in irradiation of specimens up to neutron fluences of 7 {times} 10{sup 20} n/cm{sup 2} (E > 05 MeV) Regularities in the influence of impurity elements (copper and phosphorus) on radiation embrittlement of RV materials have been investigated It is shown that radiation embrittlement of the weld metal is determined by at least four processes associated with the individual effects of copper and phosphorus, their joint effect, and the mechanism of direct buildup of radiation defects in the metal The effect of dependence of the radiation embrittlement characteristics of the WWER-440 RV materials on the neutron flux has been found It is shown that within the range of fluences from 1 {times} 10{sup 18} n/cm{sup 2} at a neutron flux of 4 {times} 10{sup 11} n/cm{sup 2} {center_dot} s, radiation embrittlement is stronger than in irradiationmore » at a neutron flux of 3 to 4 {times} 10{sup 12} n/cm{sup 2} {center_dot} s A tendency has been observed for the values of the radiation embrittlement coefficients A{sub F}, characterizing sensitivity of the steel to radiation embrittlement, to reduce with an increase of neutron fluence in irradiation of specimens with a neutron flux of 4 {times} 10{sup 11} n/cm{sup 2} {center_dot} s« less

Hole filling in a narrow conduction band in YBa 2 Cu 3-x Co x O 7-δ (x<=0.3)

Abstract: Measurements of the temperature dependence of the absolute thermopower (S) on samples of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ with 0\ensuremath{\le}x\ensuremath{\le}0.3 and \ensuremath{\delta}0.05 show that, between 100--200 K, S has a maximum that depends on x, according to the relation ${\mathit{S}}_{\mathit{m}}$(x)\ensuremath{\approxeq}(${\mathit{k}}_{\mathit{B}}$/\ensuremath{\Vert}e\ensuremath{\Vert}) ln[(1+x)/(1-x)]. This is the expected saturation value of S, for noninteracting carriers in a narrow conduction band with x doped electrons above half-filling. The temperature dependence of the resistivity (\ensuremath{\rho}) exhibits a crossover from wide-band to narrow-band behavior, in a conductor with a mean free path limited by impurities. The drop of S at higher temperatures, accompanied by a drop in d\ensuremath{\rho}/dT, can be attributed to excitation of electrons from the conduction band to higher-energy levels associated with the dopant, or to the contribution of activated hopping to the transport coefficients.

Temperature-dependent radiative decay of localized excitons in a type-II GaAs/AlAs superlattice.

Abstract: The low-temperature luminescence intensity decay following pulse excitation of localized excitons in a type-II GaAs/AlAs superlattice is nonexponential. The decay obeys a previously derived theory in which excitons experience a distribution of decay rates corresponding to a Gaussian distribution of X to \ensuremath{\Gamma} scattering matrix elements. At high temperature the decay is exponential with a rate equal to the mean of the distribution. The transition is attributed to excitons motionally averaging the distribution as temperature is increased and thermal delocalization occurs. This paper develops a theory of radiative decay which takes into account motional averaging and is valid at all temperatures. The theory has one fitting parameter \ensuremath{\gamma} which is the ratio of exciton lifetime to jump time and determines the extent of averaging performed. Good agreement is found between the theory and experimental data; however, at high excitation intensity and low exciton energy the theory must be modified to take saturation of localized states into account. The temperature dependence of the fitting parameter \ensuremath{\gamma} reveals two delocalization processes, the activation energies of which are interpreted as the localization energy and the exciton binding energy.

Stable groups, mostly of finite exponent.

Abstract: We prove certain properties of stable groups of finite exponent. In particular, an 9ΐ-group of finite exponent has normal-by-finite 2-Sylow subgroups; if it has exponent 3 2" for some n then NG(ψ(G)) > //and we may view H/K as subgroup of NG(ψ(G))/\l/(G). The connected component H° of a substable group H is the intersection with H of all definable subgroups K such that the index IH: H Π KI is finite; H° is normal in H and itself connected. If H is definable, we need only consider definable subgroups K < H of finite index. So the index \H:H°\ is at most 2 | Ί and a saturated model and for a type-definable Hthe connected component has comparable size. But in the absence of saturation or if H is just substable, H° may even be reduced to the identity! For a relatively definable H this may be remedied in some cases by considering the locally connected component //, which is the intersection of all conjugates H such that the index \H:H Π H\ is finite. By Baldwin-Saxl, this is again a relatively definable subgroup of finite index. Finally, a group is small if its theory has only countably many pure types. Received September 1, 1992; revised December 31, 1992

Electrical-resistivity studies on AuFeCr.

Abstract: Electrical-resistivity (\ensuremath{\rho}) measurements are reported for a series of ${\mathrm{Au}}_{82}$(${\mathrm{Fe}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Cr}}_{\mathit{x}}$${)}_{18}$ alloys (0\ensuremath{\le}x\ensuremath{\le}0.8) in the temperature range 4.2 K\char21{}300 K. The system emerges into a cluster glass or spin glass for xg0.1, with the end alloys ${\mathrm{Au}}_{82}$${\mathrm{Fe}}_{18}$ and ${\mathrm{Au}}_{82}$${\mathrm{Cr}}_{18}$ being reentrant and antiferromagnetic, respectively. The alloys with x\ensuremath{\ge}0.6 show pronounced resistivity maxima. The ``impurity'' resistivity \ensuremath{\Delta}\ensuremath{\rho} shows a ${\mathit{T}}^{3/2}$ dependence. The saturation of resistivity for x\ensuremath{\ge}0.4 is discussed in terms of the mean-free-path damping of the Ruderman-Kittel-Kasuga-Yosida interaction. However, a quantitative fit to a theory by Larsen does not hold for this system.

Experimental and predicted dual oximetry variability

Abstract: Objective. We wished to determine whether the individual bias (mean difference) and precision (standard deviation of the difference) values of 2 variables, arterial oxygen saturation (SaO2) and mixed venous oxygen saturation (S⊻O2), could be used to predict the bias and precision values of the combined dual oximetry variable (SaO2- S⊻O2).Methods. We simultaneously measured SaO2 by pulse oximetry and arterial blood gas co-oximetry and S⊻O2 by fiberoptic reflectance oximetry pulmonary artery catheter and venous blood gas co-oximetry in 238 data sets from 55 patients. Three different methods were used to predict the standard deviation of the difference of $$(SaO_2 - S\bar vO_2 )[s_{\Delta (SaO_2 - S\bar vO_2 )} ]$$ : simple sum, root mean square (RMS) error, and RMS error with correction term. We derived the equation for the RMS error with correction term because initial results showed that the simple sum and RMS error methods did not predict $$s_{\Delta (SaO_2 - S\bar vO_2 )} $$ well. The correction term accounts for the non-independence of simultaneous SaO2 and S⊻O2 measurements.Results. The observed overall bias of the SaO2, SvO2, and (SaO2 - S⊻O2) measurement methods were 0.17, –1.76, and 1.94, respectively. The observed overall $$s_{\Delta (SaO_2 - S\bar vO_2 )} $$ of the (SaO2 -S⊻O2) measurement method was 5.12. The simple sum method overestimated the actual $$s_{\Delta (SaO_2 - S\bar vO_2 )} $$ by 38%, the RMS error method differed from the actual $$s_{\Delta (SaO_2 - S\bar vO_2 )} $$ by 3%, and the RMS error with correction term method matched the actual $$s_{\Delta (SaO_2 - S\bar vO_2 )} $$ .Conclusion. The bias of a (SaO2 -S⊻O2) measurement method is simply the bias of the SaO2 measurement method less the bias of the S⊻O2 measurement method. $$s_{\Delta (SaO_2 - S\bar vO_2 )} $$ is best predicted by the derived equation, RMS error with correction term. The same principles and equations also apply to other situations in which 2 variables with the same dimensions are combined into 1 variable, such as (Paco2-Etco2) gradients and perfusion-pressure gradients. Although the difference between the $$s_{\Delta (SaO_2 - S\bar vO_2 )} $$ predicted by the RMS error equation and the derived RMS error equation with correction term was small, the difference may be significant for other combined variables.

Adiabatic demagnetization of quadrupolar nuclear spins in a rotating frame by use of an rf electric field.

Abstract: Adiabatic demagnetization in a rotating frame (ADRF) has been realized by means of rf-electric-field excitation. The experiments were carried out in the double quantum transition of the $^{27}\mathrm{Al}$ nuclear-spin system in ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. The excitation was caused by the time-dependent electric quadrupole interaction induced by the rf electric field. Although a strong rf electric field with an intensity of about 14 kV/cm was applied, the transverse field due to the rf electric field was so small that its role as a heat reservoir could be neglected. The observed ADRF processes and the irreversibility are analyzed in detail with use of Provotorov's saturation theory and by consideration of the spin thermodynamics. The ADRF processes are well described by equations that we have derived from Provotorov's saturation theory. This theoretical treatment is also applicable to the ADRF performed with use of an rf magnetic field under similar experimental conditions.

Measurements of saturation broadening of the Cu 5s' 4D5/2 autoionization level by the pulsed optogalvanic technique.

Abstract: The use of the optogalvanic technique to obtain the line profile of the Cu 5s' $^{4}$${\mathit{D}}_{5/2}$ autoionization level with different degrees of saturation broadening is demonstrated. The experimental results point out that the growth of the autoionization-level breadth follows the square root of the increase in the laser intensity. The measured value of the natural breadth of the Cu5s' $^{4}$${\mathit{D}}_{5/2}$ autoionization level is 7.2\ifmmode\pm\else\textpm\fi{}0.6 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The laser saturation intensity was measured by two different methods, and its value is about 0.39\ifmmode\pm\else\textpm\fi{}0.09 MW/${\mathrm{cm}}^{2}$.

Optical Multistability at the Surface of a Medium of Two-Level Atoms

Abstract: We study a symmetric layered structure consisting of two identical metal films of thickness d 1 and dielectric constant e i separated by a distance of d 2. The space between the films is uniformly filled by two-level atoms exhibiting a nonlinearity given by the dielectric function2 $$ {{1 + \left( {\alpha /\beta } \right)\left| {\vec E} \right|^2 }} $$ (1) where e20 is the linear dielectric constant, α is the nonlinearity constant and β is the saturation parameter. Note that, for very large β, Eq. 1 represents a Kerr-type nonlinearity. The whole structure is embedded between two high index prisms of dielectric constant e i ;. Let a p-polarized wave be incident on the structure at an angle θ. We present exact numerical results for the reflectivity of the plane wave from the structure under conditions when coupled surface plasmons are excited in it.

In Situ Determination of Capillary Pressure and Relative Permeability Curves Using Well Logs.

Abstract: Capillary pressure and relative permeability characteristics of a reservoir rock are presently determined through core analysis. The process of core handling and cleaning can result in significant alteration in core wettability; consequently, tests conducted on these altered cores can produce non-representative reservoir rock characteristics. This dissertation docum ents a study of the possibility of in-situ determ ination of capillary pressure and relative permeability using pressure data in the transition zone and open hole well logs. A pressure profile obtained from the formation tester defines the wettability, free water level, and hydrocarbon and water densities as well as the capillary pressure above the free water level. Correlating the pressure values to the water saturation values determ ined from the resistivity logs results in a capillary pressure/water saturation, P C(S W). curve characteristic of the reservoir. A relative permeability curve then can then be derived from this PC(S W) curve using empirical relationships. This approach was tested in the laboratory using an eight-foot vertical sandstone core to sim ulate the formation. The core was fitted with electrode arrays, and resistivity m easurem ents were used to construct the water saturation profile. The capillary pressure values were calculated from both the densities and the height above the free water level values. The free water level was indicated by a tube connected to the core setup. Chapter III documents the laboratory details of this experimental work together with its results and conclusions. A technique that can be used to extrapolate existing core data to cases where such data is absent or not representative of in-situ conditions is of interest. Chapter IV of this dissertation documents a new approach that has been developed and is based on using log data to derive a water saturation versus depth profile in the transition zone of the formation of interest. The log derived water saturation distribution is then correlated to generalized capillary pressure curves typical of the formation studied. This curve matching yields, by comparison, a capillary pressure curve specific to the formation of interest. The capillary pressure type curves are generated from already available core data and other petrophysical inform ation. R e lative perm eability curves are subsequently generated using correlations based on Purcell's model. The technique is successfully applied to several field examples. Special attention is given to cases of tight sands where relative permeability measurements on core samples are very complex, time consuming, and inaccurate due to the very small pore space available to the fluid to move through the tight sand cores. In Chapter V, the above mentioned technique is extended to tight sand cases where a special relationships characteristic of tight sands are developed and mathematically manipulated to adapt already existing relative permeability equations.