Subdiffusion of nonlinear waves in quasiperiodic potentials

19 p.

A summary of the inventory survey of Nigeria inland waters and preliminary estimates of their fish yield potentials

A summary of the inventory survey of Nigeria inland waters is presented. The survey reveals that Kano State tops the list in reservoir development with an existing water surface area of about 42,773 ha, while Anambra State has the least with about 38 hectares. No reservoir was recorded for Lagos and Rivers States. However, in aspects of existing fish ponds, a total of about 471 ha was recorded for Plateau State and about 5 ha for Niger State. Preliminary estimates of Nigeria's fish yield potentials based on established production records of comparable water bodies in the tropics, at different levels of management, show that the available water mass in the country, estimated at about 12.5 million hectares, could yield a minimum of about 334,214 metric tonnes (m.t.) of fish per annum with little or no management and a maximum of about 511,703 metric tonnes per annum with adequate management. Comparison of the potential yields from inland sources with the projected fish production in Nigeria (1981-1985) based on supply and demand statistics shows that potential yield from inland sources even at a low level of management is relatively higher than the projected inland production and more than double the observed production. The variation between the potential and the observed fish yields in the country has been attributed to the absolute lack of management strategies for our various inland waters. The paper elaborates on possible management strategies for various categories of inland waters as a prelude towards increased fish production in the country

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Hydrodynamic entrapment of bacteria swimming near a solid surface.

The near-surface motility of bacteria is important in the initial formation of biofilms and in many biomedical applications. The swimming motion of Escherichia coli near a solid surface is investigated both numerically and experimentally. A boundary element method is used to predict the hydrodynamic entrapment of E. coli bacteria, their trajectories, and the minimum separation of the cell from the surface. The numerical results show the existence of a stable swimming distance from the boundary that depends only on the shape of the cell body and the flagellum. The experimental validation of the numerical approach allows one to use the numerical method as a predictive tool to estimate with reasonable accuracy the near-wall motility of swimming bacteria of known geometry. The analysis of the numerical database demonstrated the existence of a correlation between the radius of curvature of the near-wall circular trajectory and the separation gap. Such correlation allows an indirect estimation of either of the two quantities by a direct measure of the other without prior knowledge of the cell geometry. This result may prove extremely important in those biomedical and technical applications in which the near-wall behavior of bacteria is of fundamental importance.

Autonomous rigid body attitude synchronization

Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H., & Leonard, N.E. (2001). Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In Proc. 40th IEEE conf. decision and control (pp. 4598-4603); Nair, S., Leonard, N. E. (2007). Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2(4), 595-624]. The present paper studies two separate extensions with the same energy shaping approach: (i) locally synchronizing the rigid bodies' attitudes, but without restricting their final motion and (ii) relaxing the communication topology from undirected, fixed and connected to directed, varying and uniformly connected. The specific strategies that must be developed for these extensions illustrate the limitations of attitude control with reduced information. © 2008 Elsevier Ltd.

First-principles energetics of water clusters and ice: a many-body analysis.

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.

Reactive Many-Body Expansion for a Protonated Water Cluster.

We generalize the standard many-body expansion technique that is used to approximate the total energy of a molecular system to enable the treatment of chemical reactions by quantum chemical techniques. By considering all possible assignments of atoms to monomer units of the many-body expansion and associating suitable weights with each, we construct a potential energy surface that is a smooth function of the nuclear positions. We derive expressions for this reactive many-body expansion energy and describe an algorithm for its evaluation, which scales polynomially with system size, and therefore will make the method feasible for future condensed phase simulations. We demonstrate the accuracy and smoothness of the resulting potential energy surface on a molecular dynamics trajectory of the protonated water hexamer, using the Hartree-Fock method for the many-body term and Møller-Plesset theory for the low order terms of the many-body expansion.

Electronic properties of sulfur passivated undoped-n(+) type GaAs surface studied by photoreflectance

Photoreflectance (PR) has been used to study surface electronic properties (electric field, Fermi level pinning, and density of surface states) of undoped-n(+) (UN+) GaAs treated in the solution of ammonium sulfide in isopropanol. Complex Fourier transformation (CFT) of PR spectra from passivated surface shows that the sulfur overlay on GaAs surface makes no contribution to Franz-Keldysh oscillations (FKOs). The barrier height measured by PR is derived from surface states directly, rather than the total barrier height, which includes the potentials derived from Ga-S and As-S dipole layers. Comparing with native oxidated surface, the passivation leads to 80 meV movement of surface Fermi level towards the conduction band minimum, and reduction by more than one order in density of surface states. (C) 2003 Elsevier Science B.V. All rights reserved.

Isospin dependence of three-body force rearrangement contribution

Within the isospin-dependent Brueckner framework, we investigate the contribution of three-body force ( TBF) rearrangement to isospin symmetry potential as well as its momentum and density dependence. In particular, we investigate the TBF rearrangement effects on the isospin splitting of neutron and proton effective masses in neutron-rich nuclear matter. We show that the rearrangement contribution of TBF to neutron and proton single-particle potentials is repulsive and increases rapidly with increasing density and momentum. At low densities, the influence of the TBF rearrangement on symmetry potential is rather small, and the TBF rearrangement effect becomes more and more pronounced as the density rises. At high densities, the contribution of TBF rearrangement increases considerably the symmetry potential and modifies remarkably the momentum dependence of the symmetry potential. In both cases with and without including the TBF rearrangement contribution, the predicted neutron effective mass in neutron-rich matter is greater than the proton effective mass. The TBF rearrangement effect is to decrease remarkably both the proton and neutron effective masses, and reduce the magnitude of neutron-proton effective mass splitting in neutron-rich matter at high densities.

Three-body force rearrangement effect on single particle properties in neutron-rich nuclear matter

We extend the Brueckner-Hartree-Fock (BHF) approach to include the three-body force (TBF) rearrangement contribution in calculating the neutron and proton single particle (s.p.) properties in isospin asymmetric nuclear matter. We investigate the TBF rearrangement effect on the momentum-dependence of neutron and proton s.p. potentials, the isospin splitting and especially its density dependence of the neutron and proton effective masses, and the isospin symmetry potential in neutron-rich nuclear matter by adopting the realistic Argonne V-18 two-body nucleon-nucleon interaction supplemented with a microscopic TBF. We find that at low densities, the TBF rearrangement effect is fairly weak, whereas the TBF induces a significant rearrangement effect on the s.p. properties at high densities and large momenta. The TBF rearrangement contribution to s.p. potential is shown to be repulsive, and it reduces considerably the attraction of the BHF s.p. potential. The repulsion from the TBF rearrangement turns out to be strongly momentum dependent at high densities and high momenta. As a consequence, it enhances remarkably the momentum dependence of the proton and neutron s.p. potentials and reduces the neutron and proton effective masses. At low densities, the TBF rearrangement effect on symmetry potential is almost negligible, while at high densities, it enlarges sizably the symmetry potential. At high enough densities, it may even change the high-momentum behavior of symmetry potential. In both cases, with and without including the TBF rearrangement contribution, the predicted neutron effective mass is larger than the proton one in neutron-rich matter within the BHF framework; i.e., the predicted isospin splitting of the proton and neutron effective masses in neutron-rich matter is such that m(n)(*)>= m(p)(*), in agreement with the recent Dirac-BHF predictions. The TBF rearrangement contribution reduces remarkably the magnitude of the proton-neutron effective mass splitting at high densities. At high enough densities, inclusion of the TBF rearrangement contribution even suppresses almost completely the effective mass splitting.

Surface-enhanced resonance Raman spectroscopy and spectroscopy study of redox-induced conformational equilibrium of cytochrome c adsorbed on DNA-modified metal electrode

The redox-induced conformational equilibrium of cytochrome c (cyt c) adsorbed on DNA-modified metal electrode and the interaction mechanism of DNA with cyt c have been studied by electrochemical, spectroscopic and spectroelectrochemical techniques. The results indicate that the external electric field induces potential-dependent coordination equilibrium of the adsorbed cyt c between its oxidized state (with native six-coordinate low-spin and non-native five-coordinate high-spin heme configuration) and its reduced state (with native six-coordinate low-spin heme configuration) on DNA-modified metal electrode. The strong interactions between DNA and cyt c induce the self-aggregation of cyt c adsorbed on DNA. The orientational distribution of cyt c adsorbed on DNA-modified metal electrode is potential-dependent, which results in the deviation from an ideal Nernstian behavior of the adsorbed cyt c at high electrode potentials. The electric-field-induced increase in the activation barrier of proton-transfer steps attributed to the rearrangement of the hydrogen bond network and the self-aggregation of cyt c upon adsorption on DNA-modified electrode strongly decrease the interfacial electron transfer rate.

Potential-dependent adsorption/desorption of organic adsorbate at HOPG electrode and accompanying delamination of graphite surface

In situ electrochemical scanning tunneling microscopy, alternating current voltammetry, and electrochemical quartz crystal microbalance have been employed to follow the potential-dependent adsorption/desorption processes of nucleic acid bases on highly oriented pyrolytic graphite (HOPG) electrode. The results show that (i) potential-dependent adsorption/desorption of nucleic acid bases on HOPG electrode was accompanied by delamination of the HOPG surface, and the delamination initiates from steps or kinks on the electrode surface, which provide highly active sites for adsorption; (ii) the delamination usually occurred when the electrode potential was changed or when the electrode was at potentials where the phase transition of adsorbate occurred. These results suggest that the surface stress resulting from the interaction between the substrate and adsorbate, as well as the interaction due to potential-induced surface charge distribution and the hysteresis of charge equilibrium are the main factors resulting in HOPG delamination. (C) 1999 The Electrochemical Society. S0013-4651(97)12-013-4. All rights reserved.

Seasonal variation of reproduction rates and body size of Calanus sinicus in the Southern Yellow Sea, China

Annual variations of egg production rate (EPR) and clutch size of Calanus sinicus, as well as body size of females (prosome length and dry weight), were investigated at a series of stations in the Southern Yellow Sea by onboard incubation. Calanus sinicus was spawning in all the 11 cruises investigated, and the annual variation of EPR was bimodal. Monthly average EPR was highest from May to July, respectively, 5.97, 5.36 and 6.30 eggs female(-1) d(-1), then decreased dramatically to only 1.37 eggs female(-1) d(-1) in August and attained the lowest 1.07 eggs female(-1) d(-1) in October. In November, average EPR increased again to 4.31 eggs female(-1) d(-1). Seasonal variation of clutch size was similar to EPR, except that it decreased gradually after August rather than dramatically as did EPR. Prosome length of females was maximum in May and minimum in October, but dry weight was highest in November. Monthly average EPR correlated better with prosome length than dry weight, while clutch size was rather determined by dry weight of females. It is suggested that egg production of C. sinicus was active during two discontinuous periods when both surface and bottom temperature fell into its favorite range (i.e. 10-23degreesC), and different reproductive strategies were adopted in these two reproductive peaks: other than the highest EPR, longer prosome length was also achieved by C. sinicus from May to July, while females in November developed shorter bodies but accumulated more energy for reproduction.

Characterization of topographical effects on macrophage behavior in a foreign body response model.

Current strategies to limit macrophage adhesion, fusion and fibrous capsule formation in the foreign body response have focused on modulating material surface properties. We hypothesize that topography close to biological scale, in the micron and nanometric range, provides a passive approach without bioactive agents to modulate macrophage behavior. In our study, topography-induced changes in macrophage behavior was examined using parallel gratings (250 nm-2 mum line width) imprinted on poly(epsilon-caprolactone) (PCL), poly(lactic acid) (PLA) and poly(dimethyl siloxane) (PDMS). RAW 264.7 cell adhesion and elongation occurred maximally on 500 nm gratings compared to planar controls over 48 h. TNF-alpha and VEGF secretion levels by RAW 264.7 cells showed greatest sensitivity to topographical effects, with reduced levels observed on larger grating sizes at 48 h. In vivo studies at 21 days showed reduced macrophage adhesion density and degree of high cell fusion on 2 mum gratings compared to planar controls. It was concluded that topography affects macrophage behavior in the foreign body response on all polymer surfaces examined. Topography-induced changes, independent of surface chemistry, did not reveal distinctive patterns but do affect cell morphology and cytokine secretion in vitro, and cell adhesion in vivo particularly on larger size topography compared to planar controls.

Convergent Surface Water Distributions in U.S. Cities

Earth's surface is rapidly urbanizing, resulting in dramatic changes in the abundance, distribution and character of surface water features in urban landscapes. However, the scope and consequences of surface water redistribution at broad spatial scales are not well understood. We hypothesized that urbanization would lead to convergent surface water abundance and distribution: in other words, cities will gain or lose water such that they become more similar to each other than are their surrounding natural landscapes. Using a database of more than 1 million water bodies and 1 million km of streams, we compared the surface water of 100 US cities with their surrounding undeveloped land. We evaluated differences in areal (A WB) and numeric densities (N WB) of water bodies (lakes, wetlands, and so on), the morphological characteristics of water bodies (size), and the density (D C) of surface flow channels (that is, streams and rivers). The variance of urban A WB, N WB, and D C across the 100 MSAs decreased, by 89, 25, and 71%, respectively, compared to undeveloped land. These data show that many cities are surface water poor relative to undeveloped land; however, in drier landscapes urbanization increases the occurrence of surface water. This convergence pattern strengthened with development intensity, such that high intensity urban development had an areal water body density 98% less than undeveloped lands. Urbanization appears to drive the convergence of hydrological features across the US, such that surface water distributions of cities are more similar to each other than to their surrounding landscapes. © 2014 The Author(s).