System Of Spheres Research Articles

Crystallization in the Hard Sphere Systems

Crystallization in the Hard Sphere Systems

Quantum Bound States on Some Hyperbolic Surfaces

The aim of this work is to highlight results of energy eigenstates on some noncompact finite hyperbolic surfaces. Such systems are known to exhibit both continuous and discrete spectra and are dependent on the subgroups of the modular group that underlie these surfaces. We study explicitly the cases of Maass cusp forms on the singly punctured two-torus and the triply punctured two-sphere for their eigenvalues. The eigenvalues for the torus system are doubly degenerate while for the sphere case, the eigenvalues are nondegenerate. We also note that the lowest eigenvalue of the sphere system is larger than that of the torus system.

The Yalta Conference of the “Big Three” in 1945 and Ukraine’s Appearance on the International Stage

The article analyzes the decisions of the Yalta international conference of the leaders of the Allied States, i.e. USSR, USA and UK, aimed at solving the key issues of the final stage of war with Nazi Germany and its satellites: coordination of military activities, creation of four occupation zones on German territory, declared common goal of unconditional surrender as well as the principles of the post-war demilitarization and denazification of Germany, just punishment of war criminals, compensation for damages caused by the Nazis and creation of the inter-Alliance Control Commission in Moscow.
 The article considers the agreed decisions on establishing a permanent mechanism for regular consultations among the three Foreign Ministers of the Allied States related to post-war arrangement and order in Europe and the world as well as the Allies’ policy on liberated territories. The author analyses the conditions leading to creation of the new system of relations and spheres of influence of the great powers in the world. The article contains a special analysis of Allies’ decisions regarding creation of the UN and inclusion of Ukraine into the number of states-founders of this international organization. The issues related to legal capacity of Ukraine in the post-war decades are also considered.

An Investigation into the Effects of Pressure on Gas Detection Using an Integrating Sphere as Multipass Gas Absorption Cell: Analysis and Discussion

The approach adopted in the present work was to increase the pressure within an integrating sphere system to increase the number density of molecules in the gas cell and hence to obtain a significant absorption in order to improve the sensitivity of the measurement system. This feasibility study has allowed an assessment of the net absorption gain with the rise of pressure and highlights the validity domain of the linear operating regime relative to Beer's law. Experiments were conducted on the oxygen A-band. The absorption peaks of oxygen at 760 nm typically were measured with a 50 mm diameter integrating sphere system under various pressures. Tests were performed up to 200 bar, the pressure for which the linear regime was operative, and analysed from a theoretical and experimental point of view. An experimental net absorption gain of 160 was achieved in this pressure range with the possibility of up to 650 bar while remaining in the linear regime. Finally, the experimental data obtained, in particular the absorption evolution due to the contribution of oxygen gas, seem consistent with the simulated results and are discussed in this paper.

Image method for induced surface charge from many-body system of dielectric spheres.

Charged dielectric spheres embedded in a dielectric medium provide the simplest model for many-body systems of polarizable ions and charged colloidal particles. We provide a multiple scattering formulation for the total electrostatic energy for such systems and demonstrate that the polarization energy can be rapidly evaluated by an image method that generalizes the image methods for conducting spheres. Individual contributions to the total electrostatic energy are ordered according to the number of polarized surfaces involved, and each additional surface polarization reduces the energy by a factor of (a/R)3ϵ, where a is the sphere radius, R the average inter-sphere separation, and ϵ the relevant dielectric mismatch at the interface. Explicit expressions are provided for both the energy and the forces acting on individual spheres, which can be readily implemented in Monte Carlo and molecular dynamics simulations of polarizable charged spheres, thereby avoiding costly computational techniques that introduce a surface charge distribution that requires numerical solution.

Microstructure, local dynamics, and flow behavior of colloidal suspensions with weak attractive interactions.

We present a comprehensive micro- and macrorheological study of the effect of weak depletion attraction (Ψdep ≈ 1–10 kBT) on dense colloidal suspensions stabilized by short-range repulsive interactions. We used aqueous polymer dispersions as model system and demonstrated the unique capabilities of multiple particle tracking (MPT) to disclose structural changes in such technically important systems exhibiting many characteristic features of hard sphere systems. Below the hard sphere freezing point ϕc, viscosity increases monotonically with increasing Ψdep due to the transition from a fluid to a fluid/crystalline and finally to a gel state. Above ϕc, increasing attraction strength first results in a viscosity reduction corresponding to the formation of large, permeable crystals and then in a viscosity increase when a network of dense, small crystals forms. The fraction of the fluid and crystal phase, particle concentration in each phase as well as the modulus of the micro-crystals are obtained, the latter decreases with Ψdep. Above the colloidal glass transition strong heterogeneities and different local particle mobility in the repulsive and attractive arrested states are found. Particles are trapped in the cage of neighboring particles rather than in an attractive potential well. The intermediate ergodic state exhibits uniform tracer diffusivity.

Theoretical study of the dynamic magnetic response of ferrofluid to static and alternating magnetic fields

The dynamic magnetic response of ferrofluid in a static uniform external magnetic field to a weak, linear polarized, alternating magnetic field is investigated theoretically. The ferrofluid is modeled as a system of dipolar hard spheres, suspended in a long cylindrical tube whose long axis is parallel to the direction of the static and alternating magnetic fields. The theory is based on the Fokker-Planck-Brown equation formulated for the case when the both static and alternating magnetic fields are applied. The solution of the Fokker-Planck-Brown equation describing the orientational probability density of a randomly chosen dipolar particle is expressed as a series in terms of the spherical Legendre polynomials. The obtained analytical expression connecting three neighboring coefficients of the series makes possible to determine the probability density with any order of accuracy in terms of Legendre polynomials. The analytical formula for the probability density truncated at the first Legendre polynomial is evaluated and used for the calculation of the magnetization and dynamic susceptibility spectra. In the absence of the static magnetic field the presented theory gives the correct single-particle Debye-theory result, which is the exact solution of the Fokker-Planck-Brown equation for the case of applied weak alternating magnetic field. The influence of the static magnetic field on the dynamic susceptibility is analyzed in terms of the low-frequency behavior of the real part and the position of the peak in the imaginary part.

Cluster analysis in systems of magnetic spheres and cubes

In the present work we use molecular dynamics simulations and graph-theory based cluster analysis to compare self-assembly in systems of magnetic spheres, and cubes where the dipole moment is oriented along the side of the cube in the [001] crystallographic direction. We show that under the same conditions cubes aggregate far less than their spherical counterparts. This difference can be explained in terms of the volume of phase space in which the formation of the bond is thermodynamically advantageous. It follows that this volume is much larger for a dipolar sphere than for a dipolar cube.

Generic phase diagram of binary superlattices

Emergence of a large variety of self-assembled superlattices is a dramatic recent trend in the fields of nanoparticle and colloidal sciences. Motivated by this development, we propose a model that combines simplicity with a remarkably rich phase behavior applicable to a wide range of such self-assembled systems. Those systems include nanoparticle and colloidal assemblies driven by DNA-mediated interactions, electrostatics, and possibly, controlled drying. In our model, a binary system of large and small hard spheres (L and S, respectively) interacts via selective short-range ("sticky") attraction. In its simplest version, this binary sticky sphere model features attraction only between S and L particles. We show that, in the limit when this attraction is sufficiently strong compared with [Formula: see text], the problem becomes purely geometrical: the thermodynamically preferred state should maximize the number of [Formula: see text] contacts. A general procedure for constructing the phase diagram as a function of system composition f and particle size ratio r is outlined. In this way, the global phase behavior can be calculated very efficiently for a given set of plausible candidate phases. Furthermore, the geometric nature of the problem enables us to generate those candidate phases through a well-defined and intuitive construction. We calculate the phase diagrams for both 2D and 3D systems and compare the results with existing experiments. Most of the 3D superlattices observed to date are featured in our phase diagram, whereas several more are predicted for future discovery.

The Boltzmann–Grad limit of a hard sphere system: analysis of the correlation error

We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions (correlation errors) measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order $k$ measures the event where $k$ particles are connected by a chain of interactions preventing the factorization. We show that, provided $k < \varepsilon^{-\alpha}$, such an error flows to zero with the average density $\varepsilon$, for short times, as $\varepsilon^{\gamma k}$, for some positive $\alpha,\gamma \in (0,1)$. This provides an information on the size of chaos, namely, $j$ different particles behave as dictated by the Boltzmann equation even when $j$ diverges as a negative power of $\varepsilon$. The result requires a rearrangement of Lanford perturbative series into a cumulant type expansion, and an analysis of many-recollision events.

How to model the interaction of charged Janus particles

We analyze the interaction of charged Janus particles including screening effects. The explicit interaction is mapped via a least square method on a variable number n of systematically generated tensors that reflect the angular dependence of the potential. For n = 2 we show that the interaction is equivalent to a model previously described by Erdmann, Kröger, and Hess (EKH). Interestingly, this mapping is for n = 2 not able to capture the subtleties of the interaction for small screening lengths. Rather, a larger number of tensors has to be used. We find that the characteristics of the Janus type interaction plays an important role for the aggregation behavior. We obtained cluster structures up to the size of 13 particles for n = 2 and 36 and screening lengths κ−1 = 0.1 and 1.0 via Monte Carlo simulations. The influence of the screening length is analyzed and the structures are compared to results for an electrostatic-type potential and for the multipole-expanded Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. We find that a dipole-like potential (EKH or dipole DLVO approximation) is not able to sufficiently reproduce the anisotropy effects of the potential. Instead, a higher order expansion has to be used to obtain cluster structures that are compatible with experimental observations. The resulting minimum-energy clusters are compared to those of sticky hard sphere systems. Janus particles with a short-range screened interaction resemble sticky hard sphere clusters for all considered particle numbers, whereas for long-range screening even very small clusters are structurally different.

Statistical Thermodynamics of an “Open” Hard Sphere System on the Equilibrium Fluid Isotherm: Study of Properties of the Freezing Transition Without Direct Involvement of the Equilibrium Solid Phase

Using several theoretical tools $$\ldots $$ (i) the nucleation theorem, (ii) an equivalent cavity, (iii) the reversible work of adding a cavity to an open hard sphere system, and (iv) the theory of “stability”... the authors estimated the density at which the hard sphere freezing transition occurs. No direct involvement of the equilibrium solid phase is involved. The reduced density $$\uppi a^3\rho _f/6$$ (where a is the hard sphere diameter and $$\rho _f $$ is the actual density at which freezing occurs) is found to be 0.4937 while the value obtained by computer simulation is 0.494. The agreement is good, but the new method still contains some approximation. However, the approximation is based on the idea that at a density just below $$\rho _f $$ the fluid adopts a distorted structure resembling the solid, but different enough so that long-range order vanishes. Initial loss of stability may not be involved in every fluid–solid transition, but it may be an early step in the hard sphere and related systems.

Assessing firmness and SSC of pears based on absorption and scattering properties using an automatic integrating sphere system from 400 to 1150 nm

It is important to understand the fundamental optical properties of fruit tissues when applying optical techniques for quality inspection of fruits. An automatic integrating sphere (AIS) system was used to measure the total reflectance and total transmittance of pear tissue in the wavelength range of 400–1150nm. These two measurements were used to estimate the bulk optical properties (absorption coefficient μa and reduced scattering coefficient μ’s) of tissue samples using inverse adding-doubling (IAD) method. The accuracy of AIS system was verified by using both an INO solid phantom and a set of liquid phantoms. Relationships between soluble solids content (SSC), firmness and the optical properties were investigated, with coefficients of determination of 0.40 and 0.48 for validation, respectively. In addition, the μa decreased with the increase of shelf-life time, while the μ’s did just the opposite. This study demonstrated the feasibility of detecting multiple qualities of pears by investigating the tissue optical properties. For further research, the measured optical properties of pear tissues can be used for modeling and simulation of light-fruit interaction.

Inclusion of Specialist and Generalist Stimuli in Attract-and-Kill Programs: Their Relative Efficacy in Apple Maggot Fly (Diptera: Tephritidae) Pest Management.

Investigating the chemical ecology of agricultural systems continues to be a salient part of integrated pest management programs. Apple maggot fly, a key pest of apple in eastern North America, is a visual specialist with attraction to host fruit-mimicking cues. These cues have been incorporated into red spherical traps used for both monitoring and behaviorally based management. Incorporating generalist or specialist olfactory cues can potentially increase the overall success of this management system. The primary aim of this study was to evaluate the attractiveness of a generalist olfactory cue, ammonium carbonate, and the specialist olfactory cue, a five-component apple volatile blend, when included as a component of a red attracticidal sphere system. Secondly, we assessed how critical it was to maintain minimal deviation from the optimal, full-round specialist visual stimulus provided by red spheres. Finally, attracticidal spheres were deployed with specialist olfactory cues in commercial apple orchards to evaluate their potential for effective management of apple maggot. Ammonium carbonate did not increase residency, feeding time, or mortality in the laboratory-based trials. Field deployment of specialist olfactory cues increased apple maggot captures on red spheres, while the generalist cue did not. Apple maggot tolerated some deviation from the optimal visual stimulus without reducing captures on red spheres. Attracticidal spheres hung in perimeter trees in orchards resulted in acceptable and statistically identical levels of control compared with standard insecticide programs used by growers. Overall, our study contributes valuable information for developing a reliable attract-and-kill system for apple maggot.

Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond.

We implement and optimize a particle-swap MonteCarlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct nonequilibrium protocols. We demonstrate that equilibrium fluid and nonequilibrium jammed states can have the same density, showing that the jamming transition cannot be the end point of the fluid branch.

Investigation of absorption and scattering characteristics of kiwifruit tissue using a single integrating sphere system

For a quantitative understanding of light interaction with fruit tissue, it is critical to obtain two fundamental parameters: the absorption coefficient and the scattering coefficient of the tissue. This study was to investigate the optical properties of kiwifruit tissue at the wavelength of 632.8 nm. The total reflectance and total transmittance of kiwifruit tissue from three parts (including the flesh part, the seed part, and the seed-base part) were measured using a single integrating sphere system. Based on the measured spectral signals, the absorption coefficient μa and the reduced scattering coefficient μs' of kiwifruit tissue were calculated using the inverse adding-doubling (IAD) method. Phantoms made from Intralipid 20% and India ink as well as a Biomimic solid phantom were used for system validation. The mean values of μa and μs' of different parts of the kiwifruit were 0.031-0.308 mm(-1) and 0.120-0.946 mm(-1), respectively. The results showed significant differences among the μa and μs' of the three parts of the kiwifruit. The results of this study confirmed the importance of studying the optical properties for a quantitative understanding of light interaction with fruit tissue. Further investigation of fruit optical properties will be extended to a broader spectral region and different kinds of fruits.

Features of Phase Transitions in Models of Complex Plasma

AbstractSome features of melting curves and fluid‐crystal phase transitions in complex plasmas are under discussion. The base for a consideration is the well‐known phase diagram of dusty plasma (Hamaguchi, 1997) for an equilibrium charged system with the Yukawa potential in Γ − κ plane (Γ is the Coulomb non‐ideality parameter,κ is a screening parameter). This phase diagram is converted for a one‐component Yukawa system in ordinary density ‐ temperature plane. A melting curve is converted for this system in temperature ‐ pressure plane. There are some density gap estimations based on a hypothesis of similar melting properties in Yukawa systems and Soft Spheres systems. The initial phase diagram is also converted for two one‐temperature models of complex plasmas in density – temperature plane. Here simplified variants of complex plasmas models are considered as a thermodynamically equilibrium ensemble of classical Coulomb particles: a 2‐component electroneutral system of macro‐ and microions (+Z, −1) and a 3‐component electroneutral mixture of macroions and two kinds of microions (+Z, −1, +1). The resulting phase diagram for (+Z,−1) or (−Z,+1) in ln n − ln T plane has a form of a linear combination of crystalline and fluid zones separated by the boundaries Γ = const. Parameters and locations of these zones are analyzed in dependence on macroion charge number Z. There are huge negative pressure and negative compressibility areas in the initial phase diagram if one uses equations of state (Hamaguchi,1997) and (Khrapak, 2014). Thus, questions of thermodynamic stability and an existence of an additional phase transition gas‐liquid are discussed. (© 2016 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Application of double-layered skin phantoms for optical flow imaging during laser tattoo treatments

The feasible application of double-layered skin phantoms was evaluated to identify artificial blood flow with a Doppler optical coherence tomography (DOCT) system for laser tattoo treatments. Polydimethylsiloxane (PDMS) was used to fabricate the artificial phantoms with flow channels embedded. A double-integrating sphere system with an inverse adding-doubling method quantified both the absorption and the reduced scattering coefficients for epidermis and dermis phantoms. Both OCT and caliper measurements confirmed the double-layered phantom structure (epidermis = 136 ± 17 µm vs. dermis = 3.0 ± 0.1 mm). The DOCT method demonstrated that high flow rates were associated with high image contrast, visualizing the position and the shape of the flow channel. Application of the channel-embedded skin phantoms in conjunction with DOCT can be a reliable technique to assess dynamic variations in the blood flow during and after laser tattoo treatments.

Levitation and lateral forces between a point magnetic dipole and a superconducting sphere

The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.

Broadband and wide-angle light harvesting by ultra-thin silicon solar cells with partially embedded dielectric spheres.

We propose a design of crystalline silicon thin-film solar cells (c-Si TFSCs, 2 μm-thick) configured with partially embedded dielectric spheres on the light-injecting side. The intrinsic light trapping and photoconversion are simulated by the complete optoelectronic simulation. It shows that the embedding depth of the spheres provides an effective way to modulate and significantly enhance the optical absorption. Compared to the conventional planar and front sphere systems, the optimized partially embedded sphere design enables a broadband, wide-angle, and strong optical absorption and efficient carrier transportation. Optoelectronic simulation predicts that a 2 μm-thick c-Si TFSC with half-embedded spheres shows an increment of more than 10 mA/cm2 in short-circuit current density and an enhancement ratio of more than 56% in light-conversion efficiency, compared to the conventional planar counterparts.