Stochastic lattice model describing a vector-borne disease

We employ the approach of stochastic dynamics to describe the dissemination of vector-borne diseases such as dengue, and we focus our attention on the characterization of the threshold of the epidemic. The coexistence space comprises two representative spatial structures for both human and mosquito populations. The human population has its evolution described by a process that is similar to the Susceptible-Infected-Recovered (SIR) dynamics. The population of mosquitoes follows a dynamic of the type of the Susceptible Infected-Susceptible (SIS) model. The coexistence space is a bipartite lattice constituted by two structures representing the human and mosquito populations. We develop a truncation scheme to solve the evolution equations for the densities and the two-site correlations from which we get the threshold of the disease and the reproductive ratio. We present a precise deØnition of the reproductive ratio which reveals the importance of the correlations developed in the early stage of the disease. According to our deØnition, the reproductive rate is directed related to the conditional probability of the occurrence of a susceptible human (mosquito) given the presence in the neighborhood of an infected mosquito (human). The threshold of the epidemic as well as the phase transition between the epidemic and the non-epidemic states are also obtained by performing Monte Carlo simulations. References: [1] David R. de Souza, T^ania Tom∂e, , Suani R. T. Pinho, Florisneide R. Barreto and M∂ario J. de Oliveira, Phys. Rev. E 87, 012709 (2013). [2] D. R. de Souza, T. Tom∂e and R. M. ZiÆ, J. Stat. Mech. P03006 (2011).

Theoretical Study of the Absorption Spectra of Photosynthetic Pigments

The first stage of the photosynthetic process is the extraordinary efficiency of sunlight absorption in the visible region [1]. This region corresponds to the maximum of the spectral radiance of the solar emission. The efficient absorption of visible light is one of the most important characteristics of photosynthetic pigments. In chlorophylls, for example, the absorptions are seen as a strong absorption in the region 400-450 nm in connection with other absorptions with small intensities in the region of 500-600 nm. This work aims at understanding the essential features of the absorption spectrum of photosynthetic pigments, in line with several theoretical studies in the literature [2, 3]. The absorption spectra were calculated for H2-Porphyrin, Mg-Porphyrin, and Zn-Porphyrin, and for H2-Phthalocyanine and Mg-Phthalocyanine with and without the four peripheral eugenol substituents. The geometries were optimized using the B3LYP/6-31+G(d) theoretical model. For the calculation of the absorption spectra different TD-DFT calculations were performed (B3LYP, CAM-B3LYP, O3LYP, M06-2X and BP86) along with CIS (D). For the spectra the basis set 6-311++G (d, p) was used for porphyrins and 6-31+G (d) was used for the other systems. At this stage the solvent effects were considered using the simplified continuum model (PCM). First a comparison between the results using the different methods was made. For the porphyrins the best results compared to experiment (both in position and intensities) are obtained with M06-2X and CIS (D). We also analyze the compatibility of the four-orbital model of Gouterman [4] that states that transitions could be well described by the HOMO-1, HOMO, LUMO, and LUMO+1 molecular orbitals. Our results for H2-Porphyrin shows an agreement with other theoretical results and experimental data [5]. For the phthalocyanines (including the four peripheral eugenol substituents) the results are also in good agreement compared with the experimental results given in ref [6]. Finally, the results show that the inclusion of solvent eÆects gives corrections for the spectral shift in the correct direction but numerically small. References [1] R.E. Blankenship; “Molecular Mechanisms of Photosynthesis", Blackwell Science (2002). [2] P. Jaramillo, K. Coutinho, B.J.C. Cabral and S. Canuto; Chem. Phys. Lett., 516, 250(2011). [3] L. Petit, A. Quartarolo, C. Adamo and N. Russo; J. Phys. Chem. B, 110, 2398(2006). [4] M. J. Gouterman; Mol. Spectr., 6, 138(1961). [5] M. Palummo, C. Hogan, F. Sottile, P. Bagal∂a and A. Rubio; J. Chem. Phys., 131, 084102(2009). [6] E. Agar, S. Sasmaz and A. Agar; Turk. J. Chem., 23, 131(1999).

Electron collisions with the HCOOH...(H2O)n (n=1, 2 and 3) complexes in liquid phase: the influence on the π* shape resonance of formic acid

In this conference we report cross sections for elastic collisions of low-energy electrons with the HCOOH…(H2O)n complexes, with n = 1, 2 and 3. The scattering cross sections were computed with the Schwinger multichannel method [K. Takatsuka and V. McKoy, Phys. Rev. A 24 , 2473 (1981); Phys. Rev. A 30 , 1734 (1984)] with pseudopotentials [M. H. F. Bettega, L. G. Ferreira, and M. A. P. Lima, Phys. Rev. A 47, 1111 (1993)] in the static-exchange and static-exchange plus polarization approximations, for energies from 0.5 eV to 6 eV. We considered some diÆerent hydrogen-bonded structures for the complexes that were generated with classical Monte Carlo simulations [K. Coutinho and S. Canuto, J. Chem. Phys. 113, 9132, (2000)]. The aim of this work is to investigate the effect of the surrounding water molecules on the π* shape resonance of the solute. Previous theoretical and experimental studies carried out in the gas phase reported a π* state for HCOOH at around 1.9 eV. For the n = 1 case and for all complexes, the stabilization of the resonance was observed (it appears at lower energy compared to the value obtained in the gas phase), as reported previously for the CH2O…H2O complexes [T. C. Freitas, M. A. P. Lima, S. Canuto, and M. H. F. Bettega, Phys. Rev. A 80, 062710 (2009)]. This result indicates that the presence of the solvent may affect the processes related to the π* state, such as the molecular dissociation by electron impact. For the n = 2 case we have observed both stabilization and destabilization of the π* resonance, that is associated with the hydrogen bond donor or acceptor role of the water molecules in the complexes. For the n = 3 case, preliminary static-exchange results show the stabilization of the π* state. We propose an explanation of the stabilization/destabilization of the π* state in terms of the polarization of the solute due to the surrounding water molecules and the net charge in the solute.

Applying many-body expansion aiming to make ab in initio molecular dynamics more efficient

In this present work we present a methodology that aims to apply the many-body expansion to decrease the computational cost of ab initio molecular dynamics, keeping acceptable accuracy on the results. We implemented this methodology in a program which we called ManBo. In the many-body expansion approach, we partitioned the total energy E of the system in contributions of one body, two bodies, three bodies, etc., until the contribution of the Nth body [1-3]: E = E1 + E2 + E3 + …EN. The E1 term is the sum of the internal energy of the molecules; the term E2 is the energy due to interaction between all pairs of molecules; E3 is the energy due to interaction between all trios of molecules; and so on. In Manbo we chose to truncate the expansion in the contribution of two or three bodies, both for the calculation of the energy and for the calculation of the atomic forces. In order to partially include the many-body interactions neglected when we truncate the expansion, we can include an electrostatic embedding in the electronic structure calculations, instead of considering the monomers, pairs and trios as isolated molecules in space. In simulations we made we chose to simulate water molecules, and use the Gaussian 09 as external program to calculate the atomic forces and energy of the system, as well as reference program for analyzing the accuracy of the results obtained with the ManBo. The results show that the use of the many-body expansion seems to be an interesting approach for reducing the still prohibitive computational cost of ab initio molecular dynamics. The errors introduced on atomic forces in applying such methodology are very small. The inclusion of an embedding electrostatic seems to be a good solution for improving the results with only a small increase in simulation time. As we increase the level of calculation, the simulation time of ManBo tends to largely decrease in relation to a conventional BOMD simulation of Gaussian, due to better scalability of the methodology presented. References [1] E. E. Dahlke and D. G. Truhlar; J. Chem. Theory Comput., 3, 46 (2007). [2] E. E. Dahlke and D. G. Truhlar; J. Chem. Theory Comput., 4, 1 (2008). [3] R. Rivelino, P. Chaudhuri and S. Canuto; J. Chem. Phys., 118, 10593 (2003).

A stochastic spatially structured epidemic model with diffusive processes

We developed a stochastic lattice model to describe the vector-borne disease (like yellow fever or dengue). The model is spatially structured and its dynamical rules take into account the diffusion of vectors. We consider a bipartite lattice, forming a sub-lattice of human and another occupied by mosquitoes. At each site of lattice we associate a stochastic variable that describes the occupation and the health state of a single individual (mosquito or human). The process of disease transmission in the human population follows a similar dynamic of the Susceptible-Infected-Recovered model (SIR), while the disease transmission in the mosquito population has an analogous dynamic of the Susceptible-Infected-Susceptible model (SIS) with mosquitos diffusion. The occurrence of an epidemic is directly related to the conditional probability of occurrence of infected mosquitoes (human) in the presence of susceptible human (mosquitoes) on neighborhood. The probability of diffusion of mosquitoes can facilitate the formation of pairs Susceptible-Infected enabling an increase in the size of the epidemic. Using an asynchronous dynamic update, we study the disease transmission in a population initially formed by susceptible individuals due to the introduction of a single mosquito (human) infected. We find that this model exhibits a continuous phase transition related to the existence or non-existence of an epidemic. By means of mean field approximations and Monte Carlo simulations we investigate the epidemic threshold and the phase diagram in terms of the diffusion probability and the infection probability.

A theoretical study of the characterization and the absorption spectrum of Mg: Tetracycline complexes in aqueous environment.

The complex formed by the tetracycline (TC) molecule with the Mg ion is able to prevent the replication of the genetic material in the bacterial ribosome, making an excellent antibiotic. In general, the absorption and emission spectra of TC are very sensitive to the host ions and the pH of the solvent that the set is immersed. However, the theoretical absorption spectrum available in the literature is scarce and limited to simple models that do not consider the fluctuations of the liquid. Our aim is to obtain the electronic absorption spectrum of TC and the complex Mg:TC in the ratio 1:1 and 2:1. Moreover, we analyze the changes in intensity and shifts of the bands in the systems listed. We performed the simulation using the classical Monte Carlo technique with the Lennard-Jones plus Coulomb potential applied to each atom of the both TC molecule and the Mg:TC complexes in water. The electronic absorption spectrum was obtained from the time-dependent density functional theory using different solvent models. In general, we obtained a good qualitative description of the spectra when compared with the experimental results. The Mg atom shifts the first band by 4 nm in our models, in excellent agreement to the experimental result of 4 nm. The second absorption band is found here to be useful for the characterization of the position where the ion attaches to the TC.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

Anomalous diffusion evidenced by particle tracking at high frame rates.

Diffusion is a common phenomenon in nature and generally is associated with a system trying to reach a local or a global equilibrium state, as a result of highly irregular individual particle motion. Therefore it is of fundamental importance in physics, chemistry and biology. Particle tracking in complex fluids can reveal important characteristics of its properties. In living cells, we coat the microbead with a peptide (RGD) that binds to integrin receptors at the plasma membrane, which connects to the CSK. This procedure is based on the hypothesis that the microsphere can move only if the structure where it is attached move as well. Then, the observed trajectory of microbeads is a probe of the cytoskeleton (CSK), which is governed by several factors, including thermal diffusion, pressure gradients, and molecular motors. The possibility of separating the trajectories into passive and active diffusion may give information about the viscoelasticity of the cell structure and molecular motors activity. And also we could analyze the motion via generalized Stokes-Einstein relation, avoiding the use of any active techniques. Usually a 12 to 16 Frames Per Second (FPS) system is used to track the microbeads in cell for about 5 minutes. Several factors make this FPS limitation: camera computer communication, light, computer speed for online analysis among others. Here we used a high quality camera and our own software, developed in C++ and Linux, to reach high FPS. Measurements were conducted with samples for 10£ and 20£ objectives. We performed sequentially images with different intervals, all with 2 ¹s exposure. The sequences of intervals are in milliseconds: 4 5 ms (maximum speed) 14, 25, 50 and 100 FPS. Our preliminary results highlight the difference between passive and active diffusion, since the passive diffusion is represented by a Gaussian in the distribution of displacements of the center of mass of individual beads between consecutive frames. However, the active process, or anomalous diffusion, shows as long tails in the distribution of displacements.

Comparison of physical properties of two exogenous surfactants: new parameter.

The pulmonary surfactant has essential physical properties for normal lung function. The most important property is the surface tension. In this work, it was evaluated the surface tension of two commercial exogenous surfactants used in surfactant replacement therapy, poractant alfa (Curosurf, Chiesi Farmaceuticals, Italy) and beractant (Survanta, Abbott Laboratories, USA) using new parameters. A Langmuir film balance (Minitrough, KSV Instruments, Finland) was used to measure surface tension of poractant alfa and beractant samples. For both samples, we prepared a solution of 1 mg/m dissolved in chloroform (100π`), which was applied over a subphase of milli-Q water (175 ml) in the chamber of the balance. The chamber has two moving barriers that can change its surface area between a maximal value of 112.5 cm 2 , and a minimal value of 22.5 cm 2, defining a balance cycle. Each surfactant had its surface tension evaluated during 20 balance cycles for three times. Four quantities were calculated from the experiment: Minimum Surface Tension (MTS), defined as the surface tension at minimal surface area during the first cycle; Mean Work Cycle (MWC), defined as the mean hysteresis area of the measured surface tension curve of the last 16 balance cycles; Critical Active Surface Area in Compression (CASAC) or in Expansion (CASAE), defined as the maximal chamber area where the surfactant is active on the surface in compression or expansion. The t-test was applied to verify for statistical significance of the results. Comproved with the MST is the same reported in literature, the differences between MWC, CASAC, and CASAE were statistically significant (p<0.001). The MWC, CASAC and CASAE were higher for poractant alfa than for beractant. A higher MWC for poractant alfa means higher elastic recoil of the lung in comparison with beractant. Using a different methodology, our results showed that poractant alfa is probably more effective in a surfactant replacement therapy than beractant due the use of poractant alfa in relation to the use of beractant in preterm infants with Respiratory Distress Syndrome (RDS).

Dissociative electron attachment to chloromethane.

A low energy electron may attach to a molecule, forming a metastable resonance, which may dissociate into a stable anion and a neutral radical. Chloromethane has been a good target for dissociative electron attachment studies, since it is a small molecule with a clear dissociative ‘sigma*’ shape resonance. We present potential energy curves for CH3Cl and its anion, as a function of the C-Cl distance. Due to the resonant nature of the anion, a correct description requires a treatment based on scattering calculations. In order to compute elastic cross sections and phase shifts we employed the Schwinger multichannel method, implemented with pseudopotentials of Bachelet, Hamann and Schlüter, at the static-exchange plus polarization approximation. At the equilibrium geometry, the resonance was found arround 3.3 eV, in accordance to experience. The incoming electron is captured by a ‘sigma*’ orbital located at the C-Cl bond, which will relax in the presence of this extra electron. We took this bond as the reaction coordinate, and performed several scattering calculations for a series of nuclear conformations. The phase shift obtained in each calculation was fitted by a two component function, consisting in the usual Breit-Wigner profile, which captures the resonant character, and a second order polynomial in the wave number, which accounts for the background contribution. That way, we obtained position and width of the resonance, which allowed us to build the potential energy curve. For larger distances, the anion becomes stable and usual electronic structure calculations suffice. Furthermore, the existence of a dipole-bound anion state is revealed when we employed a set of very diffuse functions. The knowledge on the behaviour of the neutral and anionic electronic states helps us in elucidating how the dissociation takes place.

Fourier´s law from a chain of coupled anharmonic oscillators under energy conserving shot noise.

We analyze the transport of heat along a chain of particles interacting through anharmonic potentials consisting of quartic terms in addition to harmonic quadratic terms and subject to heat reservoirs at its ends. Each particle is also subject to an impulsive shot noise with exponentially distributed waiting times whose effect is to change the sign of its velocity, thus conserving the energy of the chain. We show that the introduction of this energy conserving stochastic noise leads to Fourier's law. That is for large system size L the heat current J behaves as J ‘approximately’ 1/L, which amounts to say that the conductivity k is constant. The conductivity is related to the current by J = kΔT/L, where ΔT is the difference in the temperatures of the reservoirs. The behavior of heat conductivity k for small intensities¸ of the shot noise and large system sizes L are obtained by assuming a scaling behavior of the type k = ‘L POT a Psi’(L’lambda POT a/b’) where a and b are scaling exponents. For the pure harmonic case a = b = 1, characterizing a ballistic conduction of heat when the shot noise is absent. For the anharmonic case we found values for the exponents a and b smaller then 1 and thus consistent with a superdiffusive conduction of heat without the shot noise. We also show that the heat conductivity is not constant but is an increasing function of temperature.

Heat conduction in a chain of harmonic and anharmonic oscillators under the presence of an energy conserving noise

Reproducing Fourier's law of heat conduction from a microscopic stochastic model is a long standing challenge in statistical physics. As was shown by Rieder, Lebowitz and Lieb many years ago, a chain of harmonically coupled oscillators connected to two heat baths at different temperatures does not reproduce the diffusive behaviour of Fourier's law, but instead a ballistic one with an infinite thermal conductivity. Since then, there has been a substantial effort from the scientific community in identifying the key mechanism necessary to reproduce such diffusivity, which usually revolved around anharmonicity and the effect of impurities. Recently, it was shown by Dhar, Venkateshan and Lebowitz that Fourier's law can be recovered by introducing an energy conserving noise, whose role is to simulate the elastic collisions between the atoms and other microscopic degrees of freedom, which one would expect to be present in a real solid. For a one-dimensional chain this is accomplished numerically by randomly flipping - under the framework of a Poisson process with a variable “rate of collisions" - the sign of the velocity of an oscillator. In this poster we present Langevin simulations of a one-dimensional chain of oscillators coupled to two heat baths at different temperatures. We consider both harmonic and anharmonic (quartic) interactions, which are studied with and without the energy conserving noise. With these results we are able to map in detail how the heat conductivity k is influenced by both anharmonicity and the energy conserving noise. We also present a detailed analysis of the behaviour of k as a function of the size of the system and the rate of collisions, which includes a finite-size scaling method that enables us to extract the relevant critical exponents. Finally, we show that for harmonic chains, k is independent of temperature, both with and without the noise. Conversely, for anharmonic chains we find that k increases roughly linearly with the temperature of a given reservoir, while keeping the temperature difference fixed.

Irreversibility by competition on a Glauber-Ising model by means of the entropy production.

An out of equilibrium Ising model subjected to an irreversible dynamics is analyzed by means of a stochastic dynamics, on a effort that aims to understand the observed critical behavior as consequence of the intrinsic microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model with inversion symmetry and under the influence of two competing Glauber dynamics, intended to describe the stationary states using the entropy production, which characterize the system behavior and clarifies its reversibility conditions. Thus, it is considered a square lattice formed by two sublattices interconnected, each one of which is in contact with a heat bath at different temperature from the other. Analytical and numerical treatments are faced, using mean-field approximations and Monte Carlo simulations. For the one dimensional model exact results for the entropy production were obtained, though in this case the phase transition that takes place in the two dimensional counterpart is not observed, fact which is in accordance with the behavior shared by lattice models presenting inversion symmetry. Results found for the stationary state show a critical behavior of the same class as the equilibrium Ising model with a phase transition of the second order, which is evidenced by a divergence with an exponent µ ¼ 0:003 of the entropy production derivative.

Mechanical Alterations in airway smooth muscle after interaction with indoor pollutant – A mathematical model.

The viscoelasticity of mammalian lung is determined by the mechanical properties and structural regulation of the airway smooth muscle (ASM). The exposure to polluted air may deteriorate these properties with harmful consequences to individual health. Formaldehyde (FA) is an important indoor pollutant found among volatile organic compounds. This pollutant permeates through the smooth muscle tissue forming covalent bonds between proteins in the extracellular matrix and intracellular protein structure changing mechanical properties of ASM and inducing asthma symptoms, such as airway hyperresponsiveness, even at low concentrations. In the experimental scenario, the mechanical effect of FA is the stiffening of the tissue, but the mechanism behind this effect is not fully understood. Thus, the aim of this study is to reproduce the mechanical behavior of the ASM, such as contraction and stretching, under FA action or not. For this, it was created a two-dimensional viscoelastic network model based on Voronoi tessellation solved using Runge-Kutta method of fourth order. The equilibrium configuration was reached when the forces in different parts of the network were equal. This model simulates the mechanical behavior of ASM through of a network of dashpots and springs. This dashpot-spring mechanical coupling mimics the composition of the actomyosin machinery of ASM through the contraction of springs to a minimum length. We hypothesized that formation of covalent bonds, due to the FA action, can be represented in the model by a simple change in the elastic constant of the springs, while the action of methacholine (MCh) reduce the equilibrium length of the spring. A sigmoid curve of tension as a function of MCh doses was obtained, showing increased tension when the muscle strip was exposed to FA. Our simulations suggest that FA, at a concentration of 0.1 ppm, can affect the elastic properties of the smooth muscle ¯bers by a factor of 120%. We also analyze the dynamic mechanical properties, observing the viscous and elastic behavior of the network. Finally, the proposed model, although simple, incorporates the phenomenology of both MCh and FA and reproduces experimental results observed with in vitro exposure of smooth muscle to FA. Thus, this new mechanical approach incorporates several well know features of the contractile system of the cells in a tissue level model. The model can also be used in different biological scales.

Model for the Dynamics of the Cytoskeleton.

Particle tracking of microbeads attached to the cytoskeleton (CSK) reveals an intermittent dynamic. The mean squared displacement (MSD) is subdiffusive for small Δt and superdiffusive for large Δt, which are associated with periods of traps and periods of jumps respectively. The analysis of the displacements has shown a non-Gaussian behavior, what is indicative of an active motion, classifying the cells as a far from equilibrium material. Using Langevin dynamics, we reconstruct the dynamic of the CSK. The model is based on the bundles of actin filaments that link themself with the bead RGD coating, trapping it in an harmonic potential. We consider a one- dimensional motion of a particle, neglecting inertial effects (over-damped Langevin dynamics). The resultant force is decomposed in friction force, elastic force and random force, which is used as white noise representing the effect due to molecular agitation. These description until now shows a static situation where the bead performed a random walk in an elastic potential. In order to modeling the active remodeling of the CSK, we vary the equilibrium position of the potential. Inserting a motion in the well center, we change the equilibrium position linearly with time with constant velocity. The result found exhibits a MSD versus time ’tau’ with three regimes. The first regime is when ‘tau’ < ‘tau IND 0’, where ‘tau IND 0’ is the relaxation time, representing the thermal motion. At this regime the particle can diffuse freely. The second regime is a plateau, ‘tau IND 0’ < ‘tau’ < ‘tau IND 1’, representing the particle caged in the potential. Here, ‘tau IND 1’ is a characteristic time that limit the confinement period. And the third regime, ‘tau’ > ‘tau IND 1’, is when the particles are in the superdiffusive behavior. This is where most of the experiments are performed, under 20 frames per second (FPS), thus there is no experimental evidence that support the first regime. We are currently performing experiments with high frequency, up to 100 FPS, attempting to visualize this diffusive behavior. Beside the first regime, our simple model can reproduce MSD curves similar to what has been found experimentally, which can be helpful to understanding CSK structure and properties.