Repulsive Core Research Articles

Sacred Violence: Girard, Bataille and the Vicissitudes of Human Desire

The article deals with two famous attempts to analyse the relationship between affective violence and the sacred, namely those made by René Girard and Georges Bataille. Despite the apparent similarities of the problems (religious sacrifice as the affective foundation of community and the primordial role of violence therein) Girard and Bataille end up with profoundly different visions of society's entire affective economy. For Girard, religious sacrifice is a mechanism of projection and of repression by means of which the society channels its own unmotivated violence to one arbitrarily chosen individual (a classical functionalist approach); for Bataille, sacrifice is a means of sharing the experience of death which constitutes the repulsive core of the human community (a more phenomenological approach). The article shows that these differences can be traced back to two different (theoretical) sources. The first one is Durkheim's theory of the sacred, particularly his vision of the ‘collective turmoil’ as the origin of society and his interpretation of the ‘ambivalence of the sacred’. The second one is Alexandre Kojève's anthropological interpretation of Hegel, especially his theory of human desire, which has clearly influenced both theorists although they both criticise it (albeit in different fashions). What Girard and Bataille seem to propose us, are two different and even opposing models regarding both the conceptualisation of human ‘desire’ and the theoretical/methodological approach we should adopt when dealing with it.

Modelling the depuration rates of polychlorinated biphenyls in Oncorhynchus mykiss with quantum chemical descriptors

Using quantum chemical descriptors and partial least squares regression, a quantitative structure–activity relationship (QSAR) model is developed for the depuration rate constants (log k d) of 62 polychlorinated biphenyls (PCBs) in juvenile rainbow trout (Oncorhynchus mykiss). The values of the cross-validated regression coefficient () and standard deviation (SD) are 0.655 and 0.05, respectively. The high cross-validated coefficient and low standard deviation indicate that the QSAR model is well predictive. In the QSAR model, the following six descriptors are highly significant: (the most positive charge of a hydrogen atom), HOF (standard heat of formation), CCR (core–core repulsion), EE (electronic energy), α2 (squared average molecular polarisability), and S (molecular surface area). The significant descriptors show that the depuration of PCBs in rainbow trout may be mainly attributed to the biota–water partitioning process, and the reactive activity of PCB molecules may play a subordinate role.

The nuclear force from Monte Carlo simulations of lattice quantum chromodynamics

The nuclear force acting between protons and neutrons is studied in the Monte Carlo simulations of the fundamental theory of strong interaction, the quantum chromodynamics defined on the hypercubic space–time lattice. After a brief summary of the empirical nucleon–nucleon (NN) potentials that can fit the NN scattering experiments in high precision, we outline the basic formulation for deriving the potential between the extended objects such as the nucleons composed of quarks. The equal-time Bethe–Salpeter (BS) amplitude is a key ingredient for defining the NN potential on the lattice. We show the results of the numerical simulations on a 324 lattice with lattice spacing a≃0.137 fm (lattice volume (4.4 fm)4) in the quenched approximation. The calculation was carried out using the massively parallel computer Blue Gene/L at the High Energy Accelerator Research Organization (KEK). We found that the calculated NN potential at low energy has the basic features expected from the empirical NN potentials: attraction at long and medium distances, and the repulsive core at short distances. Various future directions along this line of research are also summarized.

Calculation of the two-body scattering K-matrix in configuration space by an adaptive spectral method

A spectral integral method (IEM) for solving the two-body, one-variable Lippmann–Schwinger equation for the wavefunction in configuration space is generalized to the case of the two-variable scattering K-matrix. The main difficulty is that in this case the driving term of the integral equation is discontinuous. It is found that the desirable features of the IEM, such as the economy of mesh points for a given required accuracy, are carried over also to this case even though the result is also discontinuous. The main innovation is a judicious choice of the partitions in coordinate space, plus a new recursion relation forward and backward to the point of discontinuity. For a simple exponential potential an accuracy of 7 significant figures is achieved for the K-matrix, with the number N of Chebyshev support points in each partition equal to 17. For a potential with a large repulsive core, such as the potential between two He atoms, an accuracy of 7 significant figures requires that N is increased to 65 support points per partition.

Structural Properties of a Model System with Effective Interparticle Interaction Potential Applicable in Modeling of Complex Fluids

We report grand canonical ensemble Monte Carlo (MC) simulation and theoretical studies of the structural properties of a model system described by an effective interparticle interaction potential, which incorporates basic interaction terms used in modeling of various complex fluids composed of mesoscopic particles dispersed in a solvent bath. The MC results for the bulk radial distribution function are employed to test the validity of the hard-sphere bridge function in combination with a modified hypernetted chain approximation (MHNC) in closing the Ornstein-Zernike (OZ) integral equation, while the MC data for the density profiles in different inhomogeneous environments are used to assess the validity of the third-order+second-order perturbation density functional theory (DFT). We found satisfactory agreement between the results predicted by the pure theories and simulation data, which classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids. The present investigation indicates that the bridge function approximation and density functional approximation, which are traditionally used for the study of neutral atomic fluids, also perform well for complex fluids only on condition that the underlying effective potentials include a highly repulsive core as an ingredient.

LATTICE QCD SIMULATION OF HYPERON-NUCLEON POTENTIAL

We calculate pΞ0 potentials from the equal-time Bethe-Salpeter amplitude measured in the quenched QCD simulation with the spatial lattice volume, (4.4 fm)3. The standard Wilson gauge action with the gauge coupling β = 5.7 on 324 lattice together with the standard Wilson quark action is used. The hopping parameter κud = 0.1678 is chosen for u and d quarks, which corresponds to mπ ≃ 0.37 GeV . The physical strange quark mass is used by taking the parameter κs = 0.1643 which is deduced from the physical K meson mass. The lattice spacing a = 0.1420 fm is determined by the physical ρ meson mass. We find that the pΞ0 potential has sizable spin dependence. Strong repulsive core is found in 1S0 channel while the effective central potential in the 3S1 channel has relatively weak repulsive core. The potentials also have weak attractive parts in the medium to long distance region (0.6 fm ≲ r ≲ 1.2 fm ) in both of the 1S0 and 3S1 channels.

A SYSTEMATIC STUDY OF THE TENSOR CORRELATION IN He AND Li ISOTOPES

We investigate the tensor correlations in He and Li isotopes systematically. We propose the tensor-optimized shell model (TOSM) to describe the strong tensor correlation arising from the bare nuclear force in nuclei. Using TOSM for Li isotopes, we investigate the anomalous structures of 9,10,11 Li based on the 9 Li +n+n model where the 9 Li cluster is described by TOSM. As a result, the couplings between the tensor correlation in 9 Li and the extra two neutrons emerge Pauli-blocking, which naturally increases the s2 component to develop the halo structure in 11 Li . We further describe the short-range correlation arising from the repulsive core in the bare nuclear force by the unitary correlation operator method (UCOM). We propose the new framework of TOSM+UCOM for the nuclear structure study starting from the bare nuclear force.

LATTICE QCD CALCULATION OF NUCLEAR FORCES

Quenched lattice QCD results of nuclear forces are presented. Inter-nucleon potentials are constructed from Bethe-Salpeter wave functions of two nucleon states by using a Schrödinger-type equation. The results of the central force in 1S0 channel posses the repulsive core at short distance as well as the attraction at medium distance, both of which are enhanced in the light quark mass region. A preliminary result on the tensor force is also presented with the central force in 3S1 channel.

Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation

Grand canonical Monte Carlo simulation and theoretical calculations based on Ornstein-Zernike (OZ) integral equation and third order+second order perturbation density functional theory (DFT) are performed to study a system of spherical particles interacting through a core-softened (CS) potential combining a repulsive square soft core and an attractive square well. Both theoretical predictions and simulation results reveal peculiar homogeneous and inhomogeneous local structures originating from the discontinuous nature of the CS potential. The bulk radial distribution function displays discontinuities at the distances coinciding with the ranges of the successive repulsive and attractive parts in the CS potential function. The density profiles of confined CS fluid show the shapes arising from the complex interplay among the steric effects and the competition between the repulsive and attractive parts of the CS potential. Satisfactory agreement between the theoretical results and simulation data leads to the following conclusions: (i) a modified hypernetted chain approximation combined with a hard sphere bridge function, which has been recently proposed by one of the authors of this study, is sufficiently reliable for the structural studies of CS fluid, and (ii) the third order+second order perturbation DFT, which has proven successful for the study of inhomogeneous structure of model fluids with continuous intermolecular potential function, posses a high adaptability to be applied for various types of interaction potentials and performs well also in the case of discontinuous CS model.

Auxeticity of cubic materials: The role of repulsive core interaction

Possible elastic response of anisotropic materials to uniaxial stretching is discussed. For cubic symmetry regions of different auxetic behavior are indicated and various solid structures located on elastic moduli maps. The elastic properties of two model molecular systems, the Gaussian-core model and soft-sphere solids are investigated. A generic mechanism leading to auxetic behavior in cubic materials is suggested.

Hard-sphere perturbation theory for a model of liquid Ga

Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid.

Universal Short-Range Repulsion in the Baryon System Originating from the Confinement: Approach in String-Junction Model

We show a way to unifiedly understand the origins of the repulsive core of baryon-baryon interaction and the universal repulsion of three-baryon interaction needed to avoid dramatic softening of the equation of state of neutron stars due to hyperon mixing. For this aim we adopt the string-junction model which embodies the essential aspects of the confinement in the baryon system confirmed by recent lattice QCD calculations. Key concept of this study lies in the recognition that baryonic short-range repulsion appears as the latent effect implying the energy necessary for full overlap of baryons, for the confinement to persist at such situation. Numerical results are shown and related problems are discussed.

Resonance states in 16O+16O, 12C+16O, α+16O and α+12C with modified Morse potentials

The resonance states in 16O+16O, 12C+16O, α+16O and α+12C are described using modified Morse potential proposed earlier whose success has already been demonstrated in the case of 12C+12C system. The general validity of such a potential with long range, shallow depth and repulsive soft core determined from the resonance data itself is being examined through the present study of the resonances in the above four systems. In each system, the experimental data of a large number of states have been successfully described with a modified Morse potential. The success points out a common mechanism of the origin of these states, and reaffirms authentically the diatomic-like rotational and vibrational picture of the nuclear molecular resonances proposed previously. The close resemblance between the physics of diatomic molecules and nuclear molecular resonances extending to the level of potential which is Morse type in both the cases — although belong to two different areas of physics — is further strengthened through the present study.

The role of chromatin conformations in diffusional transport of chromatin-binding proteins: Cartesian lattice simulations

In this paper, a lattice model for the diffusional transport of chromatin-binding particles in the interphase cell nucleus is proposed. Sliding effects are studied in dense networks of chromatin fibers created by three different methods: Randomly distributed, noninterconnected obstacles, a random walk chain model with an attractive step potential, and a self-avoiding random walk chain model with a hard repulsive core and attractive surroundings. By comparing a discrete and continuous version of the random walk chain model, we demonstrate that lattice discretization does not alter the diffusion of chromatin-binding particles. The influence of conformational properties of the fiber network on the particle sliding is investigated in detail while varying occupation volume, sliding probability, chain length, and persistence length. It is observed that adjacency of the monomers, the excluded volume effect incorporated in the self-avoiding random walk model, and the persistence length affect the chromatin-binding particle diffusion. It is demonstrated that sliding particles sense local chain structures. When plotting the diffusion coefficient as a function of the accessible volume for diffusing particles, the data fall onto master curves depending on the persistence length. However, once intersegment transfer is involved, chromatin-binding proteins no longer perceive local chain structures.

Green’s function approach to quantum criticality in the anisotropic Kondo necklace model

We have studied the quantum phase transition between the antiferromagnetic and spin liquid phase for the two dimensional anisotropic Kondo-necklace model. The bond operator formalism has been implemented to transform the spin Hamiltonian to a bosonic one. We have used the Green's function approach including a hard core repulsion to find the low energy excitation spectrum of the model. The bosonic excitations become gapless at the quantum critical point where the phase transition from the Kondo singlet state to long range antiferromagnetic order takes place. We have studied the effect of both inter-site (delta) and local (Delta) anisotropies on the critical point and on the critical exponent of the excitation gap in the paramagnetic phase. We have also compared our results with previous bond operator mean field calculations.

Effect of potential shape on the binding energy of the impurity states in nanotube

We analyze the effect of the additional repulsive core on the ground state energy of the off-axis neutral donor in GaAs/Ga1-xAlxAs cylindrical nanotube in the presence of the uniform magnetic field applied along the symmetry axis by using the recently developed fractal dimension method. Curves of the D0 ground state binding energies as a function of the donor distance from the axis and density states with randomly distributed donors show that the additional peaks in the curves of the density of impurity states appear due to the presence of the additional repulsive core in the middle's well. To take into account the mixing of the low lying subbands we express the wave function as a product of the combination of 1s and 2px,y wave functions with an unknown envelope function that depends only on electron–ion separation.

Bound state of the αΛΛΞ0 system

The Faddeev–Yakubovsky equations in configuration space are applied to the study of the four-body system αΛΛΞ comprising three distinct particles. We use the OBE-simulating potential of the NSC97 model for the ΛΞ and ΛΛ interactions. For the Ξα and Λα interactions we use phenomenological potentials. The Faddeev–Yakubovsky equations for the system and its subsystems are numerically solved in s-wave approach by the cluster reduction method. We evaluate the binding energy of the hypothetical multi-strangeness nucleus . We find that the existence of the ground state of this nucleus depends strongly on the behavior of the Ξα potential at small distances. In particular, for a Woods–Saxon type potential having no repulsive core, the system can be bound.

Integrals of the two-bodyTmatrix in configuration space

Integrals of the two-body scattering $T(r,{r}^{\ensuremath{'}})$ matrix over an arbitrary function $\ensuremath{\Phi}({r}^{\ensuremath{'}})$ are carried out in configuration space. The method consists of representing these integrals $\ensuremath{\varphi}(r)$ as the solution of a one-variable Lippmann-Schwinger integral equation, and numerically obtaining the solution by a spectral expansion method that is very similar to a previously developed method [the spectral integral equation method (S-IEM)] for obtaining the wave function of a Schr\"odinger equation. It is found that the desirable features of the S-IEM, such as the economy of mesh points for a given required accuracy, are carried over also to this case. Stability to eight significant figures is achieved in a MATLAB code that takes 1/3 s for its execution, using as a value of ${10}^{\ensuremath{-}8}$ for an inputted tolerance parameter. The importance of correctly treating the repulsive core for the atomic He-He interaction is demonstrated.

Universal Short-Range Repulsion in the Baryon System Originating from the Confinement

We show a way to unifiedly understand the origins of repulsive core in baryon-baryon interaction and universal repulsion in three-baryon interaction, by adopting the string-junction model which embodies the substantial aspects of the confinement in the baryon shown in the recent lattice QCD calculations. Key concept in the study lies in the recognition that short-range repulsion appears as the latent effect implying the energy necessary in order for the confinement mechanism to persist at closest approach of baryons. The short-range three-body repulsion is universal because the effect comes from the color degrees of freedom, and prevents the equation of state from the dramatic softening due to hyperon-mixing in neutron-star matter which otherwise causes contradiction with the observations on the masses of neutron stars.

An Efficient Monte Carlo Algorithm for the Fast Equilibration and Atomistic Simulation of Alkanethiol Self-Assembled Monolayers on a Au(111) Substrate

A new Monte Carlo algorithm is presented for the simulation of atomistically detailed alkanethiol self-assembled monolayers (R-SH) on a Au(111) surface. Built on a set of simpler but also more complex (sometimes nonphysical) moves, the new algorithm is capable of efficiently driving all alkanethiol molecules to the Au(111) surface, thereby leading to full surface coverage, irrespective of the initial setup of the system. This circumvents a significant limitation of previous methods in which the simulations typically started from optimally packed structures on the substrate close to thermal equilibrium. Further, by considering an extended ensemble of configurations each one of which corresponds to a different value of the sulfur-sulfur repulsive core potential, sigmass, and by allowing for configurations to swap between systems characterized by different sigmass values, the new algorithm can adequately simulate model R-SH/Au(111) systems for values of sigmass ranging from 4.25 A corresponding to the Hautman-Klein molecular model (J. Chem. Phys. 1989, 91, 4994; 1990, 93, 7483) to 4.97 A corresponding to the Siepmann-McDonald model (Langmuir 1993, 9, 2351), and practically any chain length. Detailed results are presented quantifying the efficiency and robustness of the new method. Representative simulation data for the dependence of the structural and conformational properties of the formed monolayer on the details of the employed molecular model are reported and discussed; an investigation of the variation of molecular organization and ordering on the Au(111) substrate for three CH3-(CH2)n-SH/Au(111) systems with n=9, 15, and 21 is also included.