Von Neumann’s growth model: Statistical mechanics and biological applications

We review recent work on the statistical mechanics of Von Neumann’s growth model and discuss its application to cellular metabolic networks. In this context, we present a detailed analysis of the physiological scenario underlying optimality à la Von Neumann in the metabolism of the bacterium E. coli, showing that optimal solutions are characterized by a considerable microscopic flexibility accompanied by a robust emergent picture for the key physiological functions. This suggests that the ideas behind optimal economic growth in Von Neumann’s model can be helpful in uncovering functional organization principles of cell energetics.     

Quantum mechanics in a two-dimensional spacetime: What is a wavefunction?

Conventional quantum mechanics specifies the mathematical properties of wavefunctions and relates them to physical experiments by invoking the Born postulate. There is no known direct connection between wavefunctions and any external physical object. However, in the case of a two-dimensional spacetime there is a completely classical context for wavefunctions where the connection with an external reality is transparent and unambiguous. By examining this case, we show how a classical stochastic process assembles a Dirac wavefunction based solely on the detailed counting of reversible paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ, including the ubiquitous implication of complex numbers for the latter. The appearance of wavefunctions in a context that is free of the complexities of quantum mechanics suggests the study of such models may shed some light on interpretive issues.     

First-order metal-insulator transitions in manganites: are they universal?

Conductivity data for La(2-2x)Sr(1+2xMn2O7 (x = 0.6) show a first-order transition from an orbital- or charge-ordered insulator to a metal as the temperature falls below approximately 160 K. The change in conductivity is 100 times larger than that seen previously in any single-phase manganite in zero field. The metallic low-temperature state is similar to x = 0.58, but x = 0.58 shows no evidence of orbital or charge order. This result supports a conclusion that strongly coupled magnetic-conductive transitions are first order.     

Is it possible to intervene in the EPRB correlations?

The effect of a quasi-periodic shutter inserted between the source and one of the detectors in a correlated-photon type EPRB experiment is studied. It is shown that the time and polarization correlations are expected to disappear because an intermediate quantized field system is introduced by the shutter between the source field and the detector.     

Statistical Mechanics of Horizontal Gene Transfer in?Evolutionary Ecology

The biological world, especially its majority microbial component, is strongly interacting and may be dominated by collective effects. In this review, we provide a brief introduction for statistical physicists of the way in which living cells communicate genetically through transferred genes, as well as the ways in which they can reorganize their genomes in response to environmental pressure. We discuss how genome evolution can be thought of as related to the physical phenomenon of annealing, and describe the sense in which genomes can be said to exhibit an analogue of information entropy. As a direct application of these ideas, we analyze the variation with ocean depth of transposons in marine microbial genomes, predicting trends that are consistent with recent observations using metagenomic surveys.     

Does color-magnetic interaction induce short-range diquark correlations in the proton?

Color-magnetic interaction with a smearing function found from the fit to the - splitting is strong enough to support a bound state of a single pair. We present some piloting calculations in order to illustrate the eigenenergy dependence on the cutoff parameter for different choices of the smearing function. In the threequark system the spin-spin interaction can lead to the existence of the short-range correlations in each¹ S _o qq subsystem, thereby providing the dynamical mechanism for the quark-diquark picture of the proton.     

Size-topology correlations in disk packings: terminal bidispersity in order–disorder transitions

Abstract

In random packings or tilings, the size distribution of individual elements (domains) and the statistics of numbers of neighbours of those domains are strongly correlated. In the case of circular disks forming a random packing in the plane, it has long been known empirically that a certain critical amount of bidispersity avoids crystallization of the packing. We demonstrate how the formalism of a simplified granocentric model allows for an analytical computation of the size-topology correlation as a function of both size ratio and frequency of small disks. The results, obtained without free parameters, are in excellent agreement with the empirical findings of packing simulations concerning critical (terminal) bidispersity. It is also shown that, at equal size variance, the discrete (bidisperse) disk size distributions induce stronger disorder than continuously polydisperse disks.     

A soft matter in construction – Statistical physics approach to formation and mechanics of C–S–H gels in cement

Calcium-silicate hydrate (C–S–H) is the main binding agent in cement and concrete. It forms at the beginning of cement hydration, it progressively densifies as cement hardens and is ultimately responsible of concrete performances. This hydration product is a cohesive nano-scale gel, whose structure and mechanics are still poorly understood, in spite of its practical importance. Here we review some of the open questions for this fascinating material and a statistical physics approach recently developed, which allows us to investigate the gel formation under the out-of-equilibrium conditions typical of cement hydration and the role of the nano-scale structure in C–S–H mechanics upon hardening. Our approach unveils how some distinctive features of the kinetics of cement hydration can be related to changes in the morphology of the gels and elucidates the role of nano-scale mechanical heterogeneities in the hardened C–S–H.     

Statistical correlations on the BiO surface in Bi2Sr2CaCu2O8−x single crystals

Low temperature scanning tunneling microscope techniques are applied to study statistical properties of the BiO plane in 2212 high-T_c single crystals. The correlation functions of height deviations in x and k -spaces have been numerically obtained. Long range power law correlations have been found and attributed to half lattice cell jumps of known height in the c direction. Analysis of the correlation function in k-space reveals two modulating superstructures in the b direction. The most pronounced structure is the well known superstructure with period a₁ ≈ 27 Å. The other one has period a₂ ≈ 58 Å which is a little more than twice the period of the main superstructure.     

Pure drug nanoparticles in tablets: what are the dissolution limitations?

There has been increasing interests for drug companies to incorporate drug nanoparticles into their existing formulations. However, technical knowledge in this area is still in its infancy and more study needs to be done to stimulate growth in this fledging field. There is a need to scrutinize the performance of pure drug nanoparticles in tablets, particularly relating formulation variables to their dissolution performance. Application of the pure form, synthesized without the use of surfactants or stabilizers, is often preferred to maximize drug loading and also to minimize toxicity. Cefuroxime axetil, a poorly water-soluble cephalosporin antibiotic, was used as the model drug in the formulation development. Drug release rate, tablet disintegration time, tensile strength and energy of failure were predominantly influenced by the amount of super-disintegrant, amount of surfactant, compression force and diluent species, respectively. The compression rate had minimal impact on the responses. The main hurdle confronting the effective use of pure drug nanoparticles in tablets is the difficulty in controlling aggregation in solution, which could potentially be aggravated by the tabletting process. Through the use of elevated levels of surfactants (8 w/w% sodium dodecyl sulphate), drug release from the nanoparticle preparation was enhanced from 58.0 ± 2.7% to 72.3 ± 0.7% in 10 min. Hence, it is recommended that physical formulations for pure drug nanoparticles be focused on the particle de-aggregation step in solution, if much higher rates are to be desired. In conclusion, even though pure drug nanoparticles could be easily synthesized, limitations from aggregation may need to be overcome, before successful application in tablets can be fully realized.     

Forces and currents in carbon nanostructures: are we imaging atoms?

First-principles calculations show that the rich variety of image patterns found in carbon nanostructures with the atomic force and scanning tunneling microscopes can be rationalized in terms of the chemical reactivity of the tip and the distance range explored in the experiments. For weakly reactive tips, the Pauli repulsion dominates the atomic contrast and force maxima are expected on low electronic density positions as the hollow site. With reactive tips, the interaction is strong enough to change locally the hybridization of the carbon atoms, making it possible to observe atomic resolution in both the attractive and the repulsive regime although with inverted contrast. Regarding STM images, we show that in the near-contact regime, due to current saturation, bright spots correspond to hollow positions instead of atomic sites, providing an explanation for the most common hexagonal pattern found in the experiments.     

Heterogeneity in oscillator networks: are smaller worlds easier to synchronize?

Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger. We present numerical computations and analytical estimates on synchronizability of the network in terms of its heterogeneity parameters. Our results suggest that some degree of homogeneity is expected in naturally evolved structures, such as neural networks, where synchronizability is desirable.     

How universal are hydrogen bond correlations? A density functional study of intramolecular hydrogen bonding in low-energy conformers of α-amino acids

Hydrogen bonding is one of the most important and ubiquitous interactions present in Nature. Several studies have attempted to characterise and understand the nature of this very basic interaction. These include both experimental and theoretical investigations of different types of chemical compounds, as well as systems subjected to high pressure. The O–H..O bond is of course the best studied hydrogen bond, and most studies have concentrated on intermolecular hydrogen bonding in solids and liquids. In this paper, we analyse and characterise normal hydrogen bonding of the general type, D–H...A, in intramolecular hydrogen bonding interactions. Using a first-principles density functional theory approach, we investigate low energy conformers of the twenty α-amino acids. Within these conformers, several different types of intramolecular hydrogen bonds are identified. The hydrogen bond within a given conformer occurs between two molecular groups, either both within the backbone itself, or one in the backbone and one in the side chain. In a few conformers, more than one (type of) hydrogen bond is seen to occur.

Interestingly, the strength of the hydrogen bonds in the amino acids spans quite a large range, from weak to strong. The signature of hydrogen bonding in these molecules, as reflected in their theoretical vibrational spectra, is analysed. With the new first-principles data from 51 hydrogen bonds, various parameters relating to the hydrogen bond, such as hydrogen bond length, hydrogen bond angle, bond length and vibrational frequencies are studied. Interestingly, the correlation between these parameters in these bonds is found to be in consonance with those obtained in earlier experimental studies of normal hydrogen bonds on vastly different systems. Our study provides some of the most detailed first-principles support, and the first involving vibrational frequencies, for the universality of hydrogen bond correlations in materials.     

Can the breaking of time-reversal symmetry remove degeneracies in quantum mechanics?

Reduction of spatial symmetry can remove the degeneracy of energy levels in quantum mechanics. The break of time-reversal symmetry by inclusion of a dissipative environment can have a similar effect. The corresponding time-evolution of position and momentum fluctuations can be described by a nonlinear differential equation that can lead to bifurcations and, thus, splitting of energy levels.     

Statistical properties of excited nuclei in the mass range 47 ? A ? 59

Level densities and their energy dependences for nuclei in the mass range of 47 ?? A ?? 59 were determined from the results obtained by measuring neutron-evaporation spectra in respective (p, n) reactions. The spectra of neutrons originating from the (p, n) reactions on ⁴⁷Ti, ⁴⁸Ti, ⁴⁹Ti, ⁵³Cr, ⁵⁴Cr, ⁵⁷Fe, and ⁵⁹Co nuclei were measured in the proton-energy range of 7?C11 MeV. These measurements were performed with the aid of a fast-neutron spectrometer by the time-of-flight method over the base of the EGP-15 pulsed tandem accelerator installed at the Institute for Physics and Power Engineering (Obninsk, Russia). A high resolution of the spectrometer and its stability in the time of flight made it possible to identify reliably discrete low-lying levels along with the continuum part of neutron spectra. Our measured data were analyzed within the statistical equilibrium and preequilibrium models of nuclear reactions. The respective calculations were performed with the aid of the Hauser-Feshbach formalismof statistical theory supplemented with the generalized model of a superfluid nucleus, the back-shifted Fermi gas model, and the Gilbert-Cameron composite formula for nuclear level densities. Nuclear level densities for ⁴⁷V, ⁴⁸V, ⁴⁹V, ⁵³Mn, ⁵⁴Mn, ⁵⁷Co, and ⁵⁹Ni and their energy dependences were determined. The results are discussed and compared with available experimental data and with recommendations of model-based systematics.     

What are spin currents in Heisenberg magnets?

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive current operator in the plane spanned by the local order parameters and is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.Received: 1 September 2004, Published online: 5 November 2004PACS: 75.10.Jm Quantized spin models - 75.10.Pq Spin chain models - 75.30.Ds Spin waves - 73.23.Ra Persistent currents