The influence of potassium on core and geodynamo evolution

We model the thermal evolution of the core and mantle using a parametrized convection scheme, and calculate the entropy available to drive the geodynamo as a function of time. The cooling of the core is controlled by the rate at which the mantle can remove heat. Rapid core cooling favours the operation of a geodynamo but creates an inner core that is too large; slower cooling reduces the inner core size but makes a geodynamo less likely to operate. Introducing potassium into the core retards inner core growth and provides an additional source of entropy. For our nominal model parameters, a core containing approximate to 400 ppm potassium satisfies the criteria of present-day inner core size, surface heat flux, mantle temperature and cooling rate, and positive core entropy production.We have identified three possibilities that may allow the criteria to be satisfied without potassium in the core. (1) The core thermal conductivity is less than half the generally accepted value of 50 W m(-1) K-1. (2) The core solidus and adiabat are significantly colder and shallower than results from shock experiments and ab initio simulations indicate. (3) The core heat flux has varied by no more than a factor of 2 over Earth history. All models we examined with the correct present-day inner core radius have an inner core age of < 1.5 Gyr; prior to this time the geodynamo was sustained by cooling and radioactive heat production within a completely liquid core

Thermal expansion in small metal clusters and its impact on the electric polarizability

The thermal expansion coefficients of $\mathrm{Na}_{N}$ clusters with $8 \le N \le 40$ and $\mathrm{Al}_{7}$, $\mathrm{Al}_{13}^-$ and $\mathrm{Al}_{14}^-$ are obtained from {\it ab initio} Born-Oppenheimer LDA molecular dynamics. Thermal expansion of small metal clusters is considerably larger than that in the bulk and size-dependent. We demonstrate that the average static electric dipole polarizability of Na clusters depends linearly on the mean interatomic distance and only to a minor extent on the detailed ionic configuration when the overall shape of the electron density is enforced by electronic shell effects. The polarizability is thus a sensitive indicator for thermal expansion. We show that taking this effect into account brings theoretical and experimental polarizabilities into quantitative agreement.Comment: 4 pages, 2 figures, one table. Accepted for publication in Physical Review Letters. References 10 and 23 update

Thermodynamics of Na_8 and Na_{20} clusters studied with ab-initio electronic structure methods

We study the thermodynamics of Na_8 and Na_{20} clusters using multiple-histogram methods and an ab initio treatment of the valence electrons within density functional theory. We consider the influence of various electron kinetic-energy functionals and pseudopotentials on the canonical ionic specific heats. The results for all models we consider show qualitative similarities, but also significant temperature shifts from model to model of peaks and other features in the specific-heat curves. The use of phenomenological pseudopotentials shifts the melting peak substantially (~ 50--100 K) when compared to ab-initio results. It is argued that the choice of a good pseudopotential and use of better electronic kinetic-energy functionals has the potential for performing large time scale and large sized thermodynamical simulations on clusters.Comment: LaTeX file and EPS figures. 24 pages, 13 figures. Submitted to Phys. Rev.

Does the Boltzmann principle need a dynamical correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived [M. Bianucci, R. Mannella, B. J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)] which differs from the one that follows from the Boltzmann principle S = k log (Omega(E)) via the thermodynamic relation 1/T= dS/dE by additional terms of "dynamical" character, which are argued to correct and generalize the Boltzmann principle for small systems (here Omega(E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker-Planck formalism of Bianucci et al. is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the "volume" entropy S = k log (Phi(E)) via the thermodynamic relation above for systems of any number of degrees of freedom (Phi(E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al. and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.Comment: REVTeX 4, 10 pages, 2 figures. Accepted to J. Stat. Phy

On the Temperature Dependence of the Lifetime of Thermally Isolated Metastable Clusters

The temperature dependence of the lifetime of the thermally isolated metastable N8 cubane up to its decay into N2 molecules has been calculated by the molecular dynamics method. It has been demonstrated that this dependence significantly deviates from the Arrhenius law. The applicability of the finite heat bath theory to the description of thermally isolated atomic clusters has been proved using statistical analysis of the results obtained.Comment: 14 pages, 4 figure

FANCD2 re-expression is associated with glioma grade and chemical inhibition of the Fanconi Anaemia pathway sensitises gliomas to chemotherapeutic agents.

Brain tumours kill more children and adults under 40 than any other cancer. Around half of primary brain tumours are glioblastoma multiforme (GBMs) where treatment remains a significant challenge. GBM survival rates have improved little over the last 40 years, thus highlighting an unmet need for the identification/development of novel therapeutic targets and agents to improve GBM treatment. Using archived and fresh glioma tissue, we show that in contrast to normal brain or benign schwannomas GBMs exhibit re-expression of FANCD2, a key protein of the Fanconi Anaemia (FA) DNA repair pathway, and possess an active FA pathway. Importantly, FANCD2 expression levels are strongly associated with tumour grade, revealing a potential exploitable therapeutic window to allow inhibition of the FA pathway in tumour cells, whilst sparing normal brain tissue. Using several small molecule inhibitors of the FA pathway in combination with isogenic FA-proficient/deficient glioma cell lines as well as primary GBM cultures, we demonstrate that inhibition of the FA pathway sensitises gliomas to the chemotherapeutic agents Temozolomide and Carmustine. Our findings therefore provide a strong rationale for the development of novel and potent inhibitors of the FA pathway to improve the treatment of GBMs, which may ultimately impact on patient outcome

Structure and stability of finite gold nanowires

Finite gold nanowires containing less than 1000 atoms are studied using the molecular dynamics simulation method and embedded atom potential. Nanowires with the face-centered cubic structure and the (111) oriented cross-section are prepared at T=0 K. After annealing and quenching the structure and vibrational properties of nanowires are studied at room temperature. Several of these nanowires form multi-walled structures of lasting stability. They consist of concentrical cylindrical sheets and resemble multi-walled carbon nanotubes. Vibrations are investigated by diagonalization of the dynamical matrix. It was found that several percents of vibrational modes are unstable because of uncompleted restructuring of initial fcc nanowires.Comment: 4 figures in gif forma

Taming the rugged energy landscape: Techniques for the production, reordering, and stabilization of selected cluster inherent structures

We report our studies of the potential energy surface (PES) of selected binary Lennard-Jones clusters. The effect of adding selected impurity atoms to a homogeneous cluster is explored. Inherent structures and transition states are found by combination of conjugate-gradient and eigenvector-following methods while the topography of the PES is mapped with the help of a disconnectivity analysis. We show that we can controllably induce new structures as well as reorder and stabilize existing structures that are characteristic of higher-lying minima.Comment: 9 pages, 9 figures, accepted for publication in J. Chem. Phy

Classification of phase transitions in small systems

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transitions in a finite system and to small Ar clusters.Comment: 12 pages, 4 figures, accepted for publication in Phys. Rev. Let

An orbital-free molecular dynamics study of melting in K_20, K_55, K_92, K_142, Rb_55 and Cs_55 clusters

The melting-like transition in potasium clusters K_N, with N=20, 55, 92 and 142, is studied by using an orbital-free density-functional constant-energy molecular dynamics simulation method, and compared to previous theoretical results on the melting-like transition in sodium clusters of the same sizes. Melting in potasium and sodium clusters proceeds in a similar way: a surface melting stage develops upon heating before the homogeneous melting temperature is reached. Premelting effects are nevertheless more important and more easily established in potasium clusters, and the transition regions spread over temperature intervals which are wider than in the case of sodium. For all the sizes considered, the percentage melting temperature reduction when passing from Na to K clusters is substantially larger than in the bulk. Once those two materials have been compared for a number of different cluster sizes, we study the melting-like transition in Rb_55 and Cs_55 clusters and make a comparison with the melting behavior of Na_55 and K_55. As the atomic number increases, the height of the specific heat peaks decreases, their width increases, and the melting temperature decreases as in bulk melting, but in a more pronounced way.Comment: LaTeX file. 6 pages with 17 pictures. Final version with minor change