Temperature dependence in interatomic potentials and an improved potential for Ti

The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic potentials which are used in molecular dynamics, as a model for the forces on a system. These forces should be the derivative of the free energy of the electronic system, which includes contributions from the entropy of the electronic states. This free energy is weakly temperature dependent, and although this can be safely neglected in many cases there are some systems where the electronic entropy plays a significant role. Here a method is proposed to incorporate electronic entropy in the Sommerfeld approximation into empirical potentials. The method is applied as a correction to an existing potential for titanium. Thermal properties of the new model are calculated, and a simple method for fixing the melting point and solid-solid phase transition temperature for existing models fitted to zero temperature data is presented.Comment: CCP 201

Two-band second moment model and an interatomic potential for caesium

A semi-empirical formalism is presented for deriving interatomic potentials for materials such as caesium or cerium which exhibit volume collapse phase transitions. It is based on the Finnis-Sinclair second moment tight binding approach, but incorporates two independent bands on each atom. The potential is cast in a form suitable for large-scale molecular dynamics, the computational cost being the evaluation of short ranged pair potentials. Parameters for a model potential for caesium are derived and tested

Origin of complex crystal structures of elements at pressure

We present a unifying theory for the observed complex structures of the sp-bonded elements under pressure based on nearly free electron picture (NFE). In the intermediate pressure regime the dominant contribution to crystal structure arises from Fermi-surface Brillouin zone (FSBZ) interactions - structures which allow this are favoured. This simple theory explains the observed crystal structures, transport properties, the evolution of internal and unit cell parameters with pressure. We illustrate it with experimental data for these elements and ab initio calculation for Li.Comment: 4 pages 5 figure

Total energy calculation of high pressure selenium: The origin of incommensurate modulations in Se-IV and the instability of proposed Se-II

We present calculation of the high pressure crystal structures in selenium, including rational approximants to the recently reported incommensurate phases. We show how the incommensurate phases can be intuitively explained in terms of imaginary phonon frequencies arising from Kohn anomalies in the putative undistorted phase. We also find inconsistencies between the calculated and experimental Se-II phase - the calculations show it to be a metastable metal while the experiment finds a stable semiconductor. We propose that the experimentally reported structure is probably in error.Comment: 4 pages 4 figure

Effect of Cluster Formation on Isospin Asymmetry in the Liquid-Gas Phase Transition Region

Nuclear matter within the liquid-gas phase transition region is investigated in a mean-field two-component Fermi-gas model. Following largely analytic considerations, it is shown that: (1) Due to density dependence of asymmetry energy, some of the neutron excess from the high-density phase could be expelled into the low-density region. (2) Formation of clusters in the gas phase tends to counteract this trend, making the gas phase more liquid-like and reducing the asymmetry in the gas phase. Flow of asymmetry between the spectator and midrapidity region in reactions is discussed and a possible inversion of the flow direction is indicated.Comment: 9 pages,3 figures, RevTe

The Relationship Between Stride Rates, Lengths and Body Size and their Affect on Elite Triathletes’ Running Performance During Competition

Previous research has suggested that a degree of predictability exists in the relationship between self-selected running stride rates (SR) and stride lengths (SL) with measures of body size such as mass, height and limb lengths. Significant correlations have also been revealed between these body size measures and performance and between SL and performance. However, there is also evidence to suggest that triathlon performance may be related to maintaining a longer SL during the final run. Hence, the aim of this investigation was to examine whether there was any relationship between SR and SL, with body masses and heights of senior elite triathletes during the run stage of a triathlon. The SRs and SLs of 37 male senior elite Triathlon World Championships competitors were analysed via videography and Video Expert II Coach. These values were correlated with the athletes’ body masses and heights (p\u3c0.01). The results indicated a limited relationship between height and mass with SR in the early stages of the run. However, a significant, positive correlation existed between SL and height at all points from 3 km to the end of the run. Those triathletes who were taller used longer strides. Further research is warranted to examine the effects of cycling on the subsequent run discipline during triathlon and if body size and shape of triathletes have evolved as the young sport of triathlon develops

Cadence, Stride Rate and Stride Length During Triathlon Competition

Triathlon research shows cycling alters the physiological response of subsequent running but, at present, biomechanical changes are unresolved. This study examined cycling cadence and running stride rate (SR) and length (SL) used by senior elite triathletes during competition. These variables were then compared to running and triathlon performance. Data from 51 elite male World Championships triathletes were analysed via video recordings and Video Expert II Coach. Triathletes revealed consistent cadences throughout the majority of the cycle (96.8 +2.7 rpm) and run (90.9 +2.4 rpm) disciplines. However, a cadence increase (99.6 +5.7 rpm) was recorded at the completion of the cycle prior to running. Running SR and SL was significantly lower at the end of the run indicating a level of fatigue (p\u3c0.01). Running SL was significantly and positively correlated with running and triathlon performance (p\u3c0.01) suggesting those that could maintain a longer SL had a faster run and better final finishing position

Strategy bifurcation and spatial inhomogeneity in a simple model of competing sellers

We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition to ``cheap'' sellers pricing to cover their costs, ``expensive'' sellers spontaneously appear to exploit short-term favorable situations. These expensive sellers ``speciate'' into discrete price bands. As well as variety in pricing strategy, the ``cheap'' sellers evolve a strongly correlated spatial structure, which in turn creates niches for their expensive competitors. Thus an entire ecosystem of coexisting, discrete, symmetry-breaking strategies arises.Comment: 6 pages, 6 figures, epl2; 1 new figure, include nash equilibrium analysis, typo fixe