A bending-torsion theory for thin and ultrathin rods as a Γ-limit of atomistic models

The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as Γ-limits of 3D atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness h and interatomic distance ε. First, we set up a novel theory for ultrathin rods composed of finitely many atomic fibres (ε∼h), which incorporates surface energy and new discrete terms in the limiting functional. This can be thought of as a contribution to the mechanical modelling of nanowires. Second, we treat the case where ε≪h and recover a nonlinear rod model − the modern version of Kirchhoff's rod theory

A continuum model for brittle nanowires derived from an atomistic description by Γ-convergence

Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity, it is assumed that the rod's thickness is of the same order as the interatomic distance. Fracture energy in the Γ-limit is expressed by an implicit cell formula, which covers different modes of fracture, including (complete) cracks, folds and torsional cracks. In special cases, the cell formula can be significantly simplified. Our approach applies e.g. to atomistic systems with Lennard-Jones-type potentials and is motivated by the research of ceramic nanowires

Factors Controlling Exokarst Morphology and Sediment Transport Through Caves: Comparison of Carbonate and Salt Karst

Zaradi velike topnosti NaCl se v solnem krasu lahko za stalno odlagajo v podzemlju velike količine sedimentov. Tam so posebne kraške oblike, kakršnih ni v karbonatnem krasu: veliki podzemeljski vršaji, notranje jame. Nasprotno pa se v karbonatnem krasu le majhen del sedimentov, ki jih prenaša alohtoni tok, za stalno odloži v jami, saj bi bila sicer jama kmalu zamašena (zaradi zelo slabe topnosti CaCO3 ). Na ozemlju Češke republike so bila z različnih vidikov preučevana tri kraška ozemlja z zelo dolgim razvojem in bistvenimi razlikami med površinskimi in podzemeljskimi oblikami. Avtorja menita, da je le ena bistvena razlika med Moravskim krasom in kraškimi ozemlji z razpršenim napajanjem (Češki in Chýnovski kras): v gostoti in smeri razpok, po katerih prenika kraška voda. Vse ostale razlike v površinskih in podzemeljskih kraških oblikah so nastale zaradi prvotnih razlik in njihovega vpliva na razvoj jam, posebej na prenos sedimentov in na stopnjaste oblike. Na ozemlju, kjer so le batifreatične in globokofreatične jame, se nikoli ne razvijejo slepe doline in druge navadne površinske kraške oblike zaradi zelo počasnega toka v kraških prevodnikih, kar onemogoča prenašanje sedimentov.In salt karst, very large amounts of sediment load could be permanently trapped underground, due to the high solubility of NaCl. Specific karst forms which have no equivalents in carbonate karst, occur there (huge underground alluvial fans, inlet caves). In a carbonate karst, on the other hand, only small portion of sediment carried by an allochthonous stream could be deposited permanently in the cave, otherwise the cave will become clogged (because of the very low solubility of CaCO3). Three carbonate karst areas with long-lasting development and fundamental differences in endokarst and exokarst forms were studied from many different aspects in the Czech Republic. The authors believe that there is only one primary difference between the Moravian Karst and diffuse recharge karst areas (Czech and Chùnov karsts): the frequency and orientation of fissures penetrable by groundwater. All other differences in exokarst and endokarst forms and hydrology are the results of primary difference and its influence on speleogenesis, especially on sediment transport and gradational features. In areas where only bathyphreatic and deep phreatic caves occur, blind valleys and common exokarst morphology never develop, due to the very low velocity of flow in karst conduits, which precludes transport of sediment load

Jan Malíř a kol.: Česká republika v Evropské unii 2004–2009

Recenze publikace - Jan Malíř a kol.: Česká republika v Evropské unii 2004–2009Institucionální a právní aspekty členstv

Nejrychlejší cesta v problému proudění chodců

Práce se zabývá makroskopickým modelem proudění chodců. Ukazuje, jak spolu souvisejí dvě možné definice směru, kterým se chodec za- mýšlí vydat. Jedna z nich je založena na minimalizaci jistého funkcionálu a druhá na eikonálové rovnici. Eikonálová rovnice je odvozena ve dvourozměr- ném prostoru. Při tom je bráno v úvahu to, že výstupní bod nejrychlejší cesty k východu závisí na poloze chodce. Také jsou formulovány nutné podmínky pro to, aby po částech regulární křivka minimalizovala funkcionál v přidru- žené variační úloze s nestandardní Dirichletovou okrajovou podmínkou. 1The work treats a macroscopic pedestrian flow model. It shows the link of two possible definitions of the pedestrians' preferred direction of movement, one based on minimization of a functional, the other using the eikonal equation. The eikonal equation is derived in two dimensions, taking into account that the distant endpoint of the fastest path to the exit depends on the location of the pedestrian under consideration. Also, necessary condi- tions for a piecewise regular curve to be the minimizer of a certain functional in a related two-dimensional variational problem with non-standard Dirichlet boundary condition are formulated. 1Katedra numerické matematikyDepartment of Numerical MathematicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Model víceúrovňového vládnutí a model politických sítí jako prostor a způsob rozvoje současné Evropy aneb Obejdeme se bez války?

It can be concluded that the war isn’t able to develop society (except that we ignore here ethical questions of war of course). Space of development – if we manage to eliminate the war as well as those so-called “low intensity conflicts” – can’t be found in the dimension of territorial expansion, but in the economic contact of different areas and regions. This will be of course require technological progress connected with increasing interdependence of the world. But we aren’t sure, if it is the way how to reach required unity of the human society; with another words, we aren’t sure if a “techné” will be complete in some following steps of cultural evolution with sincere concern about another people, how for example Milan Machovec recommends. We believe in the fact that this is the only way how to win an insurmountable power, which is able to overcome human being’s individualism