Standing and travelling waves in cylindrical Rayleigh-Benard convection

The Boussinesq equations for Rayleigh-Benard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25,000, the axisymmetric flow becomes unstable to standing or travelling azimuthal waves. The standing waves are slightly unstable to travelling waves. This scenario is identified as a Hopf bifurcation in a system with O(2) symmetry

Workshop on Magmatic Processes of Early Planetary Crusts: Magma Oceans and Stratiform Layered Intrusions

The significance of the lunar highland pristine cumulate samples were reevaluated with the aid of the additional insights provided by geologically constrained terrestrial investigations. This exercise involved a review of the state of knowledge about terrestrial and lunar cumulate rocks as well as an enumeration and reevaluation of the processes hypothesized to have been responsible for their formation, both classically and at present

Continuum thermodynamics of chemically reacting fluid mixtures

We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate definition of thermal energy excluding diffusive contributions. The resulting interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric in case of binary interactions. For chemically reacting systems and as a new result, the chemical interaction force is a contribution being non-symmetric outside of chemical equilibrium. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations. Moreover, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations become a strict consequence. With a classification of the factors in the binary products of the entropy production according to their parity--instead of the classical partition into so-called fluxes and driving forces--the apparent anti-symmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared to the speed of sound, the Maxwell-Stefan equations follow in the case without chemistry, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model with only mass being balanced individually. In the reactive case ..

Weak-strong uniqueness for energy-reaction-diffusion systems

We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems, which genuinely feature cross-diffusion effects. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. Weak-strong uniqueness is obtained for general entropy-dissipating reactions without growth restrictions, and certain models with a non-integrable diffusive flux. The results also apply to a class of (isoenergetic) reaction-cross-diffusion systems

Human reproduction in space. Late results

Objectius de Desenvolupament Sostenible::3 - Salut i BenestarPostprint (published version

Modelling of the binary alloy solidification process

Bibliography: leaves 129-132.A thermodynamically consistent model capable of modelling a binary alloy undergoing solidification or melting is developed. The theory is continuum based, and the solid-liquid phase change system is described macroscopically by a single set of conservation equations. The model is an extension of that presented in the literature. The thermodynamic theories of this type in the current literature are based on the assumption of local equilibrium. This assumption is not representative of most alloy solidification processes where the solid-liquid phase region, termed the mushy region, is of dendritic nature with the rates of diffusion in the liquid being orders of magnitude faster than that in the solid. The propose model includes the assumption of local non-equilibrium where solute diffusion in the solid phase is assumed to be zero. The thermodynamic formulation is expressed in terms of three thermodynamic variables: pressure, temperature and average solute concentration for both the equilibrium and non-equilibrium case. A generalized set of conservation equations of mass, energy, momentum and solute with the necessary constitutive equations is presented. A Finite Element (FE) formulation of a simplified form of the governing equations is developed. The reduced set of equations implemented in the FE formulation consists of a fully coupled heat conduction and solute diffusion formulation, with solid-liquid phase change, where the effects of pressure and convection are neglected. The FE formulation is based on the fixed grid technique where the elements are two dimensional, four noded quadrilaterals with the primary variables being enthalpy and average solute concentration. Temperature and solid mass fraction are calculated on a local level at each integration point of an element. A fully consistent Newton-Raphson method is used to solve the global coupled equations and an Euler backward difference scheme is used for the temporal discretization. The solution of the enthalpy-temperature relationship is carried out at the integration points using a Newton-Raphson method. A secant method employing the regula falsi technique takes into account sudden jumps or sharp changes in the enthalpy-temperature behaviour which occur at the phase zone interfaces. The Euler backward difference integration rule is used to calculate the solid mass fraction and its derivatives for the non-equilibrium case. Two solidification examples, using both the local equilibrium and the local non-equilibrium cases, are analyzed. The finite element results obtained for the two cases are compared, and the accuracy of the finite element model is checked. Both dendritic and eutectic phase change are tackled. Even though the discrete eutectic phase change is approximated using the fixed grid approach, the results are considered to be reasonable approximations to what occurs in reality. Favorable comparisons of the results are obtained with that in the literature and convergence of the finite element results for different mesh sizes are shown. For dilute alloy solutions, the solidification results for the local equilibrium and the local non-equilibrium cases are shown to differ markedly, whereas for near eutectic solutions little difference is observed. The use of the local non-equilibrium assumption in the finite element solidification model is shown to effect the macro-segregation of solute

Mikrokonvektīvās parādības neizotermiskās un neviendabīgās magnētisko nanodaļiņu dispersijas

Anotācija. Ferokoloīdiem – stabilām magnētisko nanodaļiņu dispersijām – piemīt vērā ņemamas magnētiskās īpašības, kuras izpaužas uz tiem iedarbojoties ar ārējo magnētisko lauku. Neizotermiskās koloidālās sistēmas savukārt izrāda ciešu saikni starp temperatūras un dispersās fāzes koncentrācijas gradientiem (Soret efekts). Tā galvenais cēlonis ir izmēru atšķirība starp binārā maisījuma komponentēm. Koncentrācijas un magnētiskā lauka gradientu mijiedarbība magnetizējamā vidē izraisa magnētiskos spēkus, kuri ietekmē siltuma un masas pārnesi. Šī teorētiskā pētījuma priekšmets ir fotoabsorbtīvo konvektīvi-difuzīvo mikrostruktūru rašanās un evolūcija ferokoloīdu slāņos ārēja magnētiskā lauka ietekmē. Tiek formulētas un risinātas dažas modeļproblēmas ar mērķi noskaidrot koncentrācijas magnētiskās konvekcijas veidošanās mehānismus koncentrācijas mikrostruktūrās, kuras tiek inducētas ar ārēja optiskā avota starojuma enerģijas absorbciju un no tās izrietošo termisko gradientu veidošanos. Ar teorētiskām metodēm tiek noteikta konvektīvās pārneses ietekme uz efektīviem transporta koeficientiem. Tiek apskatīta izstiepto fotoabsorbtīvo mikrostruktūru sekundārā hidrodinamiskā stabilitāte attiecībā pret noteicošo kontroles parametra variāciju. Skaitliskās simulācijās tika novērota izstiepto režģu destabilizācija un tai sekojoša translācijas simetrijas laušana. Savukārt, divdimensionālo tīklu stabilitātes zaudēšanai seko rotācijas simetrijas kārtas pazemināšanās. Iegūtie teorētiskie rezultāti ļauj interpretēt vai pārinterpretēt dažas fotoabsorbtīvo koncentrācijas mikrostruktūru veidošanās un evolūcijas īpatnības magnetokonvektīvas pārneses kontekstā. Koncentrācijas magnētiskās mikrokonvekcijas ietekmes analīze ļauj aprakstīt dažu iepriekš neizskaidrotu efektu mikroskopisko mehānismu. Tiek apstiprināta parazītiskās magnētiskās mikrokonvekcijas rašanās fotoabsorbtīvās mikrostruktūrās ārēja magnētiskā lauka ietekmē.Abstract. Ferrocolloids – stable dispersions of magnetic nanoparticles – possess notable magnetic properties, which become apparent in consequence of the application of the external magnetic fields and magnetic ordering of the nanoparticles. Non-isothermal colloidal systems in turn exhibit close coupling between the gradients of temperature and concentration of the dispersed phase – Soret effect - owing to the size difference between the components of the binary mixture. The interactions of the gradients of concentration and demagnetizing field in magnetizable medium contribute to the appearance of the magnetic forces affecting the regimes of heat and mass transfer. The subject of this theoretical investigation is the emergence and evolution of the photoabsorptive convective-diffusive microstructures in ferrocolloid layers under the action of the applied magnetic field. A series of model problems is formulated in order to elucidate the principal mechanisms of the formation of magnetosolutal microconvection within the concentration microstructures induced by the absorption of the incident optical intensity and the consequent appearance of the thermal gradients. The convective contributions to the effective transport coefficients are obtained by analytical and numerical methods. The secondary stability of the extended photoabsorptive microstructures is considered with respect to the variation of the control parameters. The destabilization of the extended gratings and the consequent breaking of the translational symmetry are observed in numerical simulations. In turn, the loss of stability of the bidirectional grids is followed by the reduction of the order of the rotational symmetry. The obtained theoretical results permit interpreting or reinterpreting some peculiarities of the real observations of the formation and evolution of the photoabsorptive concentration microstructures in the framework of magnetoconvective transport. The consideration of the influence of magnetosolutal microconvection in observable parameters has allowed describing the underlying microscopic mechanisms of some previously unexplained effects. In principle, the formation of the parasitic magnetic microconvection within the photoabsorptive microstructures under the action of the applied magnetic field is confirmed.Eiropas Sociālā fonda projekts «Atbalsts doktora studijām Latvijas Universitātē» Nr. 2009/0138/1DP/1.1.2.1.2./09/IPIA/VIAA/00