21 research outputs found
Computational studies of history dependence in nematic liquid crystals in random environments
Competition between local disordering and global ordering fields in nematic liquid crystals
We study the influence of external electric or magnetic field B on orientational ordering of nematic liquid crystals or of other rod-like objects (e.g. nanotubes immersed in a liquid) in the presence of random anisotropy field type of disorder. The Lebwohl-Lasher lattice type of semi-microscopic approach is used at zero temperature. Therefore, results are valid well below the transition into the isotropic phase. We calculate the correlation function of systems as a function of B, concentration p of impurities imposing random anisotropy field disorder, the disorder strength W and system dimensionality (2D and 3D systems). In order to probe memory effects we calculate correlation length ā«ā« for random and homogeneous initial configurations. We determine the crossover fields Bc(p) separating roughly the ordered and disordered regime. Memory effects are apparent only in the latter case, i.e. for B < Bc
Bend strength of alumina ceramics
StatistiÄno smo ovrednotili 5100 eksperimentalnih vrednosti upogibnih trdnosti testnih vzorcev iz redne proizvodnje korundnih keramiÄnih izdelkov. Primerjali smo teoretiÄno izraÄunano Weibullovo porazdelitev z dvema drugima pogosto uporabljenima dvoparametriÄnima porazdelitvama, normalno in log-normalno, da bi ugotovili, katera se najbolj sklada z meritvami. Za izraÄun ustreznih prostih parametrov smo uporabili metodo najveÄje verjetnosti (maximum-likelihood method). Potem smo za primerjavo rezultatov uporabili QāQ-diagrame. Potrdili smo domnevo, da se z eksperimentalnimi vrednostmi trdnosti najbolj ujema Weibullova porazdelitev.We have performed a statistical evaluation of 5100 experimental values of the bend strength of test pieces from a serial production of alumina products. The Weibull distribution was compared with two other commonly used 2-parametric distributions, i.e., normal and log-normal, in order to reveal which of them best matches the experiments. The maximum-likelihood method was used to evaluate the corresponding parameters, and then a QāQ plot was used for all the statistics. We confirmed that the Weibull distribution describes the experimental strengths most accurately
Annihilation of defects in liquid crystals
The annihilation of defect is studied theoretically in liquid crystals (LCs). We consider the annihilation of point disclinations in nematic and line edge dislocations in smectic A LC phase, respectively. We stres s qualitative similarities in these processes. The whole annihilation regime is taken into account, consisting of the pre-collision, collision, and post-collision stage
Analytical mechanics
Pri predmetu AnalitiÄna mehanika obravnavamo Å”tevilne probleme iz mehanike, predvsem dinamike, na bolj matematiÄno sistematiÄen naÄin, kot je navada pri obiÄajnih fizikalnih nalogah, npr. v zvezi z drugim Newtonovim zakonom. S tem lahko vkljuÄimo tudi kompleksnejÅ”e geometrije pri gibanju teles. KljuÄni del analitiÄne mehanike je vpeljava generaliziranih koordinat kot neodvisnih spremenljivk gibanja, s katerimi izrazimo Lagrangeevo funkcijo ali pa Hamiltonian. Nazadnje moramo reÅ”iti ustrezne diferencialne enaÄbe, da najdemo Äasovno odvisnost generaliziranih koordinat. Gravitacija in nihanje sta znaÄilni podroÄji, kjer koristno uporabimo matematiÄni formalizem analitiÄne mehanike.In the course Analytical mechanics numerous problems in mechanics, particularly topics from dynamics, are treated in a more systematic way, as compared to ordinary physical problems, e.g., in relation to second Newton law. In this way, we can also include more complex geometries in the motion of bodies. The key part od analytical mechanics is introduction of generalized coordinates as independent variables of motion, used to express either Lagrange function or Hamiltonian. Finally, the corresponding differential equations must be solved in order to find the time development of generalized coordinates. Gravitation and oscillation are typical areas where the mathematical formalism of analytical mechanics can be used
Symmetry breaking and structure of a mixture of nematic liquid crystals and anisotropic nanoparticles
Orientational ordering of a homogeneous mixture of uniaxial liquid crystalline (LC) molecules and magnetic nanoparticles (NPs) is studied using the LebwohlāLasher lattice model. We consider cases where NPs tend to be oriented perpendicularly to LC molecules due to elastic forces. We study domain-type configurations of ensembles, which are quenched from the isotropic phase. We show that for large enough concentrations of NPs the long range uniaxial nematic ordering is replaced by short range order exhibiting strong biaxiality. This suggests that the impact of NPs on orientational ordering of LCs for appropriate concentrations of NPs is reminiscent to the influence of quenched random fields which locally enforce a biaxial ordering
Higher mathematics in physics
V fiziki se da vse zakone in izreke, povezane s fizikalnimi koliÄinami, ki so odvisne od kraja in Äasa, zapisati z diferencialnimi enaÄbami. Le-te so lahko navadne ali parcialne, skalarne ali vektorske, velikokrat pa gre celo za sistem veÄ ali mnogo sklopljenih diferencialnih enaÄb, odvisno od dimenzije in kompleksnosti fizikalnega problema. Medtem ko so diferencialne enaÄbe lokalna oblika zapisa fizikalnih zakonov, zajemajo integralske enaÄbe cel prostor ali Äas ali pa doloÄeno prostorsko in Äasovno obmoÄje. ZnaÄilen zgled zapisa enaÄb v obeh oblikah so Maxwellove enaÄbe v elektromagnetizmu ali pa variacijski raÄun, povezan z minimizacijo proste energije. S postavitvijo in reÅ”evanjem (analitiÄnim ali numeriÄnim) teh enaÄb lahko zajamemo vsa podroÄja fizike, od mehanike in gibanja toÄkastih teles, kjer posebna fizikalna veja analitiÄna mehanika vpelje koncepte posploÅ”enih koordinat in impulzov, Lagrangiana in Hamiltoniana, do obravnave skalarnih in vektorskih polj v elektromagnetizmu in valovni optiki, kvantni fiziki, termodinamiki, fiziki tekoÄin, teoriji verjetnosti itd.In physics all the laws and theorems connected with the physical quantities which vary in space and time, can be written with differential equations. These can be ordinary or partial, scalar or vector, but in several cases there is a system of a few or many coupled differential equations, depending on the dimension and complexity of the physical problem. While the differential equations are the local form of writing physical laws, the integral equations contain the whole space or time, or a definite space and time area. A typical example of writing equations in both forms is a set of Maxwell equations in electromagnetism or variational calculus connected with the minimization of the free energy. By setting and solving (analytically or numerically) these equation we can capture all the areas of physics, from mechanics and movement of point-like bodies, where the special physical branch called analytical mechanics introduces the concepts of generalized coordinates and impulses, Lagrangian and Hamiltonian, up to treatment of scalar and vector fields in electromagnetism and wave optics, quantum physics, thermodynamics, physics of fluids, probability theory etc