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Simple derivation of the special theory of relativity without the speed of light axiom [article]

Ondrej Certik
2007 arXiv   pre-print
We show a very simple yet rigorous derivation of the invariance of the space-time interval (and hence the whole special relativity) just from the isotropy, homogeneity and a principle of relativity, without the need of the speed of light axiom. This article is intended as a textbook explanation of the special relativity.
arXiv:0710.3398v1 fatcat:fd4owbbtirfe5mutla4bkwe54e

Toward Modern Fortran Tooling and a Thriving Developer Community [article]

Milan Curcic, Ondřej Čertík, Brad Richardson, Sebastian Ehlert, Laurence Kedward, Arjen Markus, Ivan Pribec, Jérémie Vandenplas
2021 arXiv   pre-print
remains the dominant language used on top High Performance Computing (HPC) systems, with applications to weather and climate (Powers et al. 2017; Skamarock, Ong, and Klemp 2021) , computational chemistry (Čertík  ... 
arXiv:2109.07382v1 fatcat:arv6qgy4z5ecbmwtolw4zcekga

Numerical solution of the radial Dirac equation in pseudopotential construction [article]

Ondrej Certik
2007 arXiv   pre-print
Ondřej Šipr, CSc., for explaining me several theoretical problems.  ... 
arXiv:0710.3408v2 fatcat:q3u5ekrfqneofptk2gbv7xouuu

The virtual element method for eigenvalue problems with potential terms on polytopal meshes [article]

Ondrej Certik, Francesca Gardini, Gianmarco Manzini, Giuseppe Vacca
2018 arXiv   pre-print
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This model is a fundamental element in the numerical resolution of more complex problems from the Density Functional Theory. The VEM is based on the construction of the discrete bilinear forms of the variational formulation through certain polynomial projection
more » ... rs that are directly computable from the degrees of freedom. The method shows a great flexibility with respect to the meshes and provide a correct spectral approximation with optimal convergence rates. This point is discussed from both the theoretical and the numerical viewpoint. The performance of the method is numerically investigated by solving the Quantum Harmonic Oscillator problem with the harmonic potential and a singular eigenvalue problem with zero potential for the first eigenvalues.
arXiv:1804.00986v1 fatcat:ipxajf5j2nbepclmoxzy62exra

Three anisotropic benchmark problems for adaptive finite element methods

Pavel Solin, Ondrej Certik, Lukas Korous
2013 Applied Mathematics and Computation  
In this paper we provide three benchmark problems with known exact solutions that can be used to assess the ability of adaptive finite element algorithms to handle anisotropically-behaved solutions. The first one is a Poisson equation with a smooth solution that only changes in one spatial direction. The second one is a singularly-perturbed linear elliptic equation whose solution exhibits a boundary layer, and the last one is a two-equation system that contains a boundary layer in one solution
more » ... omponent only. In an appendix we show sample results obtained with the open source library Hermes. 1
doi:10.1016/j.amc.2010.12.080 fatcat:klsbn5bhibgctbu7ta5hjwk3jy

Integral and fractional quantum Hall Ising ferromagnets

Karel Výborný, Ondřej Čertík, Daniela Pfannkuche, Daniel Wodziński, Arkadiusz Wójs, John J. Quinn
2007 Physical Review B  
We compare quantum Hall systems at filling factor 2 to those at filling factors 2/3 and 2/5, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization P=1) and paramagnetic (P=0) incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the
more » ... ion spectra are different. At filling factor 2, we find spin domains at half-polarization (P=1/2), while antiferromagnetic order seems most favorable in the CF systems. The transition between P=0 and 1, as seen when e.g. the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompresible half-polarized state is found in some models.
doi:10.1103/physrevb.75.045434 fatcat:w5auvxm3eva2pd2bun2zgosgzy

Animal Fat as a Substrate for Production of n-6 Fatty Acids by Fungal Solid-State Fermentation

Ondrej Slaný, Tatiana Klempová, Volha Shapaval, Boris Zimmermann, Achim Kohler, Milan Čertík
2021 Microorganisms  
The method of solid-state fermentation (SSF) represents a powerful technology for the fortification of animal-based by-products. Oleaginous Zygomycetes fungi are efficient microbial cell factories used in SSF to valorize a wide range of waste and rest cereal materials. The application of this fermentation technique for utilization and biotransformation of animal-based materials represents a distinguished step in their treatment. In this study, for the first time, the strain Umbelopsis
more » ... CCF2412 was used for the bioconversion of animal fat by-products to the fermented bioproducts enriched with n-6 polyunsaturated fatty acids, mainly γ-linolenic acid (GLA). Bioconversion of both cereals and the animal fat by-product resulted in the production of fermented bioproducts enriched with not just GLA (maximal yield was 6.4 mg GLA/g of fermented bioproduct), but also with high yields of glucosamine. Moreover, the fermentation on the cornmeal matrix led to obtaining bioproduct enriched with β-carotene. An increased amount of β-carotene content improved the antioxidant stability of obtained fermented bioproducts. Furthermore, the application of Fourier-transform infrared spectroscopy for rapid analysis and characterization of the biochemical profile of obtained SSF bioproducts was also studied.
doi:10.3390/microorganisms9010170 pmid:33466747 pmcid:PMC7830168 fatcat:ks5auwifxfbd3fscjajhirbizy

Biotransformation of Animal Fat-By Products into ARA-Enriched Fermented Bioproducts by Solid-State Fermentation of Mortierella alpina

Ondrej Slaný, Tatiana Klempová, Volha Shapaval, Boris Zimmermann, Achim Kohler, Milan Čertík
2020 Journal of Fungi  
Solid-state fermentation (SSF) is a powerful fermentation technology for valorizing rest materials and by-products of different origin. Oleaginous Zygomycetes fungi are often used in SSF as an effective cell factory able to valorize a wide range of hydrophilic and hydrophobic substrates and produce lipid-enriched bioproducts. In this study, for the first time, the strain Mortierella alpina was used in SSF for the bioconversion of animal fat by-products into high value fermented bioproducts
more » ... hed with arachidonic acid (ARA). Two cereals-based matrixes mixed with four different concentrations of animal fat by-product were evaluated for finding optimal conditions of a fat-based SSF. All obtained fermented bioproducts were found to be enriched with ARA. The highest substrate utilization (25.8%) was reached for cornmeal and it was almost double than for the respective wheat bran samples. Similarly, total fatty acid content in a fermented bioproduct prepared on cornmeal is almost four times higher in contrast to wheat bran-based bioproduct. Although in general the addition of an animal fat by-product caused a gradual cessation of ARA yield in the obtained fermented bioproduct, the content of ARA in fungal biomass was higher. Thus, M. alpina CCF2861 effectively transformed exogenous fatty acids from animal fat substrate to ARA. Maximum yield of 32.1 mg of ARA/g of bioproduct was reached when using cornmeal mixed with 5% (w/w) of an animal fat by-product as substrate. Furthermore, implementation of attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy in characterization of obtained SSF bioproducts was successfully tested as an alternative tool for complex analysis, compared to traditional time-consuming methods.
doi:10.3390/jof6040236 pmid:33096607 fatcat:bh6ov7iyi5cofekt3aswtz6bu4

Immune Response and Fatty Acid Profile of Eggs from Laying Hens Fed Fermented Feed Rich in Polyunsaturated Fatty Acids

Viera Karaffová, Dagmar Mudroňová, Boris Semjon, Tatiana Klempová, Ondrej Slaný, Milan Čertík, Jozef Nagy, Martin Bartkovský, Slavomír Marcinčák
2022 Fermentation  
Western diets are dominated by the consumption of chemically modified foods, characterized by a deficiency of n-3 polyunsaturated fatty acids (PUFAs). Lack of n-3 PUFAs is also present in livestock feed, which negatively affects livestock health, including immune response, and results in a low content of n-3 PUFAs in animal products. The goal of this experiment was to study the effect of the addition of feed containing PUFAs produced by the fungus Mortierella alpina on immune parameters (IgA,
more » ... C-2, IGF-2, phagocytoses and selected lymphocyte subsets) and the composition of the intestinal microbiota of hens and egg fatty acids profile. Hens were divided into groups (control, F10—supplemented with 10% of fermented feed, F15—supplemented with 15% of fermented feed). The relative expression of all genes was markedly upregulated, mainly in the F15 group. Likewise, in F15, a significant increase in both phagocytes engulfing capacity and the level of oxidative burst was observed. Neither CD T cell subpopulations nor the CD4/CD8 ratio were significantly affected. A significant increase in small intestinal enterobacteria was observed in the F15. The fatty acid profile of eggs in both experimental groups showed an increased proportion of n-3 PUFAs and decreased n-6/n-3 PUFAs ratio. The results of this work show that the addition of 15% omega-3 acids enriched fermented feed positively affected the immune response of laying hens and improved the fatty acid composition of eggs.
doi:10.3390/fermentation8030098 fatcat:3lfus7mf6ja2pkkc5ixtrqw4jq

Production of high-value bioproducts enriched with γ-linolenic acid and β-carotene by filamentous fungi Umbelopsis isabellina using solid-state fermentations

Ondrej Slaný, Tatiana Klempová, Slavomír Marcinčák, Milan Čertík
2020 Annals of Microbiology  
Spent malt grain has been reported to serve as an inert carrier for SSF cultivations and to provide internal support in order to increase the interparticle space (Čertík et al. 2006; Čertík et al. 2008  ...  Zygomycetes fungi have been known to be highly successful in SSF (Stredanský et al. 2000; Čertík et al. 2013; Takó et al. 2015) .  ... 
doi:10.1186/s13213-020-01545-0 fatcat:zsprnsfu7fan5kjgezf3o7u4hi

Time-dependent orbital-free density functional theory for electronic stopping power: Comparison to the Mermin-Kohn-Sham theory at high temperatures

Alexander J. White, Ondrej Certik, Y. H. Ding, S. X. Hu, Lee A. Collins
2018 Physical review B  
Electronic stopping power in warm dense matter can affect energy transport and heating in astrophysical processes and internal confinement fusion. For cold condensed matter systems, stopping power can be be modeled from first-principles using real time time-dependent density functional theory (DFT). However, high temperatures (10's to 100's of eV) may be computationally prohibitive for traditional Mermin-Kohn-Sham DFT. New experimental measurements in the warm dense regime motivates the
more » ... ent of first-principles approaches which can reach these temperatures. We have developed a time-dependent orbital free density functional theory, which includes a novel nonadiabatic and temperature-dependent kinetic energy density functional, for the simulation of stopping power at any temperature. The approach is nonlinear with respect to the projectile perturbation, includes all ions and electrons, and does not require a priori determination of screened interaction potentials. Our results compare favorably with Kohn-Sham for temperatures in the WDM regime, especially nearing 100 eV. PACS numbers: I.
doi:10.1103/physrevb.98.144302 fatcat:2xyeka3sgfgmhgvgndny7hityi

Transport gap in aν=1∕3quantum Hall system: A probe for skyrmions

Annelene F. Dethlefsen, Rolf J. Haug, Karel Výborný, Ondřej Čertík, Arkadiusz Wójs
2006 Physical Review B  
The dependence of the activated gap on magnetic field is studied for the fractional filling factor~1/3. By comparing the experimental results with results from exact diagonalization calculations we are able to identify the excitation of a small antiskyrmion in the low-field regime and a cross-over to spinless excitations at higher magnetic fields. The effect of sample quality is studied. On the side of the theory, comparison between different geometries (torus and sphere) and different sizes is
more » ... carried out. Under inclusion of Landau level mixing and finite thickness, we obtain a good agreement between calculated energies and experimental results.
doi:10.1103/physrevb.74.195324 fatcat:6av74bvqxrcohfuqkypoiffhv4

Microcultivation and FTIR spectroscopy-based screening revealed a nutrient-induced co-production of high-value metabolites in oleaginous Mucoromycota fungi

Simona Dzurendova, Boris Zimmermann, Achim Kohler, Valeria Tafintseva, Ondrej Slany, Milan Certik, Volha Shapaval, Marie-Joelle Virolle
2020 PLoS ONE  
Mucoromycota fungi possess a versatile metabolism and can utilize various substrates for production of industrially important products, such as lipids, chitin/chitosan, polyphosphates, pigments, alcohols and organic acids. However, as far as commercialisation is concerned, establishing industrial biotechnological processes based on Mucoromycota fungi is still challenging due to the high production costs compared to the final product value. Therefore, the development of co-production concept is
more » ... ighly desired since more than one valuable product could be produced at the time and the process has a potentially higher viability. To develop such biotechnological strategy, we applied a high throughput approach consisting of micro-titre cultivation and FTIR spectroscopy. This approach allows single-step biochemical fingerprinting of either fungal biomass or growth media without tedious extraction of metabolites. The influence of two types of nitrogen sources and different levels of inorganic phosphorus on the co-production of lipids, chitin/chitosan and polyphosphates for nine different oleaginous Mucoromycota fungi was evaluated. FTIR analysis of biochemical composition of Mucoromycota fungi and biomass yield showed that variation in inorganic phosphorus had higher effect when inorganic nitrogen source-ammonium sulphate-was used. It was observed that: (1) Umbelopsis vinacea reached almost double biomass yield compared to other strains when yeast extract was used as nitrogen source while phosphorus limitation had little effect on the biomass yield; (2) Mucor circinelloides, Rhizopus stolonifer, Amylomyces rouxii, Absidia glauca and Lichtheimia corymbifera overproduced chitin/chitosan under the low pH caused by the limitation of inorganic phosphorus; (3) Mucor circinelloides, Amylomyces rouxii, Rhizopus stolonifer and Absidia glauca were able to store polyphosphates in addition to lipids when high concentration of inorganic phosphorus was used; (4) the biomass and lipid yield of high-value lipid producers Mortierella alpina and Mortierella hyalina were significantly increased when high concentrations of inorganic phosphorus were combined with ammonium sulphate, while the same amount of inorganic phosphorus combined with yeast extract showed negative impact on the growth and lipid accumulation. FTIR spectroscopy revealed the co-production potential of several oleaginous Mucoromycota fungi forming lipids, chitin/chitosan and polyphosphates in a single cultivation process.
doi:10.1371/journal.pone.0234870 pmid:32569317 fatcat:smtgsou2kvcjzocgl75flxxiae

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

Lorin X. Benedict, Michael P. Surh, Liam G. Stanton, Christian R. Scullard, Alfredo A. Correa, John I. Castor, Frank R. Graziani, Lee A. Collins, Ondřej Čertík, Joel D. Kress, Michael S. Murillo
2017 Physical review. E  
We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n = 10 26 cm −3 , T i = 10 5 K, and 10 7 K < T e < 10 9 K. The non-equilibrium classical MD simulations are performed with inter-particle interactions modeled by quantum
more » ... tistical potentials (QSPs). Our MD results indicate: 1. a large effect from time-varying potential energy, which we quantify by appealing to an adiabatic 2-temperature equation of state, and 2. a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result, and propose directions of further research along these lines.
doi:10.1103/physreve.95.043202 pmid:28505713 fatcat:awvcynpzxbb7vdiqcfdprzowda

dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations

Ondřej Čertík, John E. Pask, Jiří Vackář
2013 Computer Physics Communications  
A robust and general solver for the radial Schrödinger, Dirac, and Kohn--Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined
more » ... by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of 10^-8 Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number Z = 1--92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, dftatom, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.
doi:10.1016/j.cpc.2013.02.014 fatcat:o6dcceenyreqfgzliqywydv4ea
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