All-atom molecular dynamics calculation study of entire poliovirus empty capsids in solution
Energy Technology Data Exchange (ETDEWEB)
Andoh, Y.; Yoshii, N.; Yamada, A.; Kojima, H.; Mizutani, K.; Okazaki, S., E-mail: okazaki@apchem.nagoya-u.ac.jp [Department of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603 (Japan); Fujimoto, K. [Department of Pharmacy, College of Pharmaceutical Sciences, Ritsumeikan University, Nojihigashi, Kusatsu, Shiga 525-8577 (Japan); Nakagawa, A. [Institute for Protein Research, Osaka University, Yamadaoka, Suita, Osaka 565-0871 (Japan); Nomoto, A. [Institute of Microbial Chemistry, Kamiosaki, Shinagawa-ku, Tokyo 141-0021 (Japan)
2014-10-28
Small viruses that belong, for example, to the Picornaviridae, such as poliovirus and foot-and-mouth disease virus, consist simply of capsid proteins and a single-stranded RNA (ssRNA) genome. The capsids are quite stable in solution to protect the genome from the environment. Here, based on long-time and large-scale 6.5 × 10{sup 6} all-atom molecular dynamics calculations for the Mahoney strain of poliovirus, we show microscopic properties of the viral capsids at a molecular level. First, we found equilibrium rapid exchange of water molecules across the capsid. The exchange rate is so high that all water molecules inside the capsid (about 200 000) can leave the capsid and be replaced by water molecules from the outside in about 25 μs. This explains the capsid's tolerance to high pressures and deactivation by exsiccation. In contrast, the capsid did not exchange ions, at least within the present simulation time of 200 ns. This implies that the capsid can function, in principle, as a semipermeable membrane. We also found that, similar to the xylem of trees, the pressure of the solution inside the capsid without the genome was negative. This is caused by coulombic interaction of the solution inside the capsid with the capsid excess charges. The negative pressure may be compensated by positive osmotic pressure by the solution-soluble ssRNA and the counter ions introduced into it.
All-atom molecular dynamics calculation study of entire poliovirus empty capsids in solution
Andoh, Y.; Yoshii, N.; Yamada, A.; Fujimoto, K.; Kojima, H.; Mizutani, K.; Nakagawa, A.; Nomoto, A.; Okazaki, S.
2014-10-01
Small viruses that belong, for example, to the Picornaviridae, such as poliovirus and foot-and-mouth disease virus, consist simply of capsid proteins and a single-stranded RNA (ssRNA) genome. The capsids are quite stable in solution to protect the genome from the environment. Here, based on long-time and large-scale 6.5 × 106 all-atom molecular dynamics calculations for the Mahoney strain of poliovirus, we show microscopic properties of the viral capsids at a molecular level. First, we found equilibrium rapid exchange of water molecules across the capsid. The exchange rate is so high that all water molecules inside the capsid (about 200 000) can leave the capsid and be replaced by water molecules from the outside in about 25 μs. This explains the capsid's tolerance to high pressures and deactivation by exsiccation. In contrast, the capsid did not exchange ions, at least within the present simulation time of 200 ns. This implies that the capsid can function, in principle, as a semipermeable membrane. We also found that, similar to the xylem of trees, the pressure of the solution inside the capsid without the genome was negative. This is caused by coulombic interaction of the solution inside the capsid with the capsid excess charges. The negative pressure may be compensated by positive osmotic pressure by the solution-soluble ssRNA and the counter ions introduced into it.
All-atom molecular dynamics calculation study of entire poliovirus empty capsids in solution
International Nuclear Information System (INIS)
Andoh, Y.; Yoshii, N.; Yamada, A.; Kojima, H.; Mizutani, K.; Okazaki, S.; Fujimoto, K.; Nakagawa, A.; Nomoto, A.
2014-01-01
Small viruses that belong, for example, to the Picornaviridae, such as poliovirus and foot-and-mouth disease virus, consist simply of capsid proteins and a single-stranded RNA (ssRNA) genome. The capsids are quite stable in solution to protect the genome from the environment. Here, based on long-time and large-scale 6.5 × 10 6 all-atom molecular dynamics calculations for the Mahoney strain of poliovirus, we show microscopic properties of the viral capsids at a molecular level. First, we found equilibrium rapid exchange of water molecules across the capsid. The exchange rate is so high that all water molecules inside the capsid (about 200 000) can leave the capsid and be replaced by water molecules from the outside in about 25 μs. This explains the capsid's tolerance to high pressures and deactivation by exsiccation. In contrast, the capsid did not exchange ions, at least within the present simulation time of 200 ns. This implies that the capsid can function, in principle, as a semipermeable membrane. We also found that, similar to the xylem of trees, the pressure of the solution inside the capsid without the genome was negative. This is caused by coulombic interaction of the solution inside the capsid with the capsid excess charges. The negative pressure may be compensated by positive osmotic pressure by the solution-soluble ssRNA and the counter ions introduced into it
All-Atom Molecular Dynamics Simulation of Protein Translocation through an α-Hemolysin Nanopore
Di Marino, Daniele
2015-08-06
© 2015 American Chemical Society. Nanopore sensing is attracting the attention of a large and varied scientific community. One of the main issues in nanopore sensing is how to associate the measured current signals to specific features of the molecule under investigation. This is particularly relevant when the translocating molecule is a protein and the pore is sufficiently narrow to necessarily involve unfolding of the translocating protein. Recent experimental results characterized the cotranslocational unfolding of Thioredoxin (Trx) passing through an α-hemolisin pore, providing evidence for the existence of a multistep process. In this study we report the results of all-atom molecular dynamics simulations of the same system. Our data indicate that Trx translocation involves two main barriers. The first one is an unfolding barrier associated with a translocation intermediate where the N-terminal region of Trx is stuck at the pore entrance in a conformation that strongly resembles the native one. After the abrupt unfolding of the N-terminal region, the Trx enters the α-hemolisin vestibule. During this stage, the constriction is occupied not only by the translocating residue but also by a hairpin-like structure forming a tangle in the constriction. The second barrier is associated with the disentangling of this region.
All-Atom Molecular Dynamics Simulation of Protein Translocation through an α-Hemolysin Nanopore
Di Marino, Daniele; Bonome, Emma Letizia; Tramontano, Anna; Chinappi, Mauro
2015-01-01
© 2015 American Chemical Society. Nanopore sensing is attracting the attention of a large and varied scientific community. One of the main issues in nanopore sensing is how to associate the measured current signals to specific features of the molecule under investigation. This is particularly relevant when the translocating molecule is a protein and the pore is sufficiently narrow to necessarily involve unfolding of the translocating protein. Recent experimental results characterized the cotranslocational unfolding of Thioredoxin (Trx) passing through an α-hemolisin pore, providing evidence for the existence of a multistep process. In this study we report the results of all-atom molecular dynamics simulations of the same system. Our data indicate that Trx translocation involves two main barriers. The first one is an unfolding barrier associated with a translocation intermediate where the N-terminal region of Trx is stuck at the pore entrance in a conformation that strongly resembles the native one. After the abrupt unfolding of the N-terminal region, the Trx enters the α-hemolisin vestibule. During this stage, the constriction is occupied not only by the translocating residue but also by a hairpin-like structure forming a tangle in the constriction. The second barrier is associated with the disentangling of this region.
Czech Academy of Sciences Publication Activity Database
Olžyńska, Agnieszka; Zubek, M.; Roeselová, Martina; Korchowiec, J.; Cwiklik, Lukasz
2016-01-01
Roč. 1858, č. 12 (2016), s. 3120-3130 ISSN 0005-2736 R&D Projects: GA ČR GA15-14292S Institutional support: RVO:61388955 ; RVO:61388963 Keywords : phospholipid monolayers * Lung surfactant * molecular dynamics Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.498, year: 2016
Chen, Wei; Shen, Jana K.
2014-01-01
Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: 1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? 2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK a values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via co-titrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle-mesh Ewald, considering the known artifacts due to charge-compensating background plasma. PMID:25142416
Chen, Wei; Shen, Jana K
2014-10-15
Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here, we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: (1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? (2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force-shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK(a) values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via cotitrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle mesh Ewald, considering the known artifacts due to charge-compensating background plasma. Copyright © 2014 Wiley Periodicals, Inc.
Man, Viet Hoang; Li, Mai Suan; Derreumaux, Philippe; Nguyen, Phuong H.
2018-03-01
The Rayleigh-Plesset (RP) equation was derived from the first principles to describe the bubble cavitation in liquids in terms of macroscopic hydrodynamics. A number of nonequilibrium molecular dynamics studies have been carried out to validate this equation in describing the bubble inertial cavitation, but their results are contradictory and the applicability of the RP equation still remains to be examined, especially for the stable cavitation. In this work, we carry out nonequilibrium all-atom simulation to validate the applicability of the RP equation in the description of the stable cavitation of nano-sized bubbles in water. We show that although microscopic effects are not explicitly included, this equation still describes the dynamics of subnano-bubbles quite well as long as the contributions of various terms including inertial, surface tension, and viscosity are correctly taken into account. These terms are directly and inversely proportional to the amplitude and period of the cavitation, respectively. Thus, their contributions to the RP equation depend on these two parameters. This may explain the discrepancy between the current results obtained using different parameters. Finally, the accuracy of the RP equation in the current mathematical modeling studies of the ultrasound-induced blood-brain-barrier experiments is discussed in some detail.
Babakhani, Arneh; Gorfe, Alemayehu A; Gullingsrud, Justin; Kim, Judy E; Andrew McCammon, J
Peptide insertion, positioning, and stabilization in a model membrane are probed via an all-atom molecular dynamics (MD) simulation. One peptide (WL5) is simulated in each leaflet of a solvated dimyristoylglycero-3-phosphate (DMPC) membrane. Within the first 5 ns, the peptides spontaneously insert into the membrane and then stabilize during the remaining 70 ns of simulation time. In both leaflets, the peptides localize to the membrane interface, and this localization is attributed to the formation of peptide-lipid hydrogen bonds. We show that the single tryptophan residue in each peptide contributes significantly to these hydrogen bonds; specifically, the nitrogen heteroatom of the indole ring plays a critical role. The tilt angles of the indole rings relative to the membrane normal in the upper and lower leaflets are approximately 26 degrees and 54 degrees , respectively. The tilt angles of the entire peptide chain are 62 degrees and 74 degrees . The membrane induces conformations of the peptide that are characteristic of beta-sheets, and the peptide enhances the lipid ordering in the membrane. Finally, the diffusion rate of the peptides in the membrane plane is calculated (based on experimental peptide concentrations) to be approximately 6 A(2)/ns, thus suggesting a 500 ns time scale for intermolecular interactions.
Energy Technology Data Exchange (ETDEWEB)
Markutsya, Sergiy [Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States); Lamm, Monica H., E-mail: mhlamm@iastate.edu [Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States); Department of Chemical and Biological Engineering, Iowa State University, Ames, Iowa 50011 (United States)
2014-11-07
We report on a new approach for deriving coarse-grained intermolecular forces that retains the frictional contribution that is often discarded by conventional coarse-graining methods. The approach is tested for water and an aqueous glucose solution, and the results from the new implementation for coarse-grained molecular dynamics simulation show remarkable agreement with the dynamics obtained from reference all-atom simulations. The agreement between the structural properties observed in the coarse-grained and all-atom simulations is also preserved. We discuss how this approach may be applied broadly to any existing coarse-graining method where the coarse-grained models are rigorously derived from all-atom reference systems.
International Nuclear Information System (INIS)
Markutsya, Sergiy; Lamm, Monica H.
2014-01-01
We report on a new approach for deriving coarse-grained intermolecular forces that retains the frictional contribution that is often discarded by conventional coarse-graining methods. The approach is tested for water and an aqueous glucose solution, and the results from the new implementation for coarse-grained molecular dynamics simulation show remarkable agreement with the dynamics obtained from reference all-atom simulations. The agreement between the structural properties observed in the coarse-grained and all-atom simulations is also preserved. We discuss how this approach may be applied broadly to any existing coarse-graining method where the coarse-grained models are rigorously derived from all-atom reference systems
Shen, Lin; Yang, Weitao
2016-04-12
We developed a new multiresolution method that spans three levels of resolution with quantum mechanical, atomistic molecular mechanical, and coarse-grained models. The resolution-adapted all-atom and coarse-grained water model, in which an all-atom structural description of the entire system is maintained during the simulations, is combined with the ab initio quantum mechanics and molecular mechanics method. We apply this model to calculate the redox potentials of the aqueous ruthenium and iron complexes by using the fractional number of electrons approach and thermodynamic integration simulations. The redox potentials are recovered in excellent accordance with the experimental data. The speed-up of the hybrid all-atom and coarse-grained water model renders it computationally more attractive. The accuracy depends on the hybrid all-atom and coarse-grained water model used in the combined quantum mechanical and molecular mechanical method. We have used another multiresolution model, in which an atomic-level layer of water molecules around redox center is solvated in supramolecular coarse-grained waters for the redox potential calculations. Compared with the experimental data, this alternative multilayer model leads to less accurate results when used with the coarse-grained polarizable MARTINI water or big multipole water model for the coarse-grained layer.
Wallace, Jason A; Shen, Jana K
2012-11-14
Recent development of constant pH molecular dynamics (CpHMD) methods has offered promise for adding pH-stat in molecular dynamics simulations. However, until now the working pH molecular dynamics (pHMD) implementations are dependent in part or whole on implicit-solvent models. Here we show that proper treatment of long-range electrostatics and maintaining charge neutrality of the system are critical for extending the continuous pHMD framework to the all-atom representation. The former is achieved here by adding forces to titration coordinates due to long-range electrostatics based on the generalized reaction field method, while the latter is made possible by a charge-leveling technique that couples proton titration with simultaneous ionization or neutralization of a co-ion in solution. We test the new method using the pH-replica-exchange CpHMD simulations of a series of aliphatic dicarboxylic acids with varying carbon chain length. The average absolute deviation from the experimental pK(a) values is merely 0.18 units. The results show that accounting for the forces due to extended electrostatics removes the large random noise in propagating titration coordinates, while maintaining charge neutrality of the system improves the accuracy in the calculated electrostatic interaction between ionizable sites. Thus, we believe that the way is paved for realizing pH-controlled all-atom molecular dynamics in the near future.
Prior, C; Danilāne, L; Oganesyan, V S
2018-05-16
We report the first application of fully atomistic molecular dynamics (MD) simulations to the prediction of electron paramagnetic resonance (EPR) spectra of spin labelled DNA. Models for two structurally different DNA spin probes with either the rigid or flexible position of the nitroxide group in the base pair, employed in experimental studies previously, have been developed. By the application of the combined MD-EPR simulation methodology we aimed at the following. Firstly, to provide a test bed against a sensitive spectroscopic technique for the recently developed improved version of the parmbsc1 force field for MD modelling of DNA. The predicted EPR spectra show good agreement with the experimental ones available from the literature, thus confirming the accuracy of the currently employed DNA force fields. Secondly, to provide a quantitative interpretation of the motional contributions into the dynamics of spin probes in both duplex and single-strand DNA fragments and to analyse their perturbing effects on the local DNA structure. Finally, a combination of MD and EPR allowed us to test the validity of the application of the Model-Free (M-F) approach coupled with the partial averaging of magnetic tensors to the simulation of EPR spectra of DNA systems by comparing the resultant EPR spectra with those simulated directly from MD trajectories. The advantage of the M-F based EPR simulation approach over the direct propagation techniques is that it requires motional and order parameters that can be calculated from shorter MD trajectories. The reported MD-EPR methodology is transferable to the prediction and interpretation of EPR spectra of higher order DNA structures with novel types of spin labels.
Popa, Vlad; Trecroce, Danielle A; McAllister, Robert G; Konermann, Lars
2016-06-16
Electrospray ionization mass spectrometry (ESI-MS) has become an indispensable technique for examining noncovalent protein complexes. Collision-induced dissociation (CID) of these multiply protonated gaseous ions usually culminates in ejection of a single subunit with a disproportionately large amount of charge. Experiments suggest that this process involves subunit unfolding prior to separation from the residual complex, as well as H(+) migration onto the unravelling chain. Molecular dynamics (MD) simulations are a promising avenue for gaining detailed insights into these CID events. Unfortunately, typical MD algorithms do not allow for mobile protons. Here we address this limitation by implementing a strategy that combines atomistic force fields (such as OPLS/AA and CHARMM36) with a proton hopping algorithm, focusing on the tetrameric complexes transthyretin and streptavidin. Protons are redistributed over all acidic and basic sites in 20 ps intervals, subject to an energy function that reflects electrostatic interactions and proton affinities. Our simulations predict that nativelike conformers at the onset of collisional heating contain multiple salt bridges. Collisional heating initially causes subtle structural changes that lead to a gradual decline of these zwitterionic patterns. Many of the MD runs show gradual unfolding of a single subunit in conjunction with H(+) migration, culminating in subunit separation from the complex. However, there are also instances where two or more chains start to unfold simultaneously, giving rise to charge competition. The scission point where the "winning" subunit separates from the complex can be attained for different degrees of unfolding, giving rise to product ions in various charge states. The simulated product ion distributions are in close agreement with experimental CID data. Proton enrichment in the departing subunit is driven by charge-charge repulsion, but the combination of salt bridge depletion, charge migration
Dixit, Surjit B; Mezei, Mihaly; Beveridge, David L
2012-07-01
Detailed analyses of the sequence-dependent solvation and ion atmosphere of DNA are presented based on molecular dynamics (MD) simulations on all the 136 unique tetranucleotide steps obtained by the ABC consortium using the AMBER suite of programs. Significant sequence effects on solvation and ion localization were observed in these simulations. The results were compared to essentially all known experimental data on the subject. Proximity analysis was employed to highlight the sequence dependent differences in solvation and ion localization properties in the grooves of DNA. Comparison of the MD-calculated DNA structure with canonical A- and B-forms supports the idea that the G/C-rich sequences are closer to canonical A- than B-form structures, while the reverse is true for the poly A sequences, with the exception of the alternating ATAT sequence. Analysis of hydration density maps reveals that the flexibility of solute molecule has a significant effect on the nature of observed hydration. Energetic analysis of solute-solvent interactions based on proximity analysis of solvent reveals that the GC or CG base pairs interact more strongly with water molecules in the minor groove of DNA that the AT or TA base pairs, while the interactions of the AT or TA pairs in the major groove are stronger than those of the GC or CG pairs. Computation of solvent-accessible surface area of the nucleotide units in the simulated trajectories reveals that the similarity with results derived from analysis of a database of crystallographic structures is excellent. The MD trajectories tend to follow Manning's counterion condensation theory, presenting a region of condensed counterions within a radius of about 17 A from the DNA surface independent of sequence. The GC and CG pairs tend to associate with cations in the major groove of the DNA structure to a greater extent than the AT and TA pairs. Cation association is more frequent in the minor groove of AT than the GC pairs. In general, the
Energy Technology Data Exchange (ETDEWEB)
Zheng, Wenjun, E-mail: wjzheng@buffalo.edu; Glenn, Paul [Department of Physics, University at Buffalo, Buffalo, New York 14260 (United States)
2015-01-21
The Bacteriophage T4 Lysozyme (T4L) is a prototype modular protein comprised of an N-terminal and a C-domain domain, which was extensively studied to understand the folding/unfolding mechanism of modular proteins. To offer detailed structural and dynamic insights to the folded-state stability and the mechanical unfolding behaviors of T4L, we have performed extensive equilibrium and steered molecular dynamics simulations of both the wild-type (WT) and a circular permutation (CP) variant of T4L using all-atom and coarse-grained force fields. Our all-atom and coarse-grained simulations of the folded state have consistently found greater stability of the C-domain than the N-domain in isolation, which is in agreement with past thermostatic studies of T4L. While the all-atom simulation cannot fully explain the mechanical unfolding behaviors of the WT and the CP variant observed in an optical tweezers study, the coarse-grained simulations based on the Go model or a modified elastic network model (mENM) are in qualitative agreement with the experimental finding of greater unfolding cooperativity in the WT than the CP variant. Interestingly, the two coarse-grained models predict different structural mechanisms for the observed change in cooperativity between the WT and the CP variant—while the Go model predicts minor modification of the unfolding pathways by circular permutation (i.e., preserving the general order that the N-domain unfolds before the C-domain), the mENM predicts a dramatic change in unfolding pathways (e.g., different order of N/C-domain unfolding in the WT and the CP variant). Based on our simulations, we have analyzed the limitations of and the key differences between these models and offered testable predictions for future experiments to resolve the structural mechanism for cooperative folding/unfolding of T4L.
International Nuclear Information System (INIS)
Cortini, Ruggero; Cheng, Xiaolin
2017-01-01
Electrostatic interactions between DNA molecules have been extensively studied experimentally and theoretically, but several aspects (e.g. its role in determining the pitch of the cholesteric DNA phase) still remain unclear. Here, we performed large-scale all-atom molecular dynamics simulations in explicit water and 150 mM sodium chloride, to reconstruct the potential of mean force (PMF) of two DNA oligomers 24 base pairs long as a function of their interaxial angle and intermolecular distance. We find that the potential of mean force is dominated by total DNA charge, and not by the helical geometry of its charged groups. The theory of homogeneously charged cylinders fits well all our simulation data, and the fit yields the optimal value of the total compensated charge on DNA to ≈65% of its total fixed charge (arising from the phosphorous atoms), close to the value expected from Manning's theory of ion condensation. The PMF calculated from our simulations does not show a significant dependence on the handedness of the angle between the two DNA molecules, or its size is on the order of 1k B T. Thermal noise for molecules of the studied length seems to mask the effect of detailed helical charge patterns of DNA. The fact that in monovalent salt the effective interaction between two DNA molecules is independent on the handedness of the tilt may suggest that alternative mechanisms are required to understand the cholesteric phase of DNA.
Directory of Open Access Journals (Sweden)
Haruki Nakamura
2012-02-01
Full Text Available The phosphorylated kinase-inducible activation domain (pKID adopts a helix–loop–helix structure upon binding to its partner KIX, although it is unstructured in the unbound state. The N-terminal and C-terminal regions of pKID, which adopt helices in the complex, are called, respectively, αA and αB. We performed all-atom multicanonical molecular dynamics simulations of pKID with and without KIX in explicit solvents to generate conformational ensembles. Although the unbound pKID was disordered overall, αA and αB exhibited a nascent helix propensity; the propensity of αA was stronger than that of αB, which agrees with experimental results. In the bound state, the free-energy landscape of αB involved two low free-energy fractions: native-like and non-native fractions. This result suggests that αB folds according to the induced-fit mechanism. The αB-helix direction was well aligned as in the NMR complex structure, although the αA helix exhibited high flexibility. These results also agree quantitatively with experimental observations. We have detected that the αB helix can bind to another site of KIX, to which another protein MLL also binds with the adopting helix. Consequently, MLL can facilitate pKID binding to the pKID-binding site by blocking the MLL-binding site. This also supports experimentally obtained results.
Directory of Open Access Journals (Sweden)
Carles Calero
2016-04-01
Full Text Available Hydration water determines the stability and function of phospholipid membranes as well as the interaction of membranes with other molecules. Experiments and simulations have shown that water dynamics slows down dramatically as the hydration decreases, suggesting that the interfacial water that dominates the average dynamics at low hydration is slower than water away from the membrane. Here, based on all-atom molecular dynamics simulations, we provide an interpretation of the slowdown of interfacial water in terms of the structure and dynamics of water–water and water–lipid hydrogen bonds (HBs. We calculate the rotational and translational slowdown of the dynamics of water confined in stacked phospholipid membranes at different levels of hydration, from completely hydrated to poorly hydrated membranes. For all hydrations, we analyze the distribution of HBs and find that water–lipids HBs last longer than water–water HBs and that at low hydration most of the water is in the interior of the membrane. We also show that water–water HBs become more persistent as the hydration is lowered. We attribute this effect (i to HBs between water molecules that form, in turn, persistent HBs with lipids; (ii to the hindering of the H-bonding switching between water molecules due to the lower water density at the interface; and (iii to the higher probability of water–lipid HBs as the hydration decreases. Our interpretation of the large dynamic slowdown in water under dehydration is potentially relevant in understanding membrane biophysics at different hydration levels.
Mulholland, Kelly; Siddiquei, Farzana; Wu, Chun
2017-07-19
RHPS4, a potent binder to human telomeric DNA G-quadruplex, shows high efficacy in tumor cell growth inhibition. However, it's preferential binding to DNA G-quadruplex over DNA duplex (about 10 fold) remains to be improved toward its clinical application. A high resolution structure of the single-stranded telomeric DNA G-quadruplexes, or B-DNA duplex, in complex with RHPS4 is not available yet, and the binding nature of this ligand to these DNA forms remains to be elusive. In this study, we carried out 40 μs molecular dynamics binding simulations with a free ligand to decipher the binding pathway of RHPS4 to a DNA duplex and three G-quadruplex folders (parallel, antiparallel and hybrid) of the human telomeric DNA sequence. The most stable binding mode identified for the duplex, parallel, antiparallel and hybrid G-quadruplexes is an intercalation, bottom stacking, top intercalation and bottom intercalation mode, respectively. The intercalation mode with similar binding strength to both the duplex and the G-quadruplexes, explains the lack of binding selectivity of RHPS4 to the G-quadruplex form. Therefore, a ligand modification that destabilizes the duplex intercalation mode but stabilizes the G-quadruplex intercalation mode will improve the binding selectivity toward G-quadruplex. The intercalation mode of RHPS4 to both the duplex and the antiparallel and the hybrid G-quadruplex follows a base flipping-insertion mechanism rather than an open-insertion mechanism. The groove binding, the side binding and the intercalation with flipping out of base were observed to be intermediate states before the full intercalation state with paired bases.
Switching dynamics in reaction networks induced by molecular discreteness
International Nuclear Information System (INIS)
Togashi, Yuichi; Kaneko, Kunihiko
2007-01-01
To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states
Explicit all-atom modeling of realistically sized ligand-capped nanocrystals
Kaushik, Ananth P.; Clancy, Paulette
2012-01-01
We present a study of an explicit all-atom representation of nanocrystals of experimentally relevant sizes (up to 6 nm), capped with alkyl chain ligands, in vacuum. We employ all-atom molecular dynamics simulation methods in concert with a well
Bernardes, Carlos E S; Canongia Lopes, José N; Minas da Piedade, Manuel E
2013-10-31
A previously developed OPLS-based all-atom force field for organometallic compounds was extended to a series of first-, second-, and third-row transition metals based on the study of M(CO)(n) (M = Cr, Fe, Ni, Mo, Ru, or W) complexes. For materials that are solid at ambient temperature and pressure (M = Cr, Mo, W) the validation of the force field was based on reported structural data and on the standard molar enthalpies of sublimation at 298.15 K, experimentally determined by Calvet-drop microcalorimetry using samples corresponding to a specific and well-characterized crystalline phase: Δ(sub)H(m)° = 72.6 ± 0.3 kJ·mol(–1) for Cr(CO)(6), 73.4 ± 0.3 kJ·mol(–1) for Mo(CO)(6), and 77.8 ± 0.3 kJ·mol(–1) for W(CO)(6). For liquids, where problems of polymorphism or phase mixtures are absent, critically analyzed literature data were used. The force field was able to reproduce the volumetric properties of the test set (density and unit cell volume) with an average deviations smaller than 2% and the experimentally determined enthalpies of sublimation and vaporization with an accuracy better than 2.3 kJ·mol(–1). The Lennard-Jones (12-6) potential function parameters used to calculate the repulsive and dispersion contributions of the metals within the framework of the force field were found to be transferable between chromium, iron, and nickel (first row) and between molybdenum and ruthenium (second row).
Constant pressure and temperature discrete-time Langevin molecular dynamics
Energy Technology Data Exchange (ETDEWEB)
Grønbech-Jensen, Niels [Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States); Department of Mathematics, University of California, Davis, California 95616 (United States); Farago, Oded [Department of Biomedical Engineering, Ben Gurion University of the Negev, Be' er Sheva 84105 (Israel); Ilse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Be' er Sheva 84105 (Israel)
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
Discrete Biogeography Based Optimization for Feature Selection in Molecular Signatures.
Liu, Bo; Tian, Meihong; Zhang, Chunhua; Li, Xiangtao
2015-04-01
Biomarker discovery from high-dimensional data is a complex task in the development of efficient cancer diagnoses and classification. However, these data are usually redundant and noisy, and only a subset of them present distinct profiles for different classes of samples. Thus, selecting high discriminative genes from gene expression data has become increasingly interesting in the field of bioinformatics. In this paper, a discrete biogeography based optimization is proposed to select the good subset of informative gene relevant to the classification. In the proposed algorithm, firstly, the fisher-markov selector is used to choose fixed number of gene data. Secondly, to make biogeography based optimization suitable for the feature selection problem; discrete migration model and discrete mutation model are proposed to balance the exploration and exploitation ability. Then, discrete biogeography based optimization, as we called DBBO, is proposed by integrating discrete migration model and discrete mutation model. Finally, the DBBO method is used for feature selection, and three classifiers are used as the classifier with the 10 fold cross-validation method. In order to show the effective and efficiency of the algorithm, the proposed algorithm is tested on four breast cancer dataset benchmarks. Comparison with genetic algorithm, particle swarm optimization, differential evolution algorithm and hybrid biogeography based optimization, experimental results demonstrate that the proposed method is better or at least comparable with previous method from literature when considering the quality of the solutions obtained. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Explicit all-atom modeling of realistically sized ligand-capped nanocrystals
Kaushik, Ananth P.
2012-01-01
We present a study of an explicit all-atom representation of nanocrystals of experimentally relevant sizes (up to 6 nm), capped with alkyl chain ligands, in vacuum. We employ all-atom molecular dynamics simulation methods in concert with a well-tested intermolecular potential model, MM3 (molecular mechanics 3), for the studies presented here. These studies include determining the preferred conformation of an isolated single nanocrystal (NC), pairs of isolated NCs, and (presaging studies of superlattice arrays) unit cells of NC superlattices. We observe that very small NCs (3 nm) behave differently in a superlattice as compared to larger NCs (6 nm and above) due to the conformations adopted by the capping ligands on the NC surface. Short ligands adopt a uniform distribution of orientational preferences, including some that lie against the face of the nanocrystal. In contrast, longer ligands prefer to interdigitate. We also study the effect of changing ligand length and ligand coverage on the NCs on the preferred ligand configurations. Since explicit all-atom modeling constrains the maximum system size that can be studied, we discuss issues related to coarse-graining the representation of the ligands, including a comparison of two commonly used coarse-grained models. We find that care has to be exercised in the choice of coarse-grained model. The data provided by these realistically sized ligand-capped NCs, determined using explicit all-atom models, should serve as a reference standard for future models of coarse-graining ligands using united atom models, especially for self-assembly processes. © 2012 American Institute of Physics.
Complete all-atom hydrodynamics of protein unfolding in uniform flow
International Nuclear Information System (INIS)
Wang, Guan M; Sandberg, William C
2010-01-01
The unfolding dynamics of a protein, ubiquitin, pinned in several uniform flows, was studied at low and high flow rates in an all-atom style through a non-equilibrium molecular dynamics approach with explicit water molecules included. Atomic hydrodynamic force components on individual amino acids, as a function of time, due to the collisional interactions with the flowing water molecules were calculated explicitly. The protein conformational change in response to those time-varying forces was computed completely at the high flow rate up to nanosecond until the fully stretched state was reached. The end-to-end length of the single ubiquitin protein molecule at high flow rate is smoothly increasing. The step-like jumps between metastable states that describe the μm ms -1 scale force pulling experiments conducted on polyubiquitins at low flow rates, are not seen at the high flow speeds necessary to computationally probe the ns nm -1 scale regime. No unfolding was observed in the low flow rate atomic computations at nanosecond scale while partial and complete unfolding was observed in the coarse-grained low flow rate computations at microsecond scale. Examination of the all-atom computation of the time variation of the hydrodynamic forces on, and the velocity components of, the protein molecule unveiled to some extent the details of the complexity of the hydrodynamic friction variation in the nm ns -1 regime of high rate flow-driven protein unfolding. This demonstrates quantitatively that all-atom computations are more suitable than the Langevin equation or Brownian dynamics methods for probing the interaction dynamics and resulting conformational dynamics of protein unfolding in strong flows on nm ns -1 time/length scales while the reverse is true for investigation of slow, diffusively driven systems.
Beyond Modeling: All-Atom Olfactory Receptor Model Simulations
Directory of Open Access Journals (Sweden)
Peter C Lai
2012-05-01
Full Text Available Olfactory receptors (ORs are a type of GTP-binding protein-coupled receptor (GPCR. These receptors are responsible for mediating the sense of smell through their interaction with odor ligands. OR-odorant interactions marks the first step in the process that leads to olfaction. Computational studies on model OR structures can validate experimental functional studies as well as generate focused and novel hypotheses for further bench investigation by providing a view of these interactions at the molecular level. Here we have shown the specific advantages of simulating the dynamic environment that is associated with OR-odorant interactions. We present a rigorous methodology that ranges from the creation of a computationally-derived model of an olfactory receptor to simulating the interactions between an OR and an odorant molecule. Given the ubiquitous occurrence of GPCRs in the membranes of cells, we anticipate that our OR-developed methodology will serve as a model for the computational structural biology of all GPCRs.
Energy landscape of all-atom protein-protein interactions revealed by multiscale enhanced sampling.
Directory of Open Access Journals (Sweden)
Kei Moritsugu
2014-10-01
Full Text Available Protein-protein interactions are regulated by a subtle balance of complicated atomic interactions and solvation at the interface. To understand such an elusive phenomenon, it is necessary to thoroughly survey the large configurational space from the stable complex structure to the dissociated states using the all-atom model in explicit solvent and to delineate the energy landscape of protein-protein interactions. In this study, we carried out a multiscale enhanced sampling (MSES simulation of the formation of a barnase-barstar complex, which is a protein complex characterized by an extraordinary tight and fast binding, to determine the energy landscape of atomistic protein-protein interactions. The MSES adopts a multicopy and multiscale scheme to enable for the enhanced sampling of the all-atom model of large proteins including explicit solvent. During the 100-ns MSES simulation of the barnase-barstar system, we observed the association-dissociation processes of the atomistic protein complex in solution several times, which contained not only the native complex structure but also fully non-native configurations. The sampled distributions suggest that a large variety of non-native states went downhill to the stable complex structure, like a fast folding on a funnel-like potential. This funnel landscape is attributed to dominant configurations in the early stage of the association process characterized by near-native orientations, which will accelerate the native inter-molecular interactions. These configurations are guided mostly by the shape complementarity between barnase and barstar, and lead to the fast formation of the final complex structure along the downhill energy landscape.
Li, Xianfeng; Murthy, N. Sanjeeva; Becker, Matthew L.; Latour, Robert A.
2016-01-01
A multiscale modeling approach is presented for the efficient construction of an equilibrated all-atom model of a cross-linked poly(ethylene glycol) (PEG)-based hydrogel using the all-atom polymer consistent force field (PCFF). The final equilibrated all-atom model was built with a systematic simulation toolset consisting of three consecutive parts: (1) building a global cross-linked PEG-chain network at experimentally determined cross-link density using an on-lattice Monte Carlo method based on the bond fluctuation model, (2) recovering the local molecular structure of the network by transitioning from the lattice model to an off-lattice coarse-grained (CG) model parameterized from PCFF, followed by equilibration using high performance molecular dynamics methods, and (3) recovering the atomistic structure of the network by reverse mapping from the equilibrated CG structure, hydrating the structure with explicitly represented water, followed by final equilibration using PCFF parameterization. The developed three-stage modeling approach has application to a wide range of other complex macromolecular hydrogel systems, including the integration of peptide, protein, and/or drug molecules as side-chains within the hydrogel network for the incorporation of bioactivity for tissue engineering, regenerative medicine, and drug delivery applications. PMID:27013229
Energy Technology Data Exchange (ETDEWEB)
Spellings, Matthew [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Marson, Ryan L. [Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Anderson, Joshua A. [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Glotzer, Sharon C., E-mail: sglotzer@umich.edu [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States)
2017-04-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks–Chandler–Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
A real-time all-atom structural search engine for proteins.
Gonzalez, Gabriel; Hannigan, Brett; DeGrado, William F
2014-07-01
Protein designers use a wide variety of software tools for de novo design, yet their repertoire still lacks a fast and interactive all-atom search engine. To solve this, we have built the Suns program: a real-time, atomic search engine integrated into the PyMOL molecular visualization system. Users build atomic-level structural search queries within PyMOL and receive a stream of search results aligned to their query within a few seconds. This instant feedback cycle enables a new "designability"-inspired approach to protein design where the designer searches for and interactively incorporates native-like fragments from proven protein structures. We demonstrate the use of Suns to interactively build protein motifs, tertiary interactions, and to identify scaffolds compatible with hot-spot residues. The official web site and installer are located at http://www.degradolab.org/suns/ and the source code is hosted at https://github.com/godotgildor/Suns (PyMOL plugin, BSD license), https://github.com/Gabriel439/suns-cmd (command line client, BSD license), and https://github.com/Gabriel439/suns-search (search engine server, GPLv2 license).
Preformed template fluctuations promote fibril formation: Insights from lattice and all-atom models
Energy Technology Data Exchange (ETDEWEB)
Kouza, Maksim, E-mail: mkouza@chem.uw.edu.pl; Kolinski, Andrzej [Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warszaw (Poland); Co, Nguyen Truong [Department of Physics, Institute of Technology, National University of HCM City, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City (Viet Nam); Institute for Computational Science and Technology, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City (Viet Nam); Nguyen, Phuong H. [Laboratoire de Biochimie Theorique, UPR 9080 CNRS, IBPC, Universite Paris 7, 13 rue Pierre et Marie Curie, 75005 Paris (France); Li, Mai Suan, E-mail: masli@ifpan.edu.pl [Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw (Poland)
2015-04-14
Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer’s and Parkinson’s diseases. Despite the fact that the fibril formation process is very slow and thus poses a significant challenge for theoretical and experimental studies, a number of alternative pictures of molecular mechanisms of amyloid fibril formation have been recently proposed. What seems to be common for the majority of the proposed models is that fibril elongation involves the formation of pre-nucleus seeds prior to the creation of a critical nucleus. Once the size of the pre-nucleus seed reaches the critical nucleus size, its thermal fluctuations are expected to be small and the resulting nucleus provides a template for sequential (one-by-one) accommodation of added monomers. The effect of template fluctuations on fibril formation rates has not been explored either experimentally or theoretically so far. In this paper, we make the first attempt at solving this problem by two sets of simulations. To mimic small template fluctuations, in one set, monomers of the preformed template are kept fixed, while in the other set they are allowed to fluctuate. The kinetics of addition of a new peptide onto the template is explored using all-atom simulations with explicit water and the GROMOS96 43a1 force field and simple lattice models. Our result demonstrates that preformed template fluctuations can modulate protein aggregation rates and pathways. The association of a nascent monomer with the template obeys the kinetics partitioning mechanism where the intermediate state occurs in a fraction of routes to the protofibril. It was shown that template immobility greatly increases the time of incorporating a new peptide into the preformed template compared to the fluctuating template case. This observation has also been confirmed by simulation using lattice models and may be invoked to understand the role of template fluctuations in
MolProbity: all-atom structure validation for macromolecular crystallography
International Nuclear Information System (INIS)
Chen, Vincent B.; Arendall, W. Bryan III; Headd, Jeffrey J.; Keedy, Daniel A.; Immormino, Robert M.; Kapral, Gary J.; Murray, Laura W.; Richardson, Jane S.; Richardson, David C.
2010-01-01
MolProbity structure validation will diagnose most local errors in macromolecular crystal structures and help to guide their correction. MolProbity is a structure-validation web service that provides broad-spectrum solidly based evaluation of model quality at both the global and local levels for both proteins and nucleic acids. It relies heavily on the power and sensitivity provided by optimized hydrogen placement and all-atom contact analysis, complemented by updated versions of covalent-geometry and torsion-angle criteria. Some of the local corrections can be performed automatically in MolProbity and all of the diagnostics are presented in chart and graphical forms that help guide manual rebuilding. X-ray crystallography provides a wealth of biologically important molecular data in the form of atomic three-dimensional structures of proteins, nucleic acids and increasingly large complexes in multiple forms and states. Advances in automation, in everything from crystallization to data collection to phasing to model building to refinement, have made solving a structure using crystallography easier than ever. However, despite these improvements, local errors that can affect biological interpretation are widespread at low resolution and even high-resolution structures nearly all contain at least a few local errors such as Ramachandran outliers, flipped branched protein side chains and incorrect sugar puckers. It is critical both for the crystallographer and for the end user that there are easy and reliable methods to diagnose and correct these sorts of errors in structures. MolProbity is the authors’ contribution to helping solve this problem and this article reviews its general capabilities, reports on recent enhancements and usage, and presents evidence that the resulting improvements are now beneficially affecting the global database
Mathematical biology modules based on modern molecular biology and modern discrete mathematics.
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.
Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics
Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955
The Molecular Basis of Toxins’ Interactions with Intracellular Signaling via Discrete Portals
Directory of Open Access Journals (Sweden)
Adi Lahiani
2017-03-01
Full Text Available An understanding of the molecular mechanisms by which microbial, plant or animal-secreted toxins exert their action provides the most important element for assessment of human health risks and opens new insights into therapies addressing a plethora of pathologies, ranging from neurological disorders to cancer, using toxinomimetic agents. Recently, molecular and cellular biology dissecting tools have provided a wealth of information on the action of these diverse toxins, yet, an integrated framework to explain their selective toxicity is still lacking. In this review, specific examples of different toxins are emphasized to illustrate the fundamental mechanisms of toxicity at different biochemical, molecular and cellular- levels with particular consideration for the nervous system. The target of primary action has been highlighted and operationally classified into 13 sub-categories. Selected examples of toxins were assigned to each target category, denominated as portal, and the modulation of the different portal’s signaling was featured. The first portal encompasses the plasma membrane lipid domains, which give rise to pores when challenged for example with pardaxin, a fish toxin, or is subject to degradation when enzymes of lipid metabolism such as phospholipases A2 (PLA2 or phospholipase C (PLC act upon it. Several major portals consist of ion channels, pumps, transporters and ligand gated ionotropic receptors which many toxins act on, disturbing the intracellular ion homeostasis. Another group of portals consists of G-protein-coupled and tyrosine kinase receptors that, upon interaction with discrete toxins, alter second messengers towards pathological levels. Lastly, subcellular organelles such as mitochondria, nucleus, protein- and RNA-synthesis machineries, cytoskeletal networks and exocytic vesicles are also portals targeted and deregulated by other diverse group of toxins. A fundamental concept can be drawn from these seemingly different
Elucidation of amyloid beta-protein oligomerization mechanisms: discrete molecular dynamics study.
Urbanc, B; Betnel, M; Cruz, L; Bitan, G; Teplow, D B
2010-03-31
Oligomers of amyloid beta-protein (Abeta) play a central role in the pathology of Alzheimer's disease. Of the two predominant Abeta alloforms, Abeta(1-40) and Abeta(1-42), Abeta(1-42) is more strongly implicated in the disease. We elucidated the structural characteristics of oligomers of Abeta(1-40) and Abeta(1-42) and their Arctic mutants, [E22G]Abeta(1-40) and [E22G]Abeta(1-42). We simulated oligomer formation using discrete molecular dynamics (DMD) with a four-bead protein model, backbone hydrogen bonding, and residue-specific interactions due to effective hydropathy and charge. For all four peptides under study, we derived the characteristic oligomer size distributions that were in agreement with prior experimental findings. Unlike Abeta(1-40), Abeta(1-42) had a high propensity to form paranuclei (pentameric or hexameric) structures that could self-associate into higher-order oligomers. Neither of the Arctic mutants formed higher-order oligomers, but [E22G]Abeta(1-40) formed paranuclei with a similar propensity to that of Abeta(1-42). Whereas the best agreement with the experimental data was obtained when the charged residues were modeled as solely hydrophilic, further assembly from spherical oligomers into elongated protofibrils was induced by nonzero electrostatic interactions among the charged residues. Structural analysis revealed that the C-terminal region played a dominant role in Abeta(1-42) oligomer formation whereas Abeta(1-40) oligomerization was primarily driven by intermolecular interactions among the central hydrophobic regions. The N-terminal region A2-F4 played a prominent role in Abeta(1-40) oligomerization but did not contribute to the oligomerization of Abeta(1-42) or the Arctic mutants. The oligomer structure of both Arctic peptides resembled Abeta(1-42) more than Abeta(1-40), consistent with their potentially more toxic nature.
International Nuclear Information System (INIS)
More, Ameya; Dutta, B.K.; Durgaprasad, P.V.; Arya, A.K.
2012-01-01
Fe-Cr based Ferritic/Martensitic (F/M) steels are the candidate structural materials for future fusion reactors. In this work, a multi-scale approach comprising atomistic Molecular Dynamics (MD) simulations and Discrete Dislocation Dynamics (DDD) simulations are used to model the effect of irradiation dose on the flow stress of F/M steels. At the atomic scale, molecular dynamics simulations are used to study the dislocation interaction with irradiation induced defects, i.e. voids and He bubbles. Whereas, the DDD simulations are used to estimate the change in flow stress of the material as a result of irradiation hardening. (author)
Protein folding simulations: from coarse-grained model to all-atom model.
Zhang, Jian; Li, Wenfei; Wang, Jun; Qin, Meng; Wu, Lei; Yan, Zhiqiang; Xu, Weixin; Zuo, Guanghong; Wang, Wei
2009-06-01
Protein folding is an important and challenging problem in molecular biology. During the last two decades, molecular dynamics (MD) simulation has proved to be a paramount tool and was widely used to study protein structures, folding kinetics and thermodynamics, and structure-stability-function relationship. It was also used to help engineering and designing new proteins, and to answer even more general questions such as the minimal number of amino acid or the evolution principle of protein families. Nowadays, the MD simulation is still undergoing rapid developments. The first trend is to toward developing new coarse-grained models and studying larger and more complex molecular systems such as protein-protein complex and their assembling process, amyloid related aggregations, and structure and motion of chaperons, motors, channels and virus capsides; the second trend is toward building high resolution models and explore more detailed and accurate pictures of protein folding and the associated processes, such as the coordination bond or disulfide bond involved folding, the polarization, charge transfer and protonate/deprotonate process involved in metal coupled folding, and the ion permeation and its coupling with the kinetics of channels. On these new territories, MD simulations have given many promising results and will continue to offer exciting views. Here, we review several new subjects investigated by using MD simulations as well as the corresponding developments of appropriate protein models. These include but are not limited to the attempt to go beyond the topology based Gō-like model and characterize the energetic factors in protein structures and dynamics, the study of the thermodynamics and kinetics of disulfide bond involved protein folding, the modeling of the interactions between chaperonin and the encapsulated protein and the protein folding under this circumstance, the effort to clarify the important yet still elusive folding mechanism of protein BBL
International Nuclear Information System (INIS)
Rescigno, T.N.; Bender, C.F.; McKoy, B.V.; Langhoff, P.W.
1978-01-01
Theoretical investigations of photoexcitation and ionization cross sections in molecular nitrogen are reported employing the recently devised Stieltjes--Tchebycheff moment-theory technique in the static-exchange approximation. The coupled-channel equations for photoabsorption are separated approximately by identifying the important physically distinct excitation processes associated with formation of the three lowest electronic states of the parent molecular ion. Approximate Rydberg series and pseudospectra of transition frequencies and oscillator strengths are constructed for the seven individual channel components identified using Hartree--Fock ionic core functions and normalizable Gaussian orbitals to describe the photoexcited and ejected electrons. Detailed comparisons of the theoretically determined discrete excitation series with available spectral data indicate general accord between the calculated and observed excitation frequencies and oscillator strengths, although there are some discrepancies and certain Rydberg series have apparently not yet been identified in the measured spectra. The total Stieltjes--Tchebycheff vertical photoionization cross section obtained from the discrete pseudospectra is in excellent agreement with recent electron--ion coincidence measurement of the cross section for parent--ion production from threshold to 50 eV excitation energy. Similarly, e calculated vertical partial cross sections for the production of the three lowest electronic states in the parent molecular ion are in excellent accord with the results of recent electron--electron coincidence and synchrotron--radiation branching ratio measurements. The origins of particularly intense resonancelike features in the discrete and continuum portions of the photoabsorption cross sections are discussed in terms of excitations into valencelike molecular orbitals
DeMarco, Kevin R; Bekker, Slava; Clancy, Colleen E; Noskov, Sergei Y; Vorobyov, Igor
2018-01-01
Interactions of drug molecules with lipid membranes play crucial role in their accessibility of cellular targets and can be an important predictor of their therapeutic and safety profiles. Very little is known about spatial localization of various drugs in the lipid bilayers, their active form (ionization state) or translocation rates and therefore potency to bind to different sites in membrane proteins. All-atom molecular simulations may help to map drug partitioning kinetics and thermodynamics, thus providing in-depth assessment of drug lipophilicity. As a proof of principle, we evaluated extensively lipid membrane partitioning of d-sotalol, well-known blocker of a cardiac potassium channel K v 11.1 encoded by the hERG gene, with reported substantial proclivity for arrhythmogenesis. We developed the positively charged (cationic) and neutral d-sotalol models, compatible with the biomolecular CHARMM force field, and subjected them to all-atom molecular dynamics (MD) simulations of drug partitioning through hydrated lipid membranes, aiming to elucidate thermodynamics and kinetics of their translocation and thus putative propensities for hydrophobic and aqueous hERG access. We found that only a neutral form of d-sotalol accumulates in the membrane interior and can move across the bilayer within millisecond time scale, and can be relevant to a lipophilic channel access. The computed water-membrane partitioning coefficient for this form is in good agreement with experiment. There is a large energetic barrier for a cationic form of the drug, dominant in water, to cross the membrane, resulting in slow membrane translocation kinetics. However, this form of the drug can be important for an aqueous access pathway through the intracellular gate of hERG. This route will likely occur after a neutral form of a drug crosses the membrane and subsequently re-protonates. Our study serves to demonstrate a first step toward a framework for multi-scale in silico safety pharmacology
Directory of Open Access Journals (Sweden)
Kevin R. DeMarco
2018-02-01
Full Text Available Interactions of drug molecules with lipid membranes play crucial role in their accessibility of cellular targets and can be an important predictor of their therapeutic and safety profiles. Very little is known about spatial localization of various drugs in the lipid bilayers, their active form (ionization state or translocation rates and therefore potency to bind to different sites in membrane proteins. All-atom molecular simulations may help to map drug partitioning kinetics and thermodynamics, thus providing in-depth assessment of drug lipophilicity. As a proof of principle, we evaluated extensively lipid membrane partitioning of d-sotalol, well-known blocker of a cardiac potassium channel Kv11.1 encoded by the hERG gene, with reported substantial proclivity for arrhythmogenesis. We developed the positively charged (cationic and neutral d-sotalol models, compatible with the biomolecular CHARMM force field, and subjected them to all-atom molecular dynamics (MD simulations of drug partitioning through hydrated lipid membranes, aiming to elucidate thermodynamics and kinetics of their translocation and thus putative propensities for hydrophobic and aqueous hERG access. We found that only a neutral form of d-sotalol accumulates in the membrane interior and can move across the bilayer within millisecond time scale, and can be relevant to a lipophilic channel access. The computed water-membrane partitioning coefficient for this form is in good agreement with experiment. There is a large energetic barrier for a cationic form of the drug, dominant in water, to cross the membrane, resulting in slow membrane translocation kinetics. However, this form of the drug can be important for an aqueous access pathway through the intracellular gate of hERG. This route will likely occur after a neutral form of a drug crosses the membrane and subsequently re-protonates. Our study serves to demonstrate a first step toward a framework for multi-scale in silico safety
Hu, Yuan; Sinha, Sudipta Kumar; Patel, Sandeep
2014-10-16
Using the translocation of short, charged cationic oligo-arginine peptides (mono-, di-, and triarginine) from bulk aqueous solution into model DMPC bilayers, we explore the question of the similarity of thermodynamic and structural predictions obtained from molecular dynamics simulations using all-atom and Martini coarse-grain force fields. Specifically, we estimate potentials of mean force associated with translocation using standard all-atom (CHARMM36 lipid) and polarizable and nonpolarizable Martini force fields, as well as a series of modified Martini-based parameter sets. We find that we are able to reproduce qualitative features of potentials of mean force of single amino acid side chain analogues into model bilayers. In particular, modifications of peptide-water and peptide-membrane interactions allow prediction of free energy minima at the bilayer-water interface as obtained with all-atom force fields. In the case of oligo-arginine peptides, the modified parameter sets predict interfacial free energy minima as well as free energy barriers in almost quantitative agreement with all-atom force field based simulations. Interfacial free energy minima predicted by a modified coarse-grained parameter set are -2.51, -4.28, and -5.42 for mono-, di-, and triarginine; corresponding values from all-atom simulations are -0.83, -3.33, and -3.29, respectively, all in units of kcal/mol. We found that a stronger interaction between oligo-arginine and the membrane components and a weaker interaction between oligo-arginine and water are crucial for producing such minima in PMFs using the polarizable CG model. The difference between bulk aqueous and bilayer center states predicted by the modified coarse-grain force field are 11.71, 14.14, and 16.53 kcal/mol, and those by the all-atom model are 6.94, 8.64, and 12.80 kcal/mol; those are of almost the same order of magnitude. Our simulations also demonstrate a remarkable similarity in the structural aspects of the ensemble of
Genheden, Samuel
2017-10-01
We present the estimation of solvation free energies of small solutes in water, n-octanol and hexane using molecular dynamics simulations with two MARTINI models at different resolutions, viz. the coarse-grained (CG) and the hybrid all-atom/coarse-grained (AA/CG) models. From these estimates, we also calculate the water/hexane and water/octanol partition coefficients. More than 150 small, organic molecules were selected from the Minnesota solvation database and parameterized in a semi-automatic fashion. Using either the CG or hybrid AA/CG models, we find considerable deviations between the estimated and experimental solvation free energies in all solvents with mean absolute deviations larger than 10 kJ/mol, although the correlation coefficient is between 0.55 and 0.75 and significant. There is also no difference between the results when using the non-polarizable and polarizable water model, although we identify some improvements when using the polarizable model with the AA/CG solutes. In contrast to the estimated solvation energies, the estimated partition coefficients are generally excellent with both the CG and hybrid AA/CG models, giving mean absolute deviations between 0.67 and 0.90 log units and correlation coefficients larger than 0.85. We analyze the error distribution further and suggest avenues for improvements.
Genheden, Samuel
2017-10-01
We present the estimation of solvation free energies of small solutes in water, n-octanol and hexane using molecular dynamics simulations with two MARTINI models at different resolutions, viz. the coarse-grained (CG) and the hybrid all-atom/coarse-grained (AA/CG) models. From these estimates, we also calculate the water/hexane and water/octanol partition coefficients. More than 150 small, organic molecules were selected from the Minnesota solvation database and parameterized in a semi-automatic fashion. Using either the CG or hybrid AA/CG models, we find considerable deviations between the estimated and experimental solvation free energies in all solvents with mean absolute deviations larger than 10 kJ/mol, although the correlation coefficient is between 0.55 and 0.75 and significant. There is also no difference between the results when using the non-polarizable and polarizable water model, although we identify some improvements when using the polarizable model with the AA/CG solutes. In contrast to the estimated solvation energies, the estimated partition coefficients are generally excellent with both the CG and hybrid AA/CG models, giving mean absolute deviations between 0.67 and 0.90 log units and correlation coefficients larger than 0.85. We analyze the error distribution further and suggest avenues for improvements.
Ceccarelli, Michele; Barthel, Floris P.; Malta, Tathiane M.; Sabedot, Thais S.; Salama, Sofie R.; Murray, Bradley A.; Morozova, Olena; Newton, Yulia; Radenbaugh, Amie; Pagnotta, Stefano M.; Anjum, Samreen; Wang, Jiguang; Manyam, Ganiraju; Zoppoli, Pietro; Ling, Shiyung; Rao, Arjun A.; Grifford, Mia; Cherniack, Andrew D.; Zhang, Hailei; Poisson, Laila; Carlotti, Carlos Gilberto; Pretti da Cunha Tirapelli, Daniela; Rao, Arvind; Mikkelsen, Tom; Lau, Ching C.; Yung, W.K. Alfred; Rabadan, Raul; Huse, Jason; Brat, Daniel J.; Lehman, Norman L.; Barnholtz-Sloan, Jill S.; Zheng, Siyuan; Hess, Kenneth; Rao, Ganesh; Meyerson, Matthew; Beroukhim, Rameen; Cooper, Lee; Akbani, Rehan; Wrensch, Margaret; Haussler, David; Aldape, Kenneth D.; Laird, Peter W.; Gutmann, David H.; Noushmehr, Houtan; Iavarone, Antonio; Verhaak, Roel G.W.
2015-01-01
SUMMARY Therapy development for adult diffuse glioma is hindered by incomplete knowledge of somatic glioma driving alterations and suboptimal disease classification. We defined the complete set of genes associated with 1,122 diffuse grade II-III-IV gliomas from The Cancer Genome Atlas and used molecular profiles to improve disease classification, identify molecular correlations, and provide insights into the progression from low- to high-grade disease. Whole genome sequencing data analysis determined that ATRX but not TERT promoter mutations are associated with increased telomere length. Recent advances in glioma classification based on IDH mutation and 1p/19q co-deletion status were recapitulated through analysis of DNA methylation profiles, which identified clinically relevant molecular subsets. A subtype of IDH-mutant glioma was associated with DNA demethylation and poor outcome; a group of IDH-wildtype diffuse glioma showed molecular similarity to pilocytic astrocytoma and relatively favorable survival. Understanding of cohesive disease groups may aid improved clinical outcomes. PMID:26824661
Examining the origins of the hydration force between lipid bilayers using all-atom simulations.
Gentilcore, Anastasia N; Michaud-Agrawal, Naveen; Crozier, Paul S; Stevens, Mark J; Woolf, Thomas B
2010-05-01
Using 237 all-atom double bilayer simulations, we examined the thermodynamic and structural changes that occur as a phosphatidylcholine lipid bilayer stack is dehydrated. The simulated system represents a micropatch of lipid multilayer systems that are studied experimentally using surface force apparatus, atomic force microscopy and osmotic pressure studies. In these experiments, the hydration level of the system is varied, changing the separation between the bilayers, in order to understand the forces that the bilayers feel as they are brought together. These studies have found a curious, strongly repulsive force when the bilayers are very close to each other, which has been termed the "hydration force," though the origins of this force are not clearly understood. We computationally reproduce this repulsive, relatively free energy change as bilayers come together and make qualitative conclusions as to the enthalpic and entropic origins of the free energy change. This analysis is supported by data showing structural changes in the waters, lipids and salts that have also been seen in experimental work. Increases in solvent ordering as the bilayers are dehydrated are found to be essential in causing the repulsion as the bilayers come together.
Accelerating all-atom MD simulations of lipids using a modified virtual-sites technique
DEFF Research Database (Denmark)
Loubet, Bastien; Kopec, Wojciech; Khandelia, Himanshu
2014-01-01
We present two new implementations of the virtual sites technique which completely suppresses the degrees of freedom of the hydrogen atoms in a lipid bilayer allowing for an increased time step of 5 fs in all-atom simulations of the CHARMM36 force field. One of our approaches uses the derivation...... of the virtual sites used in GROMACS while the other uses a new definition of the virtual sites of the CH2 groups. Our methods is tested on a DPPC (no unsaturated chain), a POPC (one unsaturated chain), and a DOPC (two unsaturated chains) lipid bilayers. We calculate various physical properties of the membrane...... of our simulations with and without virtual sites and explain the differences and similarity observed. The best agreements are obtained for the GROMACS original virtual sites on the DOPC bilayer where we get an area per lipid of 67.3 ± 0.3 A˚2 without virtual sites and 67.6 ± 0.3 A˚2 with virtual sites...
Pandey, Ras; Kuang, Zhifeng; Farmer, Barry; Kim, Sang; Naik, Rajesh
2012-02-01
Recently, Kim et al. [1] have found that peptides P1: HSSYWYAFNNKT and P2: EPLQLKM bind selectively to graphene surfaces and edges respectively which are critical in modulating both the mechanical as well as electronic transport properties of graphene. Such distinctions in binding sites (edge versus surface) observed in electron micrographs were verified by computer simulation by an all-atomic model that captures the pi-pi bonding. We propose a hierarchical approach that involves input from the all-atom Molecular Dynamics (MD) study (with atomistic detail) into a coarse-grained Monte Carlo simulation to extend this study further to a larger scale. The binding energy of a free amino acid with the graphene sheet from all-atom simulation is used in the interaction parameter for the coarse-grained approach. Peptide chain executes its stochastic motion with the Metropolis algorithm. We investigate a number of local and global physical quantities and find that peptide P1 is likely to bind more strongly to graphene sheet than P2 and that it is anchored by three residues ^4Y^5W^6Y. [1] S.N. Kim et al J. Am. Chem. Soc. 133, 14480 (2011).
Li, Kenli; Zou, Shuting; Xv, Jin
2008-01-01
Elliptic curve cryptographic algorithms convert input data to unrecognizable encryption and the unrecognizable data back again into its original decrypted form. The security of this form of encryption hinges on the enormous difficulty that is required to solve the elliptic curve discrete logarithm problem (ECDLP), especially over GF(2(n)), n in Z+. This paper describes an effective method to find solutions to the ECDLP by means of a molecular computer. We propose that this research accomplishment would represent a breakthrough for applied biological computation and this paper demonstrates that in principle this is possible. Three DNA-based algorithms: a parallel adder, a parallel multiplier, and a parallel inverse over GF(2(n)) are described. The biological operation time of all of these algorithms is polynomial with respect to n. Considering this analysis, cryptography using a public key might be less secure. In this respect, a principal contribution of this paper is to provide enhanced evidence of the potential of molecular computing to tackle such ambitious computations.
Development and application of a free energy force field for all atom protein folding
International Nuclear Information System (INIS)
Verma, A.
2007-11-01
Proteins are the workhorses of all cellular life. They constitute the building blocks and the machinery of all cells and typically function in specific three-dimensional conformations into which each protein folds. Currently over one million protein sequences are known, compared to about 40,000 structures deposited in the Protein Data Bank (the world-wide database of protein structures). Reliable theoretical methods for protein structure prediction could help to reduce the gap between sequence and structural databases and elucidate the biological information in structurally unresolved sequences. In this thesis we explore an approach for protein structure prediction and folding that is based on the Anfinsen's hypothesis that most proteins in their native state are in thermodynamic equilibrium with their environment. We have developed a free energy forcefield (PFF02) that locates the native conformation of many proteins from all structural classes at the global minimum of the free-energy model. We have validated the forcefield against a large decoy set (Rosetta). The average root mean square deviation (RMSD) for the lowest energy structure for the 32 proteins of the decoy set was only 2.14 Aa from the experimental conformation. We have successfully implemented and used stochastic optimization methods, such as the basin hopping technique and evolutionary algorithms for all atom protein structure prediction. The evolutionary algorithm performs exceptionally well on large supercomputational architectures, such as BlueGene and MareNostrum. Using the PFF02 forcefield, we were able to fold 13 proteins (12-56 amino acids), which include helix, sheet and mixed secondary structure. On average the predicted structure of these proteins deviated from their experimental conformation by only 2.89 Aa RMSD. (orig.)
Directory of Open Access Journals (Sweden)
Manfred Beleut
Full Text Available Despite the individually different molecular alterations in tumors, the malignancy associated biological traits are strikingly similar. Results of a previous study using renal cell carcinoma (RCC as a model pointed towards cancer-related features, which could be visualized as three groups by microarray based gene expression analysis. In this study, we used a mathematic model to verify the presence of these groups in RCC as well as in other cancer types. We developed an algorithm for gene-expression deviation profiling for analyzing gene expression data of a total of 8397 patients with 13 different cancer types and normal tissues. We revealed three common Cancer Transcriptomic Profiles (CTPs which recurred in all investigated tumors. Additionally, CTPs remained robust regardless of the functions or numbers of genes analyzed. CTPs may represent common genetic fingerprints, which potentially reflect the closely related biological traits of human cancers.
Eisenberg, Azaria Solomon; Juszczak, Laura J
2013-07-05
Molecular dynamics (MD), coupled with fluorescence data for charged dipeptides of tryptophanyl glutamic acid (Trp-Glu), reveal a detailed picture of how specific conformation affects fluorescence. Fluorescence emission spectra and time-resolved emission measurements have been collected for all four charged species. MD simulations 20 to 30 ns in length have also been carried out for the Trp-Glu species, as simulation provides aqueous phase conformational data that can be correlated with the fluorescence data. The calculations show that each dipeptide species is characterized by a similar set of six, discrete Chi 1, Chi 2 dihedral angle pairs. The preferred Chi 1 angles--60°, 180°, and 300°--play the significant role in positioning the terminal amine relative to the indole ring. A Chi 1 angle of 60° results in the arching of the backbone over the indole ring and no interaction of the ring with the terminal amine. Chi 1 values of 180° and 300° result in an extension of the backbone away from the indole ring and a NH3 cation-π interaction with indole. This interaction is believed responsible for charge transfer quenching. Two fluorescence lifetimes and their corresponding amplitudes correlate with the Chi 1 angle probability distribution for all four charged Trp-Glu dipeptides. Fluorescence emission band maxima are also consistent with the proposed pattern of terminal amine cation quenching of fluorescence. Copyright © 2013 Wiley Periodicals, Inc.
Bottari, Giovanni; de la Torre, Gema; Torres, Tomas
2015-04-21
Phthalocyanines (Pcs) are macrocyclic and aromatic compounds that present unique electronic features such as high molar absorption coefficients, rich redox chemistry, and photoinduced energy/electron transfer abilities that can be modulated as a function of the electronic character of their counterparts in donor-acceptor (D-A) ensembles. In this context, carbon nanostructures such as fullerenes, carbon nanotubes (CNTs), and, more recently, graphene are among the most suitable Pc "companions". Pc-C60 ensembles have been for a long time the main actors in this field, due to the commercial availability of C60 and the well-established synthetic methods for its functionalization. As a result, many Pc-C60 architectures have been prepared, featuring different connectivities (covalent or supramolecular), intermolecular interactions (self-organized or molecularly dispersed species), and Pc HOMO/LUMO levels. All these elements provide a versatile toolbox for tuning the photophysical properties in terms of the type of process (photoinduced energy/electron transfer), the nature of the interactions between the electroactive units (through bond or space), and the kinetics of the formation/decay of the photogenerated species. Some recent trends in this field include the preparation of stimuli-responsive multicomponent systems with tunable photophysical properties and highly ordered nanoarchitectures and surface-supported systems showing high charge mobilities. A breakthrough in the Pc-nanocarbon field was the appearance of CNTs and graphene, which opened a new avenue for the preparation of intriguing photoresponsive hybrid ensembles showing light-stimulated charge separation. The scarce solubility of these 1-D and 2-D nanocarbons, together with their lower reactivity with respect to C60 stemming from their less strained sp(2) carbon networks, has not meant an unsurmountable limitation for the preparation of variety of Pc-based hybrids. These systems, which show improved
An all-atom, active site exploration of antiviral drugs that target Flaviviridae polymerases
Czech Academy of Sciences Publication Activity Database
Valdés, James J.; Gil, V.A.; Butterill, Philip T.; Růžek, Daniel
2016-01-01
Roč. 97, OCT (2016), s. 2552-2565 ISSN 0022-1317 R&D Projects: GA MŠk(CZ) EE2.3.30.0032; GA ČR GB14-36098G; GA MZd(CZ) NV16-34238A EU Projects: European Commission(XE) 316304 - MODBIOLIN Institutional support: RVO:60077344 Keywords : dependent RNA-polymerase * c virus polymerase * de-novo initiation * hepatitis C * allosteric inhibitors * nucleoside inhibitors * molecular dynamics * encephalitis virus * protein-structure * cluster-analysis Subject RIV: EE - Microbiology, Virology Impact factor: 2.838, year: 2016
Hierarchical atom type definitions and extensible all-atom force fields.
Jin, Zhao; Yang, Chunwei; Cao, Fenglei; Li, Feng; Jing, Zhifeng; Chen, Long; Shen, Zhe; Xin, Liang; Tong, Sijia; Sun, Huai
2016-03-15
The extensibility of force field is a key to solve the missing parameter problem commonly found in force field applications. The extensibility of conventional force fields is traditionally managed in the parameterization procedure, which becomes impractical as the coverage of the force field increases above a threshold. A hierarchical atom-type definition (HAD) scheme is proposed to make extensible atom type definitions, which ensures that the force field developed based on the definitions are extensible. To demonstrate how HAD works and to prepare a foundation for future developments, two general force fields based on AMBER and DFF functional forms are parameterized for common organic molecules. The force field parameters are derived from the same set of quantum mechanical data and experimental liquid data using an automated parameterization tool, and validated by calculating molecular and liquid properties. The hydration free energies are calculated successfully by introducing a polarization scaling factor to the dispersion term between the solvent and solute molecules. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
All-atom simulation study of protein PTH(1-34) by using the Wang-Landau sampling method
Energy Technology Data Exchange (ETDEWEB)
Kim, Seung-Yeon [Korea National University of Transportation, Chungju (Korea, Republic of); Kwak, Woo-Seop [Chosun University, Gwangju (Korea, Republic of)
2014-12-15
We perform simulations of the N-terminal 34-residue protein fragment PTH(1-34), consisting of 581 atoms, of the 84-residue human parathyroid hormone by using the all-atom ECEPP/3 force field and the Wang-Landau sampling method. Through a massive high-performance computation, the density of states and the partition function Z(T), as a continuous function of T, are obtained for PTH(1-34). From the continuous partition function Z(T), the partition function zeros of PTH(1-34) are evaluated for the first time. From both the specific heat and the partition function zeros, two characteristic transition temperatures are obtained for the all-atom protein PTH(1-34). The higher transition temperature T{sub 1} and the lower transition temperature T{sub 2} of PTH(1-34) can be interpreted as the collapse temperature T{sub θ} and the folding temperature T{sub f} , respectively.
All-atom normal-mode analysis reveals an RNA-induced allostery in a bacteriophage coat protein.
Dykeman, Eric C; Twarock, Reidun
2010-03-01
Assembly of the T=3 bacteriophage MS2 is initiated by the binding of a 19 nucleotide RNA stem loop from within the phage genome to a symmetric coat protein dimer. This binding event effects a folding of the FG loop in one of the protein subunits of the dimer and results in the formation of an asymmetric dimer. Since both the symmetric and asymmetric forms of the dimer are needed for the assembly of the protein container, this allosteric switch plays an important role in the life cycle of the phage. We provide here details of an all-atom normal-mode analysis of this allosteric effect. The results suggest that asymmetric contacts between the A -duplex RNA phosphodiester backbone of the stem loop with the EF loop in one coat protein subunit results in an increased dynamic behavior of its FG loop. The four lowest-frequency modes, which encompass motions predominantly on the FG loops, account for over 90% of the increased dynamic behavior due to a localization of the vibrational pattern on a single FG loop. Finally, we show that an analysis of the allosteric effect using an elastic network model fails to predict this localization effect, highlighting the importance of using an all-atom full force field method for this problem.
Chiang, Howard Hsueh-hao
2009-01-01
Preparative and analytical methods developed by separation scientists have played an important role in the history of molecular biology. One such early method is gel electrophoresis, a technique that uses various types of gel as its supporting medium to separate charged molecules based on size and other properties. Historians of science, however, have only recently begun to pay closer attention to this material epistemological dimension of biomolecular science. This paper substantiates the historiographical thread that explores the relationship between modern laboratory practice and the production of scientific knowledge. It traces the historical development of gel electrophoresis from the mid-1940s to the mid-1960s, with careful attention to the interplay between technical developments and disciplinary shifts, especially the rise of molecular biology in this time-frame. Claiming that the early 1950s marked a decisive shift in the evolution of electrophoretic methods from moving boundary to zone electrophoresis, I reconstruct various trajectories in which scientists such as Oliver Smithies sought out the most desirable solid supporting medium for electrophoretic instrumentation. Biomolecular knowledge, I argue, emerged in part from this process of seeking the most appropriate supporting medium that allowed for discrete molecular separation and visualization. The early 1950s, therefore, marked not only an important turning point in the history of separation science, but also a transformative moment in the history of the life sciences as the growth of molecular biology depended in part on the epistemological access to the molecular realm available through these evolving technologies.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Lindahl, Erik; Azuara, Cyril; Koehl, Patrice; Delarue, Marc
2006-07-01
Normal mode analysis (NMA) is an efficient way to study collective motions in biomolecules that bypasses the computational costs and many limitations associated with full dynamics simulations. The NOMAD-Ref web server presented here provides tools for online calculation of the normal modes of large molecules (up to 100,000 atoms) maintaining a full all-atom representation of their structures, as well as access to a number of programs that utilize these collective motions for deformation and refinement of biomolecular structures. Applications include the generation of sets of decoys with correct stereochemistry but arbitrary large amplitude movements, the quantification of the overlap between alternative conformations of a molecule, refinement of structures against experimental data, such as X-ray diffraction structure factors or Cryo-EM maps and optimization of docked complexes by modeling receptor/ligand flexibility through normal mode motions. The server can be accessed at the URL http://lorentz.immstr.pasteur.fr/nomad-ref.php.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...
DEFF Research Database (Denmark)
Busch, Peter Andre; Zinner Henriksen, Helle
2018-01-01
discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
International Nuclear Information System (INIS)
Lee, T.D.
1985-01-01
This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics
Discrete dynamics versus analytic dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2014-01-01
For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
Discrete gradients in discrete classical mechanics
International Nuclear Information System (INIS)
Renna, L.
1987-01-01
A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated
International Nuclear Information System (INIS)
Jee, Jun Goo
2010-01-01
It has been shown that AMD refinement is very useful for defining an intermolecular hydrogen bond in NMR structure calculation. The refined structure also provides a clue for explaining the pH dependence in Ub and UIM complexes. As reported by Choi et al., serine-mediated hydrogen bonds are the third most populated hydrogen bonds found in protein-protein intermolecular interactions, after the backbone-backbone and backbone-aspartate ones. The abundance imposes the requirement of an method to determine the interface of protein-protein complexes. The precise geometry is particularly important in the complex structures between Ub and UBDs. Ub recognizes various targets with the same surface, where both hydrophobic and hydrophobic interactions are involved. Hence, the details of the hydrophilic interactions are necessary to find the common binding modes. The structure determination of a biomolecule by NMR depends heavily on the distance restraints derived by the NOE cross peaks that are observed between two protons within 6 A through space. Therefore, the existence of the NOE peaks and their correct assignments to two corresponding protons are essential for an accurate and precise structure determination. Recent developments of NOE assignment and calculation algorithms have enabled the determination of protein 3D structures without any manual interpretation, provided chemical shifts are assigned in most atoms and sufficient NOE peaks exist. Along with these advances, the necessity of determining complicated structures such as complexes is increasing
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-01-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
International Nuclear Information System (INIS)
Schlueter, J.A.; Geiser, U.; Williams, J.M.
1996-01-01
A new approach to synthesis of organic superconductors has recently been pioneered which involves the use of large discrete molecular anions as the charge-compensating entities in these charge transfer salts. The organic electron-donor molecule bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF or ET) has been electrocrystallized with the novel organometallic M(CF 3 ) 4 - (M=Cu, Ag, Au) anions in a variety of 1,1,2-trihaloethane solvents. Over 20 organic superconductors have been synthesized which can be described by (ET) 2 M(CF 3 ) 4 (1,1,2- trihaloethane). These solvated salts are shown to have highly anisotropic physical properties which can be tuned via modifications of each of their three molecular components: ET electron donor molecule, M(CF 3 ) 4 - anion, and neutral 1,1,2- trihaloethane solvent molecule. Superconductivity has also been observed in an ET salt containing the discrete SF 5 CH 2 CF 2 SO 3 - anion with onset temperature near 5.2 K
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Lu, Shih-I.
2018-01-01
We use the discrete solvent reaction field model to evaluate the linear and second-order nonlinear optical susceptibilities of 3-methyl-4-nitropyridine-1-oxyde crystal. In this approach, crystal environment is created by supercell architecture. A self-consistent procedure is used to obtain charges and polarizabilities for environmental atoms. Impact of atomic polarizabilities on the properties of interest is highlighted. This approach is shown to give the second-order nonlinear optical susceptibilities within error bar of experiment as well as the linear optical susceptibilities in the same order as experiment. Similar quality of calculations are also applied to both 4-N,N-dimethylamino-3-acetamidonitrobenzene and 2-methyl-4-nitroaniline crystals.
Gould, Tim; Bučko, Tomáš
2016-08-09
Using time-dependent density functional theory (TDDFT) with exchange kernels, we calculate and test imaginary frequency-dependent dipole polarizabilities for all atoms and many ions in rows 1-6 of the periodic table. These are then integrated over frequency to produce C6 coefficients. Results are presented under different models: straight TDDFT calculations using two different kernels; "benchmark" TDDFT calculations corrected by more accurate quantum chemical and experimental data; and "benchmark" TDDFT with frozen orbital anions. Parametrizations are presented for 411+ atoms and ions, allowing results to be easily used by other researchers. A curious relationship, C6,XY ∝ [αX(0)αY(0)](0.73), is found between C6 coefficients and static polarizabilities α(0). The relationship C6,XY = 2C6,XC6,Y/[(αX/αY)C6,Y + (αY/αX)C6,X] is tested and found to work well (30% errors) in a small fraction of cases.
Time Discretization Techniques
Gottlieb, S.; Ketcheson, David I.
2016-01-01
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include
Discrete breathers in graphane: Effect of temperature
Energy Technology Data Exchange (ETDEWEB)
Baimova, J. A., E-mail: julia.a.baimova@gmail.com [Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation); Murzaev, R. T.; Lobzenko, I. P.; Dmitriev, S. V. [Russian Academy of Sciences, Institute for Metals Superplasticity Problems (Russian Federation); Zhou, Kun [Nanyang Technological University, School of Mechanical and Aerospace Engineering (Singapore)
2016-05-15
The discrete breathers in graphane in thermodynamic equilibrium in the temperature range 50–600 K are studied by molecular dynamics simulation. A discrete breather is a hydrogen atom vibrating along the normal to a sheet of graphane at a high amplitude. As was found earlier, the lifetime of a discrete breather at zero temperature corresponds to several tens of thousands of vibrations. The effect of temperature on the decay time of discrete breathers and the probability of their detachment from a sheet of graphane are studied in this work. It is shown that closely spaced breathers can exchange energy with each other at zero temperature. The data obtained suggest that thermally activated discrete breathers can be involved in the dehydrogenation of graphane, which is important for hydrogen energetics.
Domingo, Alex; Rodriguez-Fortea, Antonio; Swart, Marcel; de Graaf, Coen; Broer-Braam, Henderika
2012-01-01
We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the
Ensemble simulations with discrete classical dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2013-01-01
For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\\tilde{H}$ with energy $\\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\\tilde{H}$. $\\tilde......{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics...
Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J; Torrens, Francisco
2012-11-01
In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating
Baecklund transformations for discrete Painleve equations: Discrete PII-PV
International Nuclear Information System (INIS)
Sakka, A.; Mugan, U.
2006-01-01
Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations
Discrete Gabor transform and discrete Zak transform
Bastiaans, M.J.; Namazi, N.M.; Matthews, K.
1996-01-01
Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of
Czech Academy of Sciences Publication Activity Database
Kilian, Patrik; Valdés, James J.; Lecina-Casas, D.; Chrudimský, T.; Růžek, Daniel
2013-01-01
Roč. 20, 2013-Dec (2013), s. 304-311 ISSN 1567-1348 R&D Projects: GA ČR GAP502/11/2116; GA MŠk(CZ) EE2.3.30.0032 Institutional support: RVO:60077344 Keywords : Tahyna virus * Orthobunyavirus * California complex * Genetic variability * Large genomic segment Subject RIV: EB - Genetics ; Molecular Biology Impact factor: 3.264, year: 2013
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Homogenization of discrete media
International Nuclear Information System (INIS)
Pradel, F.; Sab, K.
1998-01-01
Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)
International Nuclear Information System (INIS)
Aydin, Alhun; Sisman, Altug
2016-01-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Energy Technology Data Exchange (ETDEWEB)
Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr
2016-03-22
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Discrete repulsive oscillator wavefunctions
International Nuclear Information System (INIS)
Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo
2009-01-01
For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.
Energy Technology Data Exchange (ETDEWEB)
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Izadi, F A; Bagirov, G
2009-01-01
With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati
Daskalakis, Vangelis
2018-05-07
The assembly and disassembly of protein complexes within cells are crucial life-sustaining processes. In photosystem II (PSII) of higher plants, there is a delicate yet obscure balance between light harvesting and photo-protection under fluctuating light conditions, that involves protein-protein complexes. Recent breakthroughs in molecular dynamics (MD) simulations are combined with new approaches herein to provide structural and energetic insight into such a complex between the CP29 minor antenna and the PSII subunit S (PsbS). The microscopic model involves extensive sampling of bound and dissociated states at atomic resolution in the presence of photo-protective zeaxanthin (Zea), and reveals well defined protein-protein cross-sections. The complex is placed within PSII, and macroscopic connections are emerging (PsbS-CP29-CP24-CP47) along the energy transfer pathways from the antenna to the PSII core. These connections explain macroscopic observations in the literature, while the previously obscured atomic scale details are now revealed. The implications of these findings are discussed in the context of the Non-Photochemical Quenching (NPQ) of chlorophyll fluorescence, the down-regulatory mechanism of photosynthesis, that enables the protection of PSII against excess excitation load. Zea is found at the PsbS-CP29 cross-section and a pH-dependent equilibrium between PsbS dimer/monomers and the PsbS-CP29 dissociation/association is identified as the target for engineering tolerant plants with increased crop and biomass yields. Finally, the new MD based approaches can be used to probe protein-protein interactions in general, and the PSII structure provided can initiate large scale molecular simulations of the photosynthetic apparatus, under NPQ conditions.
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Adaptive Discrete Hypergraph Matching.
Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao
2018-02-01
This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
International Nuclear Information System (INIS)
Williams, Ruth M
2006-01-01
A review is given of a number of approaches to discrete quantum gravity, with a restriction to those likely to be relevant in four dimensions. This paper is dedicated to Rafael Sorkin on the occasion of his sixtieth birthday
Discrete computational structures
Korfhage, Robert R
1974-01-01
Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize
Homogenization of discrete media
Energy Technology Data Exchange (ETDEWEB)
Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)
1998-11-01
Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.
DISCRETE MATHEMATICS/NUMBER THEORY
Mrs. Manju Devi*
2017-01-01
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...
Directory of Open Access Journals (Sweden)
Prateek Sharma
2015-04-01
Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Exarchakis, Georgios; Lücke, Jörg
2017-11-01
Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
Prateek Sharma
2015-01-01
Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of ev...
Indian Academy of Sciences (India)
We also describe discrete-time systems in terms of difference ... A more modern alternative, especially for larger systems, is to convert ... In other words, ..... picture?) State-variable equations are also called state-space equations because the ...
Discrete Lorentzian quantum gravity
Loll, R.
2000-01-01
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2017-01-01
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy
Discrete mKdV and discrete sine-Gordon flows on discrete space curves
International Nuclear Information System (INIS)
Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro
2014-01-01
In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)
Discrete mathematics with applications
Koshy, Thomas
2003-01-01
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects*...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
Czech Academy of Sciences Publication Activity Database
Mesiar, Radko; Li, J.; Pap, E.
2013-01-01
Roč. 54, č. 3 (2013), s. 357-364 ISSN 0888-613X R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : concave integral * pseudo-addition * pseudo-multiplication Subject RIV: BA - General Mathematics Impact factor: 1.977, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-discrete pseudo-integrals.pdf
Discrete variational Hamiltonian mechanics
International Nuclear Information System (INIS)
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
International Nuclear Information System (INIS)
Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew
2006-01-01
This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure
Discrete port-Hamiltonian systems
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2006-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
A paradigm for discrete physics
International Nuclear Information System (INIS)
Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.
1987-01-01
An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity
Two new discrete integrable systems
International Nuclear Information System (INIS)
Chen Xiao-Hong; Zhang Hong-Qing
2013-01-01
In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Ã 1 . By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity
Hirsch, M; Peinado, E; Valle, J W F
2010-01-01
We propose a new motivation for the stability of dark matter (DM). We suggest that the same non-abelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z2 subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches, while reactor angle equal to zero gives no CP violation in neutrino oscillations.
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
International Nuclear Information System (INIS)
Souza, Manoelito M. de
1997-01-01
We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Poisson hierarchy of discrete strings
International Nuclear Information System (INIS)
Ioannidou, Theodora; Niemi, Antti J.
2016-01-01
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Poisson hierarchy of discrete strings
Energy Technology Data Exchange (ETDEWEB)
Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)
2016-01-28
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Dark discrete gauge symmetries
International Nuclear Information System (INIS)
Batell, Brian
2011-01-01
We investigate scenarios in which dark matter is stabilized by an Abelian Z N discrete gauge symmetry. Models are surveyed according to symmetries and matter content. Multicomponent dark matter arises when N is not prime and Z N contains one or more subgroups. The dark sector interacts with the visible sector through the renormalizable kinetic mixing and Higgs portal operators, and we highlight the basic phenomenology in these scenarios. In particular, multiple species of dark matter can lead to an unconventional nuclear recoil spectrum in direct detection experiments, while the presence of new light states in the dark sector can dramatically affect the decays of the Higgs at the Tevatron and LHC, thus providing a window into the gauge origin of the stability of dark matter.
International Nuclear Information System (INIS)
Noyes, H.P.; Starson, S.
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces ''fields'' with the relativistic Wheeler-Feynman ''action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will ''fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs
Nonequilibrium and generalized-ensemble molecular dynamics simulations for amyloid fibril
Energy Technology Data Exchange (ETDEWEB)
Okumura, Hisashi [Research Center for Computational Science, Institute for Molecular Science, Okazaki, Aichi 444-8585 (Japan); Department of Structural Molecular Science, The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585 (Japan)
2015-12-31
Amyloids are insoluble and misfolded fibrous protein aggregates and associated with more than 20 serious human diseases. We perform all-atom molecular dynamics simulations of amyloid fibril assembly and disassembly.
Control of Discrete Event Systems
Smedinga, Rein
1989-01-01
Systemen met discrete gebeurtenissen spelen in vele gebieden een rol. In dit proefschrift staat de volgorde van gebeurtenissen centraal en worden tijdsaspecten buiten beschouwing gelaten. In dat geval kunnen systemen met discrete gebeurtenissen goed worden gemodelleerd door gebruik te maken van
Discrete Mathematics and Its Applications
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
Discrete Mathematics and Curriculum Reform.
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Connections on discrete fibre bundles
International Nuclear Information System (INIS)
Manton, N.S.; Cambridge Univ.
1987-01-01
A new approach to gauge fields on a discrete space-time is proposed, in which the fundamental object is a discrete version of a principal fibre bundle. If the bundle is twisted, the gauge fields are topologically non-trivial automatically. (orig.)
Discrete dynamic modeling of cellular signaling networks.
Albert, Réka; Wang, Rui-Sheng
2009-01-01
Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.
Modern approaches to discrete curvature
Romon, Pascal
2017-01-01
This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.
Discretion and Disproportionality
Directory of Open Access Journals (Sweden)
Jason A. Grissom
2015-12-01
Full Text Available Students of color are underrepresented in gifted programs relative to White students, but the reasons for this underrepresentation are poorly understood. We investigate the predictors of gifted assignment using nationally representative, longitudinal data on elementary students. We document that even among students with high standardized test scores, Black students are less likely to be assigned to gifted services in both math and reading, a pattern that persists when controlling for other background factors, such as health and socioeconomic status, and characteristics of classrooms and schools. We then investigate the role of teacher discretion, leveraging research from political science suggesting that clients of government services from traditionally underrepresented groups benefit from diversity in the providers of those services, including teachers. Even after conditioning on test scores and other factors, Black students indeed are referred to gifted programs, particularly in reading, at significantly lower rates when taught by non-Black teachers, a concerning result given the relatively low incidence of assignment to own-race teachers among Black students.
International Nuclear Information System (INIS)
Vlad, Valentin I.; Ionescu-Pallas, Nicholas
2000-10-01
The Planck radiation spectrum of ideal cubic and spherical cavities, in the region of small adiabatic invariance, γ = TV 1/3 , is shown to be discrete and strongly dependent on the cavity geometry and temperature. This behavior is the consequence of the random distribution of the state weights in the cubic cavity and of the random overlapping of the successive multiplet components, for the spherical cavity. The total energy (obtained by summing up the exact contributions of the eigenvalues and their weights, for low values of the adiabatic invariance) does not obey any longer Stefan-Boltzmann law. The new law includes a corrective factor depending on γ and imposes a faster decrease of the total energy to zero, for γ → 0. We have defined the double quantized regime both for cubic and spherical cavities by the superior and inferior limits put on the principal quantum numbers or the adiabatic invariance. The total energy of the double quantized cavities shows large differences from the classical calculations over unexpected large intervals, which are measurable and put in evidence important macroscopic quantum effects. (author)
Perfect discretization of path integrals
International Nuclear Information System (INIS)
Steinhaus, Sebastian
2012-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Perfect discretization of path integrals
Steinhaus, Sebastian
2012-05-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
The origin of discrete particles
Bastin, T
2009-01-01
This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction
Synchronization Techniques in Parallel Discrete Event Simulation
Lindén, Jonatan
2018-01-01
Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...
3-D Discrete Analytical Ridgelet Transform
Helbert , David; Carré , Philippe; Andrès , Éric
2006-01-01
International audience; In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines:...
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Discrete geometric structures for architecture
Pottmann, Helmut
2010-01-01
. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization
Causal Dynamics of Discrete Surfaces
Directory of Open Access Journals (Sweden)
Pablo Arrighi
2014-03-01
Full Text Available We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
Perfect discretization of path integrals
Steinhaus, Sebastian
2011-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discu...
Alfa, Attahiru S
2016-01-01
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...
Discrete Curvature Theories and Applications
Sun, Xiang
2016-08-25
Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the
Analysis of Discrete Mittag - Leffler Functions
Directory of Open Access Journals (Sweden)
N. Shobanadevi
2015-03-01
Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.
Foundations of a discrete physics
International Nuclear Information System (INIS)
McGoveran, D.; Noyes, P.
1988-01-01
Starting from the principles of finiteness, discreteness, finite computability and absolute nonuniqueness, we develop the ordering operator calculus, a strictly constructive mathematical system having the empirical properties required by quantum mechanical and special relativistic phenomena. We show how to construct discrete distance functions, and both rectangular and spherical coordinate systems(with a discrete version of ''π''). The richest discrete space constructible without a preferred axis and preserving translational and rotational invariance is shown to be a discrete 3-space with the usual symmetries. We introduce a local ordering parameter with local (proper) time-like properties and universal ordering parameters with global (cosmological) time-like properties. Constructed ''attribute velocities'' connect ensembles with attributes that are invariant as the appropriate time-like parameter increases. For each such attribute, we show how to construct attribute velocities which must satisfy the '' relativistic Doppler shift'' and the ''relativistic velocity composition law,'' as well as the Lorentz transformations. By construction, these velocities have finite maximum and minimum values. In the space of all attributes, the minimum of these maximum velocities will predominate in all multiple attribute computations, and hence can be identified as a fundamental limiting velocity, General commutation relations are constructed which under the physical interpretation are shown to reduce to the usual quantum mechanical commutation relations. 50 refs., 18 figs
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Integrable structure in discrete shell membrane theory.
Schief, W K
2014-05-08
We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.
Degree distribution in discrete case
International Nuclear Information System (INIS)
Wang, Li-Na; Chen, Bin; Yan, Zai-Zai
2011-01-01
Vertex degree of many network models and real-life networks is limited to non-negative integer. By means of measure and integral, the relation of the degree distribution and the cumulative degree distribution in discrete case is analyzed. The degree distribution, obtained by the differential of its cumulative, is only suitable for continuous case or discrete case with constant degree change. When degree change is not a constant but proportional to degree itself, power-law degree distribution and its cumulative have the same exponent and the mean value is finite for power-law exponent greater than 1. -- Highlights: → Degree change is the crux for using the cumulative degree distribution method. → It suits for discrete case with constant degree change. → If degree change is proportional to degree, power-law degree distribution and its cumulative have the same exponent. → In addition, the mean value is finite for power-law exponent greater than 1.
On the discrete Gabor transform and the discrete Zak transform
Bastiaans, M.J.; Geilen, M.C.W.
1996-01-01
Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal (or synthesis window) and the inverse operation -- the Gabor transform -- with which Gabor's expansion coefficients can be determined, are introduced. It is shown how, in the case of a
Discrete Choice and Rational Inattention
DEFF Research Database (Denmark)
Fosgerau, Mogens; Melo, Emerson; de Palma, André
2017-01-01
This paper establishes a general equivalence between discrete choice and rational inattention models. Matejka and McKay (2015, AER) showed that when information costs are modelled using the Shannon entropy, the result- ing choice probabilities in the rational inattention model take the multinomial...... logit form. We show that when information costs are modelled using a class of generalized entropies, then the choice probabilities in any rational inattention model are observationally equivalent to some additive random utility discrete choice model and vice versa. This equivalence arises from convex...
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-01-01
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a
Solving discrete zero point problems
van der Laan, G.; Talman, A.J.J.; Yang, Z.F.
2004-01-01
In this paper an algorithm is proposed to .nd a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space IRn.Starting with a given integral point, the algorithm generates a .nite sequence of adjacent integral simplices of varying dimension and
Succinct Sampling from Discrete Distributions
DEFF Research Database (Denmark)
Bringmann, Karl; Larsen, Kasper Green
2013-01-01
We revisit the classic problem of sampling from a discrete distribution: Given n non-negative w-bit integers x_1,...,x_n, the task is to build a data structure that allows sampling i with probability proportional to x_i. The classic solution is Walker's alias method that takes, when implemented...
Symplectomorphisms and discrete braid invariants
Czechowski, Aleksander; Vandervorst, Robert
2017-01-01
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of D2, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition, we utilize the Conley index theory of discrete braid classes as introduced in Ghrist et
The remarkable discreteness of being
Indian Academy of Sciences (India)
Life is a discrete, stochastic phenomenon: for a biological organism, the time of the two most important events of its life (reproduction and death) is random and these events change the number of individuals of the species by single units. These facts can have surprising, counterintuitive consequences. I review here three ...
Discrete tomography in neutron radiography
International Nuclear Information System (INIS)
Kuba, Attila; Rodek, Lajos; Kiss, Zoltan; Rusko, Laszlo; Nagy, Antal; Balasko, Marton
2005-01-01
Discrete tomography (DT) is an imaging technique for reconstructing discrete images from their projections using the knowledge that the object to be reconstructed contains only a few homogeneous materials characterized by known discrete absorption values. One of the main reasons for applying DT is that we will hopefully require relatively few projections. Using discreteness and some a priori information (such as an approximate shape of the object) we can apply two DT methods in neutron imaging by reducing the problem to an optimization task. The first method is a special one because it is only suitable if the object is composed of cylinders and sphere shapes. The second method is a general one in the sense that it can be used for reconstructing objects of any shape. Software was developed and physical experiments performed in order to investigate the effects of several reconstruction parameters: the number of projections, noise levels, and complexity of the object to be reconstructed. We give a summary of the experimental results and make a comparison of the results obtained using a classical reconstruction technique (FBP). The programs we developed are available in our DT reconstruction program package DIRECT
Discrete elements method of neutron transport
International Nuclear Information System (INIS)
Mathews, K.A.
1988-01-01
In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution
Discrete gauge symmetries in discrete MSSM-like orientifolds
International Nuclear Information System (INIS)
Ibáñez, L.E.; Schellekens, A.N.; Uranga, A.M.
2012-01-01
Motivated by the necessity of discrete Z N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z 2 (R-parity) and Z 3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.
Positivity for Convective Semi-discretizations
Fekete, Imre; Ketcheson, David I.; Loczi, Lajos
2017-01-01
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations
Quantum chaos on discrete graphs
International Nuclear Information System (INIS)
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
Dark energy from discrete spacetime.
Directory of Open Access Journals (Sweden)
Aaron D Trout
Full Text Available Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Emissivity of discretized diffusion problems
International Nuclear Information System (INIS)
Densmore, Jeffery D.; Davidson, Gregory; Carrington, David B.
2006-01-01
The numerical modeling of radiative transfer by the diffusion approximation can produce artificially damped radiation propagation if spatial cells are too optically thick. In this paper, we investigate this nonphysical behavior at external problem boundaries by examining the emissivity of the discretized diffusion approximation. We demonstrate that the standard cell-centered discretization produces an emissivity that is too low for optically thick cells, a situation that leads to the lack of radiation propagation. We then present a modified boundary condition that yields an accurate emissivity regardless of cell size. This modified boundary condition can be used with a deterministic calculation or as part of a hybrid transport-diffusion method for increasing the efficiency of Monte Carlo simulations. We also discuss the range of applicability, as a function of cell size and material properties, when this modified boundary condition is employed in a hybrid technique. With a set of numerical calculations, we demonstrate the accuracy and usefulness of this modified boundary condition
Discrete symmetries in the MSSM
Energy Technology Data Exchange (ETDEWEB)
Schieren, Roland
2010-12-02
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)
Domain Discretization and Circle Packings
DEFF Research Database (Denmark)
Dias, Kealey
A circle packing is a configuration of circles which are tangent with one another in a prescribed pattern determined by a combinatorial triangulation, where the configuration fills a planar domain or a two-dimensional surface. The vertices in the triangulation correspond to centers of circles...... to domain discretization problems such as triangulation and unstructured mesh generation techniques. We wish to ask ourselves the question: given a cloud of points in the plane (we restrict ourselves to planar domains), is it possible to construct a circle packing preserving the positions of the vertices...... and constrained meshes having predefined vertices as constraints. A standard method of two-dimensional mesh generation involves conformal mapping of the surface or domain to standardized shapes, such as a disk. Since circle packing is a new technique for constructing discrete conformal mappings, it is possible...
Discrete Bose-Einstein spectra
International Nuclear Information System (INIS)
Vlad, Valentin I.; Ionescu-Pallas, Nicholas
2001-03-01
The Bose-Einstein energy spectrum of a quantum gas, confined in a rigid cubic box, is shown to become discrete and strongly dependent on the box geometry (size L), temperature, T and atomic mass number, A at , in the region of small γ=A at TV 1/3 . This behavior is the consequence of the random state degeneracy in the box. Furthermore, we demonstrate that the total energy does not obey the conventional law any longer, but a new law, which depends on γ and on the quantum gas fugacity. This energy law imposes a faster decrease to zero than it is classically expected, for γ→0. The lighter the gas atoms, the higher the temperatures or the box size, for the same effects in the discrete Bose-Einstein regime. (author)
Discrete symmetries in the MSSM
International Nuclear Information System (INIS)
Schieren, Roland
2010-01-01
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z R 4 symmetry is discovered which solves the μ-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z R 4 is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z R 4 symmetry and other desirable features. (orig.)
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
Discrete mathematics using a computer
Hall, Cordelia
2000-01-01
Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...
Duality for discrete integrable systems
International Nuclear Information System (INIS)
Quispel, G R W; Capel, H W; Roberts, J A G
2005-01-01
A new class of discrete dynamical systems is introduced via a duality relation for discrete dynamical systems with a number of explicitly known integrals. The dual equation can be defined via the difference of an arbitrary linear combination of integrals and its upshifted version. We give an example of an integrable mapping with two parameters and four integrals leading to a (four-dimensional) dual mapping with four parameters and two integrals. We also consider a more general class of higher-dimensional mappings arising via a travelling-wave reduction from the (integrable) MKdV partial-difference equation. By differencing the trace of the monodromy matrix we obtain a class of novel dual mappings which is shown to be integrable as level-set-dependent versions of the original ones
Observability of discretized partial differential equations
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
Effective lagrangian description on discrete gauge symmetries
International Nuclear Information System (INIS)
Banks, T.
1989-01-01
We exhibit a simple low-energy lagrangian which describes a system with a discrete remnant of a spontaneously broken continuous gauge symmetry. The lagrangian gives a simple description of the effects ascribed to such systems by Krauss and Wilczek: black holes carry discrete hair and interact with cosmic strings, and wormholes cannot lead to violation of discrete gauge symmetries. (orig.)
Discrete port-Hamiltonian systems : mixed interconnections
Talasila, Viswanath; Clemente-Gallardo, J.; Schaft, A.J. van der
2005-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
Discrete fractional solutions of a Legendre equation
Yılmazer, Resat
2018-01-01
One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.
Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
Cresson, Jacky; Pierret, Frédéric
2015-01-01
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.
Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents
Agafonov, S. I.
2005-01-01
It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.
International Nuclear Information System (INIS)
Zhang Yufeng; Fan Engui; Zhang Yongqing
2006-01-01
With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations
Toluene model for molecular dynamics simulations in the ranges 298
Fioroni, M.; Vogt, D.
2004-01-01
An all-atom model for toluene is presented in the framework of classical molecular dynamics (MD). The model has been parametrized under the GROMOS96 force field to reproduce the physicochemical properties of the neat liquid. Four new atom types have been introduced, distinguishing between carbons
Cuspidal discrete series for projective hyperbolic spaces
DEFF Research Database (Denmark)
Andersen, Nils Byrial; Flensted-Jensen, Mogens
2013-01-01
Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...
Space-Time Discrete KPZ Equation
Cannizzaro, G.; Matetski, K.
2018-03-01
We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.
Application of network methods for understanding evolutionary dynamics in discrete habitats.
Greenbaum, Gili; Fefferman, Nina H
2017-06-01
In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene-flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population-genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene-flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. © 2017 John Wiley & Sons Ltd.
Integrable discretizations of the short pulse equation
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro
2010-01-01
In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Radiative transfer on discrete spaces
Preisendorfer, Rudolph W; Stark, M; Ulam, S
1965-01-01
Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. This book describes in detail with mathematical precision the radiometric interactions of light-scattering media in terms of a few well established principles.Organized into four parts encompassing 15 chapters, this volume begins with an overview of the derivations of the practical formulas and the arrangement of formulas leading to numerical solution procedures of radiative transfer problems in plane-parallel media. This text then constructs radiative tran
3-D discrete analytical ridgelet transform.
Helbert, David; Carré, Philippe; Andres, Eric
2006-12-01
In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.
Fermion systems in discrete space-time
International Nuclear Information System (INIS)
Finster, Felix
2007-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure
Fermion systems in discrete space-time
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)
2007-05-15
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion Systems in Discrete Space-Time
Finster, Felix
2006-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion systems in discrete space-time
Finster, Felix
2007-05-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Inevitable randomness in discrete mathematics
Beck, Jozsef
2009-01-01
Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the 3n+1 conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P...
Quantum evolution by discrete measurements
International Nuclear Information System (INIS)
Roa, L; Guevara, M L Ladron de; Delgado, A; Olivares-RenterIa, G; Klimov, A B
2007-01-01
In this article we review two ways of driving a quantum system to a known pure state via a sequence discrete of von Neumann measurements. The first of them assumes that the initial state of the system is unknown, and the evolution is attained only with the help of two non-commuting observables. For this method, the overall success probability is maximized when the eigentstates of the involved observables constitute mutually unbiased bases. The second method assumes the initial state is known and it uses N observables which are consecutively measured to make the state of the system approach the target state. The probability of success of this procedure converges to 1 as the number of observables increases
Quantum evolution by discrete measurements
Energy Technology Data Exchange (ETDEWEB)
Roa, L [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Guevara, M L Ladron de [Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta (Chile); Delgado, A [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Olivares-RenterIa, G [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Klimov, A B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico)
2007-10-15
In this article we review two ways of driving a quantum system to a known pure state via a sequence discrete of von Neumann measurements. The first of them assumes that the initial state of the system is unknown, and the evolution is attained only with the help of two non-commuting observables. For this method, the overall success probability is maximized when the eigentstates of the involved observables constitute mutually unbiased bases. The second method assumes the initial state is known and it uses N observables which are consecutively measured to make the state of the system approach the target state. The probability of success of this procedure converges to 1 as the number of observables increases.
Discrete stochastic processes and applications
Collet, Jean-François
2018-01-01
This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.
Discrete calculus methods for counting
Mariconda, Carlo
2016-01-01
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...
Modeling discrete competitive facility location
Karakitsiou, Athanasia
2015-01-01
This book presents an up-to-date review of modeling and optimization approaches for location problems along with a new bi-level programming methodology which captures the effect of competition of both producers and customers on facility location decisions. While many optimization approaches simplify location problems by assuming decision making in isolation, this monograph focuses on models which take into account the competitive environment in which such decisions are made. New insights in modeling, algorithmic and theoretical possibilities are opened by this approach and new applications are possible. Competition on equal term plus competition between market leader and followers are considered in this study, consequently bi-level optimization methodology is emphasized and further developed. This book provides insights regarding modeling complexity and algorithmic approaches to discrete competitive location problems. In traditional location modeling, assignment of customer demands to supply sources are made ...
Discrete modelling of drapery systems
Thoeni, Klaus; Giacomini, Anna
2016-04-01
Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R
A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations
International Nuclear Information System (INIS)
Xu Xixiang; Cao Weili
2007-01-01
Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.
Geometry and Hamiltonian mechanics on discrete spaces
International Nuclear Information System (INIS)
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
Cuspidal discrete series for semisimple symmetric spaces
DEFF Research Database (Denmark)
Andersen, Nils Byrial; Flensted-Jensen, Mogens; Schlichtkrull, Henrik
2012-01-01
We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical discrete series are non-cuspidal. (C) 2012 Elsevier Inc. All...
Discrete Riccati equation solutions: Distributed algorithms
Directory of Open Access Journals (Sweden)
D. G. Lainiotis
1996-01-01
Full Text Available In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. The proposed distributed algorithms are theoretically interesting and computationally attractive.
Painleve test and discrete Boltzmann equations
International Nuclear Information System (INIS)
Euler, N.; Steeb, W.H.
1989-01-01
The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs
Variance Swap Replication: Discrete or Continuous?
Directory of Open Access Journals (Sweden)
Fabien Le Floc’h
2018-02-01
Full Text Available The popular replication formula to price variance swaps assumes continuity of traded option strikes. In practice, however, there is only a discrete set of option strikes traded on the market. We present here different discrete replication strategies and explain why the continuous replication price is more relevant.
Discretization vs. Rounding Error in Euler's Method
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Discrete/PWM Ballast-Resistor Controller
King, Roger J.
1994-01-01
Circuit offers low switching loss and automatic compensation for failure of ballast resistor. Discrete/PWM ballast-resistor controller improved shunt voltage-regulator circuit designed to supply power from high-resistance source to low-impedance bus. Provides both coarse discrete voltage levels (by switching of ballast resistors) and continuous fine control of voltage via pulse-width modulation.
Current Density and Continuity in Discretized Models
Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente Gallardo, J.J.; Clemente-Gallardo, J.; van der Schaft, Arjan
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to
Discrete mathematics in the high school curriculum
Anderson, I.; Asch, van A.G.; van Lint, J.H.
2004-01-01
In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various
Discrete Fourier analysis of multigrid algorithms
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the
Parallel Stochastic discrete event simulation of calcium dynamics in neuron.
Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W
2017-09-26
The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.
Handbook on modelling for discrete optimization
Pitsoulis, Leonidas; Williams, H
2006-01-01
The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this. It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment...
Discrete elements method of neutral particle transport
International Nuclear Information System (INIS)
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method
Spatially localized, temporally quasiperiodic, discrete nonlinear excitations
International Nuclear Information System (INIS)
Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.
1995-01-01
In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution
Laplacians on discrete and quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2013-01-01
We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)
Exploring RNA structure by integrative molecular modelling
DEFF Research Database (Denmark)
Masquida, Benoît; Beckert, Bertrand; Jossinet, Fabrice
2010-01-01
RNA molecular modelling is adequate to rapidly tackle the structure of RNA molecules. With new structured RNAs constituting a central class of cellular regulators discovered every year, the need for swift and reliable modelling methods is more crucial than ever. The pragmatic method based...... on interactive all-atom molecular modelling relies on the observation that specific structural motifs are recurrently found in RNA sequences. Once identified by a combination of comparative sequence analysis and biochemical data, the motifs composing the secondary structure of a given RNA can be extruded...
International Nuclear Information System (INIS)
Ding Qing
2007-01-01
We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model
Compatible Spatial Discretizations for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
Transverse discrete breathers in unstrained graphene
Barani, Elham; Lobzenko, Ivan P.; Korznikova, Elena A.; Soboleva, Elvira G.; Dmitriev, Sergey V.; Zhou, Kun; Marjaneh, Aliakbar Moradi
2017-02-01
Discrete breathers (DB) are spatially localized vibrational modes of large amplitude in defect-free nonlinear lattices. The search for DBs in graphene is of high importance, taking into account that this one atom thick layer of carbon is promising for a number of applications. There exist several reports on successful excitation of DBs in graphene, based on molecular dynamics and ab initio simulations. In a recent work by Hizhnyakov with co-authors the possibility to excite a DB with atoms oscillating normal to the graphene sheet has been reported. In the present study we use a systematic approach for finding initial conditions to excite transverse DBs in graphene. The approach is based on the analysis of the frequency-amplitude dependence for a delocalized, short-wavelength vibrational mode. This mode is a symmetry-dictated exact solution to the dynamic equations of the atomic motion, regardless the mode amplitude and regardless the type of interatomic potentials used in the simulations. It is demonstrated that if the AIREBO potential is used, the mode frequency increases with the amplitude bifurcating from the upper edge of the phonon spectrum for out-of-plane phonons. Then a bell-shaped function is superimposed on this delocalized mode to obtain a spatially localized vibrational mode, i.e., a DB. Placing the center of the bell-shaped function at different positions with respect to the lattice sites, three different DBs are found. Typically, the degree of spatial localization of DBs increases with the DB amplitude, but the transverse DBs in graphene reported here demonstrate the opposite trend. The results are compared to those obtained with the use of the Savin interatomic potential and no transverse DBs are found in this case. The results of this study contribute to a better understanding of the nonlinear dynamics of graphene and they call for the ab initio simulations to verify which of the two potentials used in this study is more precise.
Armen, Roger S; Chen, Jianhan; Brooks, Charles L
2009-10-13
Incorporating receptor flexibility into molecular docking should improve results for flexible proteins. However, the incorporation of explicit all-atom flexibility with molecular dynamics for the entire protein chain may also introduce significant error and "noise" that could decrease docking accuracy and deteriorate the ability of a scoring function to rank native-like poses. We address this apparent paradox by comparing the success of several flexible receptor models in cross-docking and multiple receptor ensemble docking for p38α mitogen-activated protein (MAP) kinase. Explicit all-atom receptor flexibility has been incorporated into a CHARMM-based molecular docking method (CDOCKER) using both molecular dynamics (MD) and torsion angle molecular dynamics (TAMD) for the refinement of predicted protein-ligand binding geometries. These flexible receptor models have been evaluated, and the accuracy and efficiency of TAMD sampling is directly compared to MD sampling. Several flexible receptor models are compared, encompassing flexible side chains, flexible loops, multiple flexible backbone segments, and treatment of the entire chain as flexible. We find that although including side chain and some backbone flexibility is required for improved docking accuracy as expected, docking accuracy also diminishes as additional and unnecessary receptor flexibility is included into the conformational search space. Ensemble docking results demonstrate that including protein flexibility leads to to improved agreement with binding data for 227 active compounds. This comparison also demonstrates that a flexible receptor model enriches high affinity compound identification without significantly increasing the number of false positives from low affinity compounds.
Towards molecular electronics with large-area molecular junctions
Akkerman, HB; Blom, PWM; de Leeuw, DM; de Boer, B
2006-01-01
Electronic transport through single molecules has been studied extensively by academic(1-8) and industrial(9,10) research groups. Discrete tunnel junctions, or molecular diodes, have been reported using scanning probes(11,12), break junctions(13,14), metallic crossbars(6) and nanopores(8,15). For
Rabideau, Brooks D; Agarwal, Animesh; Ismail, Ahmed E
2013-04-04
Explicit, all-atom molecular dynamics simulations are used to study the breakup of small bundles of cellulose Iα and Iβ in the ionic liquids [BMIM]Cl, [EMIM]Ac, and [DMIM]DMP. In all cases, significant breakup of the bundles is observed with the initial breakup following a common underlying mechanism. Anions bind strongly to the hydroxyl groups of the exterior strands of the bundle, forming negatively charged complexes. Binding also weakens the intrastrand hydrogen bonds present in the cellulose strands, providing greater strand flexibility. Cations then intercalate between the individual strands, likely due to charge imbalances, providing the bulk to push the individual moieties apart and initiating the separation. The peeling of an individual strand from the main bundle is observed in [EMIM]Ac with an analysis of its hydrogen bonds with other strands showing that the chain detaches glucan by glucan from the main bundle in discrete, rapid events. Further analysis shows that the intrastrand hydrogen bonds of each glucan tend to break for a sustained period of time before the interstrand hydrogen bonds break and strand detachment occurs. Examination of similar nonpeeling strands shows that, without this intrastrand hydrogen bond breakage, the structural rigidity of the individual unit can hinder its peeling despite interstrand hydrogen bond breakage.
Perfect discretization of reparametrization invariant path integrals
International Nuclear Information System (INIS)
Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian
2011-01-01
To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.
Perfect discretization of reparametrization invariant path integrals
Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian
2011-05-01
To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.
Higher dimensional discrete Cheeger inequalities
Directory of Open Access Journals (Sweden)
Anna Gundert
2015-01-01
Full Text Available For graphs there exists a strong connection between spectral and combinatorial expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the lower bound of which states that $\\lambda(G \\leq h(G$, where $\\lambda(G$ is the second smallest eigenvalue of the Laplacian of a graph $G$ and $h(G$ is the Cheeger constant measuring the edge expansion of $G$. We are interested in generalizations of expansion properties to finite simplicial complexes of higher dimension (or uniform hypergraphs. Whereas higher dimensional Laplacians were introduced already in 1945 by Eckmann, the generalization of edge expansion to simplicial complexes is not straightforward. Recently, a topologically motivated notion analogous to edge expansion that is based on $\\mathbb{Z}_2$-cohomology was introduced by Gromov and independently by Linial, Meshulam and Wallach. It is known that for this generalization there is no direct higher dimensional analogue of the lower bound of the Cheeger inequality. A different, combinatorially motivated generalization of the Cheeger constant, denoted by $h(X$, was studied by Parzanchevski, Rosenthal and Tessler. They showed that indeed $\\lambda(X \\leq h(X$, where $\\lambda(X$ is the smallest non-trivial eigenvalue of the ($(k-1$-dimensional upper Laplacian, for the case of $k$-dimensional simplicial complexes $X$ with complete $(k-1$-skeleton. Whether this inequality also holds for $k$-dimensional complexes with non-com\\-plete$(k-1$-skeleton has been an open question.We give two proofs of the inequality for arbitrary complexes. The proofs differ strongly in the methods and structures employed,and each allows for a different kind of additional strengthening of the original result.
International Nuclear Information System (INIS)
Maruno, Ken-ichi; Biondini, Gino
2004-01-01
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)
Hairs of discrete symmetries and gravity
Energy Technology Data Exchange (ETDEWEB)
Choi, Kang Sin [Scranton Honors Program, Ewha Womans University, Seodaemun-Gu, Seoul 03760 (Korea, Republic of); Center for Fields, Gravity and Strings, CTPU, Institute for Basic Sciences, Yuseong-Gu, Daejeon 34047 (Korea, Republic of); Kim, Jihn E., E-mail: jihnekim@gmail.com [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of); Center for Axion and Precision Physics Research (IBS), 291 Daehakro, Yuseong-Gu, Daejeon 34141 (Korea, Republic of); Kyae, Bumseok [Department of Physics, Pusan National University, 2 Busandaehakro-63-Gil, Geumjeong-Gu, Busan 46241 (Korea, Republic of); Nam, Soonkeon [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of)
2017-06-10
Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair) at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.
Hairs of discrete symmetries and gravity
Directory of Open Access Journals (Sweden)
Kang Sin Choi
2017-06-01
Full Text Available Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.
Discrete Morse functions for graph configuration spaces
International Nuclear Information System (INIS)
Sawicki, A
2012-01-01
We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear. (paper)
Discrete Tomography and Imaging of Polycrystalline Structures
DEFF Research Database (Denmark)
Alpers, Andreas
High resolution transmission electron microscopy is commonly considered as the standard application for discrete tomography. While this has yet to be technically realized, new applications with a similar flavor have emerged in materials science. In our group at Ris� DTU (Denmark's National...... Laboratory for Sustainable Energy), for instance, we study polycrystalline materials via synchrotron X-ray diffraction. Several reconstruction problems arise, most of them exhibit inherently discrete aspects. In this talk I want to give a concise mathematical introduction to some of these reconstruction...... problems. Special focus is on their relationship to classical discrete tomography. Several open mathematical questions will be mentioned along the way....
Stochastic Kuramoto oscillators with discrete phase states
Jörg, David J.
2017-09-01
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.
Stochastic Kuramoto oscillators with discrete phase states.
Jörg, David J
2017-09-01
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.
Discrete-Time Biomedical Signal Encryption
Directory of Open Access Journals (Sweden)
Victor Grigoraş
2017-12-01
Full Text Available Chaotic modulation is a strong method of improving communication security. Analog and discrete chaotic systems are presented in actual literature. Due to the expansion of digital communication, discrete-time systems become more efficient and closer to actual technology. The present contribution offers an in-depth analysis of the effects chaos encryption produce on 1D and 2D biomedical signals. The performed simulations show that modulating signals are precisely recovered by the synchronizing receiver if discrete systems are digitally implemented and the coefficients precisely correspond. Channel noise is also applied and its effects on biomedical signal demodulation are highlighted.
Discrete symmetries and de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Cotăescu, Ion I., E-mail: gpascu@physics.uvt.ro; Pascu, Gabriel, E-mail: gpascu@physics.uvt.ro [West University of Timişoara, V. Pârvan Ave. 4, RO-300223 Timişoara (Romania)
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Exterior difference systems and invariance properties of discrete mechanics
International Nuclear Information System (INIS)
Xie Zheng; Xie Duanqiang; Li Hongbo
2008-01-01
Invariance properties describe the fundamental physical laws in discrete mechanics. Can those properties be described in a geometric way? We investigate an exterior difference system called the discrete Euler-Lagrange system, whose solution has one-to-one correspondence with solutions of discrete Euler-Lagrange equations, and use it to define the first integrals. The preservation of the discrete symplectic form along the discrete Hamilton phase flows and the discrete Noether's theorem is also described in the language of difference forms
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
Can time be a discrete dynamical variable
International Nuclear Information System (INIS)
Lee, T.D.
1983-01-01
The possibility that time can be regarded as a discrete dynamical variable is examined through all phases of mechanics: from classical mechanics to nonrelativistic quantum mechanics, and to relativistic quantum field theories. (orig.)
Local discrete symmetries from superstring derived models
International Nuclear Information System (INIS)
Faraggi, A.E.
1996-10-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Inferring gene networks from discrete expression data
Zhang, L.; Mallick, B. K.
2013-01-01
graphical models applied to continuous data, which give a closedformmarginal likelihood. In this paper,we extend network modeling to discrete data, specifically data from serial analysis of gene expression, and RNA-sequencing experiments, both of which
A discrete control model of PLANT
Mitchell, C. M.
1985-01-01
A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.
Running Parallel Discrete Event Simulators on Sierra
Energy Technology Data Exchange (ETDEWEB)
Barnes, P. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Jefferson, D. R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-12-03
In this proposal we consider porting the ROSS/Charm++ simulator and the discrete event models that run under its control so that they run on the Sierra architecture and make efficient use of the Volta GPUs.
Effective Hamiltonian for travelling discrete breathers
MacKay, Robert S.; Sepulchre, Jacques-Alexandre
2002-05-01
Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.
Comparing the Discrete and Continuous Logistic Models
Gordon, Sheldon P.
2008-01-01
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
Keywords: Discrete-time delay system, Sliding mode control, nonlinear sliding ... of engineering systems such as chemical process control, delay in the actuator ...... instrumentation from Motilal Nehru National Institute of Technology (MNNIT),.
Rich dynamics of discrete delay ecological models
International Nuclear Information System (INIS)
Peng Mingshu
2005-01-01
We study multiple bifurcations and chaotic behavior of a discrete delay ecological model. New form of chaos for the 2-D map is observed: the combination of potential period doubling and reverse period-doubling leads to cascading bubbles
Discrete and Continuous Models for Partitioning Problems
Lellmann, Jan; Lellmann, Bjö rn; Widmann, Florian; Schnö rr, Christoph
2013-01-01
-based techniques. This work is concerned with the sources of such artifacts. We discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples. Moreover, we consider
Memorized discrete systems and time-delay
Luo, Albert C J
2017-01-01
This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.
Testing Preference Axioms in Discrete Choice experiments
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Østerdal, Lars Peter; Tjur, Tue
Recent studies have tested the preference axioms of completeness and transitivity, and have detected other preference phenomena such as unstability, learning- and tiredness effects, ordering effects and dominance, in stated preference discrete choice experiments. However, it has not been explicitly...... of the preference axioms and other preference phenomena in the context of stated preference discrete choice experiments, and examine whether or how these can be subject to meaningful (statistical) tests...
Quadratic Term Structure Models in Discrete Time
Marco Realdon
2006-01-01
This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...
Symmetries in discrete-time mechanics
International Nuclear Information System (INIS)
Khorrami, M.
1996-01-01
Based on a general formulation for discrete-time quantum mechanics, introduced by M. Khorrami (Annals Phys. 224 (1995), 101), symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous. Copyright copyright 1996 Academic Press, Inc
Nonlinear integrodifferential equations as discrete systems
Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.
1999-06-01
We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.
Definable maximal discrete sets in forcing extensions
DEFF Research Database (Denmark)
Törnquist, Asger Dag; Schrittesser, David
2018-01-01
Let be a Σ11 binary relation, and recall that a set A is -discrete if no two elements of A are related by . We show that in the Sacks and Miller forcing extensions of L there is a Δ12 maximal -discrete set. We use this to answer in the negative the main question posed in [5] by showing...
Application of multivariate splines to discrete mathematics
Xu, Zhiqiang
2005-01-01
Using methods developed in multivariate splines, we present an explicit formula for discrete truncated powers, which are defined as the number of non-negative integer solutions of linear Diophantine equations. We further use the formula to study some classical problems in discrete mathematics as follows. First, we extend the partition function of integers in number theory. Second, we exploit the relation between the relative volume of convex polytopes and multivariate truncated powers and giv...
Discrete symmetries and solar neutrino mixing
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D.; Mayr, P.; Nilles, H.P. (Physik Dept., Technische Univ. Muenchen, Garching (Germany) Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Muenchen (Germany))
1992-05-21
We study the question of resonant solar neutrino mixing in the framework of the supersymmetric extension of the standard model. Discrete symmetries that are consistent with solar neutrino mixing and proton stability are classified. In the minimal model they are shown to lead to two distinct patterns of allowed dimension-four operators. Imposing anomaly freedom, only three different discrete Z{sub N}-symmetries (with N=2, 3, 6) are found to be phenomenologically acceptable. (orig.).
Discrete symmetries and solar neutrino mixing
International Nuclear Information System (INIS)
Kapetanakis, D.; Mayr, P.; Nilles, H.P.
1992-01-01
We study the question of resonant solar neutrino mixing in the framework of the supersymmetric extension of the standard model. Discrete symmetries that are consistent with solar neutrino mixing and proton stability are classified. In the minimal model they are shown to lead to two distinct patterns of allowed dimension-four operators. Imposing anomaly freedom, only three different discrete Z N -symmetries (with N=2, 3, 6) are found to be phenomenologically acceptable. (orig.)
Discrete symmetries and coset space dimensional reduction
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1989-01-01
We consider the discrete symmetries of all the six-dimensional coset spaces and we apply them in gauge theories defined in ten dimensions which are dimensionally reduced over these homogeneous spaces. Particular emphasis is given in the consequences of the discrete symmetries on the particle content as well as on the symmetry breaking a la Hosotani of the resulting four-dimensional theory. (orig.)
On discrete models of space-time
International Nuclear Information System (INIS)
Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.
1992-02-01
Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)
Discrete approximations to vector spin models
Energy Technology Data Exchange (ETDEWEB)
Van Enter, Aernout C D [University of Groningen, Johann Bernoulli Institute of Mathematics and Computing Science, Postbus 407, 9700 AK Groningen (Netherlands); Kuelske, Christof [Ruhr-Universitaet Bochum, Fakultaet fuer Mathematik, D44801 Bochum (Germany); Opoku, Alex A, E-mail: A.C.D.v.Enter@math.rug.nl, E-mail: Christof.Kuelske@ruhr-uni-bochum.de, E-mail: opoku@math.leidenuniv.nl [Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden (Netherlands)
2011-11-25
We strengthen a result from Kuelske and Opoku (2008 Electron. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)
Discrete approximations to vector spin models
International Nuclear Information System (INIS)
Van Enter, Aernout C D; Külske, Christof; Opoku, Alex A
2011-01-01
We strengthen a result from Külske and Opoku (2008 Electron. J. Probab. 13 1307–44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)
A study of discrete nonlinear systems
International Nuclear Information System (INIS)
Dhillon, H.S.
2001-04-01
An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)
Mohamed, Mamdouh S.
2016-02-11
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves
International Nuclear Information System (INIS)
Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro
2012-01-01
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)
Discrete modeling considerations in multiphase fluid dynamics
International Nuclear Information System (INIS)
Ransom, V.H.; Ramshaw, J.D.
1988-01-01
The modeling of multiphase flows play a fundamental role in light water reactor safety. The main ingredients in our discrete modeling Weltanschauung are the following considerations: (1) Any physical model must be cast into discrete form for a digital computer. (2) The usual approach of formulating models in differential form and then discretizing them is potentially hazardous. It may be preferable to formulate the model in discrete terms from the outset. (3) Computer time and storage constraints limit the resolution that can be employed in practical calculations. These limits effectively define the physical phenomena, length scales, and time scales which cannot be directly represented in the calculation and therefore must be modeled. This information should be injected into the model formulation process at an early stage. (4) Practical resolution limits are generally so coarse that traditional convergence and truncation-error analyses become irrelevant. (5) A discrete model constitutes a reduced description of a physical system, from which fine-scale details are eliminated. This elimination creates a statistical closure problem. Methods from statistical physics may therefore be useful in the formulation of discrete models. In the present paper we elaborate on these themes and illustrate them with simple examples. 48 refs
Theoretical Basics of Teaching Discrete Mathematics
Directory of Open Access Journals (Sweden)
Y. A. Perminov
2012-01-01
Full Text Available The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training.
Current density and continuity in discretized models
International Nuclear Information System (INIS)
Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.
Discrete Calculus as a Bridge between Scales
Degiuli, Eric; McElwaine, Jim
2012-02-01
Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310
Recent developments in discrete ordinates electron transport
International Nuclear Information System (INIS)
Morel, J.E.; Lorence, L.J. Jr.
1986-01-01
The discrete ordinates method is a deterministic method for numerically solving the Boltzmann equation. It was originally developed for neutron transport calculations, but is routinely used for photon and coupled neutron-photon transport calculations as well. The computational state of the art for coupled electron-photon transport (CEPT) calculations is not as developed as that for neutron transport calculations. The only production codes currently available for CEPT calculations are condensed-history Monte Carlo codes such as the ETRAN and ITS codes. A deterministic capability for production calculations is clearly needed. In response to this need, we have begun the development of a production discrete ordinates code for CEPT calculations. The purpose of this paper is to describe the basic approach we are taking, discuss the current status of the project, and present some new computational results. Although further characterization of the coupled electron-photon discrete ordinates method remains to be done, the results to date indicate that the discrete ordinates method can be just as accurate and from 10 to 100 times faster than the Monte Carlo method for a wide variety of problems. We stress that these results are obtained with standard discrete ordinates codes such as ONETRAN. It is clear that even greater efficiency can be obtained by developing a new generation of production discrete ordinates codes specifically designed to solve the Boltzmann-Fokker-Planck equation. However, the prospects for such development in the near future appear to be remote
Discrete symmetries and their stringy origin
International Nuclear Information System (INIS)
Mayorga Pena, Damian Kaloni
2014-05-01
Discrete symmetries have proven to be very useful in controlling the phenomenology of theories beyond the standard model. In this work we explore how these symmetries emerge from string compactifications. Our approach is twofold: On the one hand, we consider the heterotic string on orbifold backgrounds. In this case the discrete symmetries can be derived from the orbifold conformal field theory, and it can be shown that they are in close relation with the orbifold geometry. We devote special attention to R-symmetries, which arise from discrete remnants of the Lorentz group in compact space. Further we discuss the physical implications of these symmetries both in the heterotic mini-landscape and in newly constructed models based on the Z 2 x Z 4 orbifold. In both cases we observe that the discrete symmetries favor particular locations in the orbifold where the particles of standard model should live. On the other hand we consider a class of F-theory models exhibiting an SU(5) gauge group, times additional U(1) symmetries. In this case, the smooth compactification background does not permit us to track the discrete symmetries as transparently as in orbifold models. Hence, we follow a different approach and search for discrete subgroups emerging after the U(1)s are broken. We observe that in this approach it is possible to obtain the standard Z 2 matter parity of the MSSM.
Discrete integrable systems and deformations of associative algebras
International Nuclear Information System (INIS)
Konopelchenko, B G
2009-01-01
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.
Amplifying (Im)perfection: The Impact of Crystallinity in Discrete and Disperse Block Co-oligomers.
van Genabeek, Bas; Lamers, Brigitte A G; de Waal, Bas F M; van Son, Martin H C; Palmans, Anja R A; Meijer, E W
2017-10-25
Crystallinity is seldomly utilized as part of the microphase segregation process in ultralow-molecular-weight block copolymers. Here, we show the preparation of two types of discrete, semicrystalline block co-oligomers, comprising an amorphous oligodimethylsiloxane block and a crystalline oligo-l-lactic acid or oligomethylene block. The self-assembly of these discrete materials results in lamellar structures with unforeseen uniformity in the domain spacing. A systematic introduction of dispersity reveals the extreme sensitivity of the microphase segregation process toward chain length dispersity in the crystalline block.
International Nuclear Information System (INIS)
Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C
2014-01-01
The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)
Convergence of posteriors for discretized log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...... when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example....
Discrete Feature Model (DFM) User Documentation
International Nuclear Information System (INIS)
Geier, Joel
2008-06-01
This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this software, the
Discrete Feature Model (DFM) User Documentation
Energy Technology Data Exchange (ETDEWEB)
Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))
2008-06-15
This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this
Accelerating Molecular Dynamic Simulation on Graphics Processing Units
Friedrichs, Mark S.; Eastman, Peter; Vaidyanathan, Vishal; Houston, Mike; Legrand, Scott; Beberg, Adam L.; Ensign, Daniel L.; Bruns, Christopher M.; Pande, Vijay S.
2009-01-01
We describe a complete implementation of all-atom protein molecular dynamics running entirely on a graphics processing unit (GPU), including all standard force field terms, integration, constraints, and implicit solvent. We discuss the design of our algorithms and important optimizations needed to fully take advantage of a GPU. We evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core. PMID:19191337
Discrete stochastic analogs of Erlang epidemic models.
Getz, Wayne M; Dougherty, Eric R
2018-12-01
Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.
Positivity for Convective Semi-discretizations
Fekete, Imre
2017-04-19
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.
Noether symmetries of discrete mechanico–electrical systems
International Nuclear Information System (INIS)
Fu Jingli; Xie Fengping; Chen Benyong
2008-01-01
This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results. (general)
Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.
Jason, Peter; Johansson, Magnus
2016-01-01
We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.
Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.
1996-01-01
Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major…
Limit sets for the discrete spectrum of complex Jacobi matrices
International Nuclear Information System (INIS)
Golinskii, L B; Egorova, I E
2005-01-01
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the matrix elements ensuring the finiteness of the discrete spectrum is found. An example of a Jacobi matrix with discrete spectrum having a unique limit point is constructed. These results are discrete analogues of Pavlov's well-known results on Schroedinger operators with complex potential on a half-axis.
Euler-Poincare reduction for discrete field theories
International Nuclear Information System (INIS)
Vankerschaver, Joris
2007-01-01
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed
Integrals of Motion for Discrete-Time Optimal Control Problems
Torres, Delfim F. M.
2003-01-01
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.
The ultimatum game: Discrete vs. continuous offers
Dishon-Berkovits, Miriam; Berkovits, Richard
2014-09-01
In many experimental setups in social-sciences, psychology and economy the subjects are requested to accept or dispense monetary compensation which is usually given in discrete units. Using computer and mathematical modeling we show that in the framework of studying the dynamics of acceptance of proposals in the ultimatum game, the long time dynamics of acceptance of offers in the game are completely different for discrete vs. continuous offers. For discrete values the dynamics follow an exponential behavior. However, for continuous offers the dynamics are described by a power-law. This is shown using an agent based computer simulation as well as by utilizing an analytical solution of a mean-field equation describing the model. These findings have implications to the design and interpretation of socio-economical experiments beyond the ultimatum game.
Symmetric, discrete fractional splines and Gabor systems
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2006-01-01
In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continu......In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing...... the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases....
Sputtering calculations with the discrete ordinated method
International Nuclear Information System (INIS)
Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.
1977-01-01
The purpose of this work is to investigate the applicability of the discrete ordinates (S/sub N/) method to light ion sputtering problems. In particular, the neutral particle discrete ordinates computer code, ANISN, was used to calculate sputtering yields. No modifications to this code were necessary to treat charged particle transport. However, a cross section processing code was written for the generation of multigroup cross sections; these cross sections include a modification to the total macroscopic cross section to account for electronic interactions and small-scattering-angle elastic interactions. The discrete ordinates approach enables calculation of the sputtering yield as functions of incident energy and angle and of many related quantities such as ion reflection coefficients, angular and energy distributions of sputtering particles, the behavior of beams penetrating thin foils, etc. The results of several sputtering problems as calculated with ANISN are presented
Modeling discrete time-to-event data
Tutz, Gerhard
2016-01-01
This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are expla...
Direct Discrete Method for Neutronic Calculations
International Nuclear Information System (INIS)
Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid
2002-01-01
The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)
An algebra of discrete event processes
Heymann, Michael; Meyer, George
1991-01-01
This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.
Is Fitts' law continuous in discrete aiming?
Directory of Open Access Journals (Sweden)
Rita Sleimen-Malkoun
Full Text Available The lawful continuous linear relation between movement time and task difficulty (i.e., index of difficulty; ID in a goal-directed rapid aiming task (Fitts' law has been recently challenged in reciprocal performance. Specifically, a discontinuity was observed at critical ID and was attributed to a transition between two distinct dynamic regimes that occurs with increasing difficulty. In the present paper, we show that such a discontinuity is also present in discrete aiming when ID is manipulated via target width (experiment 1 but not via target distance (experiment 2. Fitts' law's discontinuity appears, therefore, to be a suitable indicator of the underlying functional adaptations of the neuro-muscular-skeletal system to task properties/requirements, independently of reciprocal or discrete nature of the task. These findings open new perspectives to the study of dynamic regimes involved in discrete aiming and sensori-motor mechanisms underlying the speed-accuracy trade-off.
Acceleration techniques for the discrete ordinate method
International Nuclear Information System (INIS)
Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas
2013-01-01
In this paper we analyze several acceleration techniques for the discrete ordinate method with matrix exponential and the small-angle modification of the radiative transfer equation. These techniques include the left eigenvectors matrix approach for computing the inverse of the right eigenvectors matrix, the telescoping technique, and the method of false discrete ordinate. The numerical simulations have shown that on average, the relative speedup of the left eigenvector matrix approach and the telescoping technique are of about 15% and 30%, respectively. -- Highlights: ► We presented the left eigenvector matrix approach. ► We analyzed the method of false discrete ordinate. ► The telescoping technique is applied for matrix operator method. ► Considered techniques accelerate the computations by 20% in average.
Discrete quantum geometries and their effective dimension
International Nuclear Information System (INIS)
Thuerigen, Johannes
2015-01-01
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.
Synchronization Of Parallel Discrete Event Simulations
Steinman, Jeffrey S.
1992-01-01
Adaptive, parallel, discrete-event-simulation-synchronization algorithm, Breathing Time Buckets, developed in Synchronous Parallel Environment for Emulation and Discrete Event Simulation (SPEEDES) operating system. Algorithm allows parallel simulations to process events optimistically in fluctuating time cycles that naturally adapt while simulation in progress. Combines best of optimistic and conservative synchronization strategies while avoiding major disadvantages. Algorithm processes events optimistically in time cycles adapting while simulation in progress. Well suited for modeling communication networks, for large-scale war games, for simulated flights of aircraft, for simulations of computer equipment, for mathematical modeling, for interactive engineering simulations, and for depictions of flows of information.
Speeding Up Network Simulations Using Discrete Time
Lucas, Aaron; Armbruster, Benjamin
2013-01-01
We develop a way of simulating disease spread in networks faster at the cost of some accuracy. Instead of a discrete event simulation (DES) we use a discrete time simulation. This aggregates events into time periods. We prove a bound on the accuracy attained. We also discuss the choice of step size and do an analytical comparison of the computational costs. Our error bound concept comes from the theory of numerical methods for SDEs and the basic proof structure comes from the theory of numeri...
PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
DEFF Research Database (Denmark)
Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.
2010-01-01
The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...
Digital and discrete geometry theory and algorithms
Chen, Li
2014-01-01
This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a
A Low Complexity Discrete Radiosity Method
Chatelier , Pierre Yves; Malgouyres , Rémy
2006-01-01
International audience; Rather than using Monte Carlo sampling techniques or patch projections to compute radiosity, it is possible to use a discretization of a scene into voxels and perform some discrete geometry calculus to quickly compute visibility information. In such a framework , the radiosity method may be as precise as a patch-based radiosity using hemicube computation for form-factors, but it lowers the overall theoretical complexity to an O(N log N) + O(N), where the O(N) is largel...
Modeling and simulation of discrete event systems
Choi, Byoung Kyu
2013-01-01
Computer modeling and simulation (M&S) allows engineers to study and analyze complex systems. Discrete-event system (DES)-M&S is used in modern management, industrial engineering, computer science, and the military. As computer speeds and memory capacity increase, so DES-M&S tools become more powerful and more widely used in solving real-life problems. Based on over 20 years of evolution within a classroom environment, as well as on decades-long experience in developing simulation-based solutions for high-tech industries, Modeling and Simulation of Discrete-Event Systems is the only book on
Logic and discrete mathematics a concise introduction
Conradie, Willem
2015-01-01
A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy
Semiclassical expanding discrete space-times
International Nuclear Information System (INIS)
Cobb, W.K.; Smalley, L.L.
1981-01-01
Given the close ties between general relativity and geometry one might reasonably expect that quantum effects associated with gravitation might also be tied to the geometry of space-time, namely, to some sort of discreteness in space-time itself. In particular it is supposed that space-time consists of a discrete lattice of points rather than the usual continuum. Since astronomical evidence seems to suggest that the universe is expanding, the lattice must also expand. Some of the implications of such a model are that the proton should presently be stable, and the universe should be closed although the mechanism for closure is quantum mechanical. (author)
Systematization of Accurate Discrete Optimization Methods
Directory of Open Access Journals (Sweden)
V. A. Ovchinnikov
2015-01-01
Full Text Available The object of study of this paper is to define accurate methods for solving combinatorial optimization problems of structural synthesis. The aim of the work is to systemize the exact methods of discrete optimization and define their applicability to solve practical problems.The article presents the analysis, generalization and systematization of classical methods and algorithms described in the educational and scientific literature.As a result of research a systematic presentation of combinatorial methods for discrete optimization described in various sources is given, their capabilities are described and properties of the tasks to be solved using the appropriate methods are specified.
Multiband discrete ordinates method: formalism and results
International Nuclear Information System (INIS)
Luneville, L.
1998-06-01
The multigroup discrete ordinates method is a classical way to solve transport equation (Boltzmann) for neutral particles. Self-shielding effects are not correctly treated due to large variations of cross sections in a group (in the resonance range). To treat the resonance domain, the multiband method is introduced. The main idea is to divide the cross section domain into bands. We obtain the multiband parameters using the moment method; the code CALENDF provides probability tables for these parameters. We present our implementation in an existing discrete ordinates code: SN1D. We study deep penetration benchmarks and show the improvement of the method in the treatment of self-shielding effects. (author)
Self-Assembly of Discrete Metal Complexes in Aqueous Solution via Block Copolypeptide Amphiphiles
Directory of Open Access Journals (Sweden)
Timothy J. Deming
2013-01-01
Full Text Available The integration of discrete metal complexes has been attracting significant interest due to the potential of these materials for soft metal-metal interactions and supramolecular assembly. Additionally, block copolypeptide amphiphiles have been investigated concerning their capacity for self-assembly into structures such as nanoparticles, nanosheets and nanofibers. In this study, we combined these two concepts by investigating the self-assembly of discrete metal complexes in aqueous solution using block copolypeptides. Normally, discrete metal complexes such as [Au(CN2]−, when molecularly dispersed in water, cannot interact with one another. Our results demonstrated, however, that the addition of block copolypeptide amphiphiles such as K183L19 to [Au(CN2]− solutions induced one-dimensional integration of the discrete metal complex, resulting in photoluminescence originating from multinuclear complexes with metal-metal interactions. Transmission electron microscopy (TEM showed a fibrous nanostructure with lengths and widths of approximately 100 and 20 nm, respectively, which grew to form advanced nanoarchitectures, including those resembling the weave patterns of Waraji (traditional Japanese straw sandals. This concept of combining block copolypeptide amphiphiles with discrete coordination compounds allows the design of flexible and functional supramolecular coordination systems in water.
Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces
Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.
2012-01-01
Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved
International Nuclear Information System (INIS)
Ching, J.; Oblow, E.M.; Goldstein, H.
1976-01-01
An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Inoguchi, Jun-ichi; Kajiwara, Kenji; Ohta, Yasuhiro
2011-01-01
We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations. (paper)
An innovative discrete multilevel sampler design
International Nuclear Information System (INIS)
Marvin, B.K.; De Clercq, P.J.; Taylor, B.B.; Mauro, D.M.
1995-01-01
An innovative, small-diameter PVC discrete multilevel sampler (DMLS) was designed for the Electric Power Research Institute (EPRI) to provide low-cost, discrete groundwater samples from shallow aquifers. When combined with appropriately-sized direct push soil sampling technologies, high resolution aquifer characterization can be achieved during initial site assessment or remediation monitoring activities. The sampler is constructed from 1-inch diameter PVC well materials, containing polyethylene tubing threaded through PVC disks. Self-expanding annular and internal bentonite seals were developed which isolate discrete sampling zones. The DMLS design allows customization of sampling and isolation zone lengths to suit site-specific goals. Installation of the DMLS is achieved using a temporary, expendable-tipped casting driven by direct push methods. This technique minimizes mobilization costs, site and soil column disturbances, and allows rapid installation in areas of limited overhead clearance. Successful pilot installations of the DMLS prototype have been made at a former manufactured gas plant (MGP) site and a diesel fuel spill site. Analysis of groundwater samples from these sites, using relative compound distributions and contaminant concentration profiling, confirmed that representative discrete samples were collected. This design provides both economical and versatile groundwater monitoring during all phases of site assessment and remediation
Integrated two-section discrete mode laser
Anandarajah, P.M.; Latkowski, S.; Browning, C.; Zhou, R.; O'Carroll, J.; Phelan, R.; Kelly, B.; O'Gorman, J.; Barry, L.P.
2012-01-01
The authors present the design and characterization of a novel integrated two-section discrete mode index patterned diode laser source. The two slotted regions etched into the laser ridge waveguide are formed in the same fabrication step as the ridge, thus avoiding the requirement for complex
About Multi-Heston SDE Discretization
Directory of Open Access Journals (Sweden)
Tiberiu Socaciu
2013-07-01
Full Text Available Abstract: in this paper we show how can estimate a financial derivative based on a support if assume for the support a Multi-Heston model.Keywords: Euler Maruyama discretization method, Monte Carlo simulation, Heston model, Double-Heston model, Multi-Heston model.
Transversals in non-discrete groups
Indian Academy of Sciences (India)
Transversals in non-discrete groups. RAMJI LAL and R P SHUKLA. Department of Mathematics, University of Allahabad, Allahabad 211 002, India. E-mail: ramjilal@mri.ernet.in; rps@mri.ernet.in. MS received 2 August 2004; revised 4 August 2005. Abstract. The concept of 'topological right transversal' is introduced to study ...
Attractors for discrete periodic dynamical systems
John E. Franke; James F. Selgrade
2003-01-01
A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...
Model-Checking Discrete Duration Calculus
DEFF Research Database (Denmark)
Hansen, Michael Reichhardt
1994-01-01
can do model-checking. The subset we consider is expressive enough to formalize the requirements to the gas burner system given by A.P. Ravn (1993); but only for a discrete time domain. Model-checking is done by reducing the correctness problem ℳ|=𝒟 to the inclusion problem of regular...
Discrete Events as Units of Perceived Time
Liverence, Brandon M.; Scholl, Brian J.
2012-01-01
In visual images, we perceive both space (as a continuous visual medium) and objects (that inhabit space). Similarly, in dynamic visual experience, we perceive both continuous time and discrete events. What is the relationship between these units of experience? The most intuitive answer may be similar to the spatial case: time is perceived as an…
Discrete dispersion models and their Tweedie asymptotics
DEFF Research Database (Denmark)
Jørgensen, Bent; Kokonendji, Célestin C.
2016-01-01
The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this ap......The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place...... in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models...... with power variance functions. Using the factorial cumulant generating function as tool, we introduce a dilation operation as a discrete analogue of scaling, generalizing binomial thinning. The Poisson-Tweedie factorial dispersion models are closed under dilation, which in turn leads to a Poisson...
Multivariate Discrete First Order Stochastic Dominance
DEFF Research Database (Denmark)
Tarp, Finn; Østerdal, Lars Peter
This paper characterizes the principle of first order stochastic dominance in a multivariate discrete setting. We show that a distribution f first order stochastic dominates distribution g if and only if f can be obtained from g by iteratively shifting density from one outcome to another...
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
2013-01-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis...
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
Discrete choice models with multiplicative error terms
DEFF Research Database (Denmark)
Fosgerau, Mogens; Bierlaire, Michel
2009-01-01
The conditional indirect utility of many random utility maximization (RUM) discrete choice models is specified as a sum of an index V depending on observables and an independent random term ε. In general, the universe of RUM consistent models is much larger, even fixing some specification of V due...
Choice certainty in Discrete Choice Experiments
DEFF Research Database (Denmark)
Uggeldahl, Kennet Christian; Jacobsen, Catrine; Lundhede, Thomas
2016-01-01
In this study, we conduct a Discrete Choice Experiment (DCE) using eye tracking technology to investigate if eye movements during the completion of choice sets reveal information about respondents’ choice certainty. We hypothesise that the number of times that respondents shift their visual...
Ordinal Welfare Comparisons with Multiple Discrete Indicators
DEFF Research Database (Denmark)
Arndt, Channing; Distante, Roberta; Hussain, M. Azhar
We develop an ordinal method for making welfare comparisons between populations with multidimensional discrete well-being indicators observed at the micro level. The approach assumes that, for each well-being indicator, the levels can be ranked from worse to better; however, no assumptions are made...
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
The Discrete Element Method (DEM) is used to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. In the DEM, the material is simulated on a grain-by-grain basis, and defining the micromechanical properties...
Discrete breathers in Bose–Einstein condensates
International Nuclear Information System (INIS)
Franzosi, Roberto; Politi, Antonio; Livi, Roberto; Oppo, Gian-Luca
2011-01-01
Discrete breathers, originally introduced in the context of biopolymers and coupled nonlinear oscillators, are also localized modes of excitation of Bose–Einstein condensates (BEC) in periodic potentials such as those generated by counter-propagating laser beams in an optical lattice. Static and dynamical properties of breather states are analysed in the discrete nonlinear Schrödinger equation that is derived in the limit of deep potential wells, tight-binding and the superfluid regime of the condensate. Static and mobile breathers can be formed by progressive re-shaping of initial Gaussian wave-packets or by transporting atomic density towards dissipative boundaries of the lattice. Static breathers generated via boundary dissipations are determined via a transfer-matrix approach and discussed in the two analytic limits of highly localized and very broad profiles. Mobile breathers that move across the lattice are well approximated by modified analytical expressions derived from integrable models with two independent parameters: the core-phase gradient and the peak amplitude. Finally, possible experimental realizations of discrete breathers in BEC in optical lattices are discussed in the presence of residual harmonic trapping and in interferometry configurations suitable to investigate discrete breathers' interactions. (invited article)
Discrete Event Simulation of Distributed Team Communication
2012-03-22
performs, and auditory information that is provided through multiple audio devices with speech response. This paper extends previous discrete event workload...2008, pg. 1) notes that “Architecture modeling furnishes abstrac- tions for use in managing complexities, allowing engineers to visualise the proposed
Discrete expansions of continuum wave functions
International Nuclear Information System (INIS)
Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.
1980-01-01
Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)
Failure diagnosis using discrete event models
International Nuclear Information System (INIS)
Sampath, M.; Sengupta, R.; Lafortune, S.; Teneketzis, D.; Sinnamohideen, K.
1994-01-01
We propose a Discrete Event Systems (DES) approach to the failure diagnosis problem. We present a methodology for modeling physical systems in a DES framework. We discuss the notion of diagnosability and present the construction procedure of the diagnoser. Finally, we illustrate our approach using a Heating, Ventilation and Air Conditioning (HVAC) system
A Discrete Dynamical Model of Signed Partitions
Directory of Open Access Journals (Sweden)
G. Chiaselotti
2013-01-01
Full Text Available We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems.
A Note on Discrete Mathematics and Calculus.
O'Reilly, Thomas J.
1987-01-01
Much of the current literature on the topic of discrete mathematics and calculus during the first two years of an undergraduate mathematics curriculum is cited. A relationship between the recursive integration formulas and recursively defined polynomials is described. A Pascal program is included. (Author/RH)
Analysis hierarchical model for discrete event systems
Ciortea, E. M.
2015-11-01
The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.
Fair value accounting and managerial discretion
Byrne, A.; Clacher, I.; Hillier, D.; Hodgson, A.
2008-01-01
We analyse the extent to which managers exercise discretion under fair value accounting and the value relevance of these disclosures. Utilising a sample of firms that apply the UK fair value pension accounting standard, (FRS-17), we examine the main determinants of the assumptions managers use to
Electroless plating apparatus for discrete microsized particles
International Nuclear Information System (INIS)
Mayer, A.
1978-01-01
Method and apparatus are disclosed for producing very uniform coatings of a desired material on discrete microsized particles by electroless techniques. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with each other for a time sufficient for such to occur
Discrete structures in F-theory compactifications
Energy Technology Data Exchange (ETDEWEB)
Till, Oskar
2016-05-04
In this thesis we study global properties of F-theory compactifications on elliptically and genus-one fibered Calabi-Yau varieties. This is motivated by phenomenological considerations as well as by the need for a deeper understanding of the set of consistent F-theory vacua. The global geometric features arise from discrete and arithmetic structures in the torus fiber and can be studied in detail for fibrations over generic bases. In the case of elliptic fibrations we study the role of the torsion subgroup of the Mordell-Weil group of sections in four dimensional compactifications. We show how the existence of a torsional section restricts the admissible matter representations in the theory. This is shown to be equivalent to inducing a non-trivial fundamental group of the gauge group. Compactifying F-theory on genus-one fibrations with multisections gives rise to discrete selection rules. In field theory the discrete symmetry is a broken U(1) symmetry. In the geometry the higgsing corresponds to a conifold transition. We explain in detail the origin of the discrete symmetry from two different M-theory phases and put the result into the context of torsion homology. Finally we systematically construct consistent gauge fluxes on genus-one fibrations and show that these induce an anomaly free chiral spectrum.
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Discrete-time rewards model-checked
Larsen, K.G.; Andova, S.; Niebert, Peter; Hermanns, H.; Katoen, Joost P.
2003-01-01
This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and
Discrete Mathematics Course Supported by CAS MATHEMATICA
Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.
2017-01-01
In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…
Electrolytic plating apparatus for discrete microsized particles
International Nuclear Information System (INIS)
Mayer, A.
1976-01-01
Method and apparatus are disclosed for electrolytically producing very uniform coatings of a desired material on discrete microsized particles. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with a powered cathode for a time sufficient for such to occur. 4 claims, 2 figures
Neutrino mass and mixing with discrete symmetry
International Nuclear Information System (INIS)
King, Stephen F; Luhn, Christoph
2013-01-01
This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A 4 , S 4 and Δ(96). (review article)
Reproductive Health Services Discrete-Event Simulation
Lee, Sungjoo; Giles, Denise F.; Goldsman, David; Cook, Douglas A.; Mishra, Ninad; McCarthy, Brian
2006-01-01
Low resource healthcare environments are often characteristic of patient flow patterns with varying patient risks, extensive patient waiting times, uneven workload distributions, and inefficient service delivery. Models from industrial and systems engineering allow for a greater examination of processes by applying discrete-event computer simulation techniques to evaluate and optimize hospital performance.
Hybrid discrete-time neural networks.
Cao, Hongjun; Ibarz, Borja
2010-11-13
Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.
Web-Based Implementation of Discrete Mathematics
Love, Tanzy; Keinert, Fritz; Shelley, Mack
2006-01-01
The Department of Mathematics at Iowa State University teaches a freshman-level Discrete Mathematics course with total enrollment of about 1,800 students per year. The traditional format includes large lectures, with about 150 students each, taught by faculty and temporary instructors in two class sessions per week and recitation sections, with…
Discrete Mathematics and the Secondary Mathematics Curriculum.
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Applied Behavior Analysis: Beyond Discrete Trial Teaching
Steege, Mark W.; Mace, F. Charles; Perry, Lora; Longenecker, Harold
2007-01-01
We discuss the problem of autism-specific special education programs representing themselves as Applied Behavior Analysis (ABA) programs when the only ABA intervention employed is Discrete Trial Teaching (DTT), and often for limited portions of the school day. Although DTT has many advantages to recommend its use, it is not well suited to teach…
Discrete dislocation modelling of submicron indentation
Widjaja, A; Van der Giessen, E; Needleman, A
2005-01-01
Indentation of a planar single crystal by a circular rigid indenter is analyzed using discrete dislocation plasticity. The crystal has three slip systems and is initially dislocation-free, but edge dislocations can nucleate from point sources inside the crystal. The lattice resistance to dislocation
Infant differential behavioral responding to discrete emotions.
Walle, Eric A; Reschke, Peter J; Camras, Linda A; Campos, Joseph J
2017-10-01
Emotional communication regulates the behaviors of social partners. Research on individuals' responding to others' emotions typically compares responses to a single negative emotion compared with responses to a neutral or positive emotion. Furthermore, coding of such responses routinely measure surface level features of the behavior (e.g., approach vs. avoidance) rather than its underlying function (e.g., the goal of the approach or avoidant behavior). This investigation examined infants' responding to others' emotional displays across 5 discrete emotions: joy, sadness, fear, anger, and disgust. Specifically, 16-, 19-, and 24-month-old infants observed an adult communicate a discrete emotion toward a stimulus during a naturalistic interaction. Infants' responses were coded to capture the function of their behaviors (e.g., exploration, prosocial behavior, and security seeking). The results revealed a number of instances indicating that infants use different functional behaviors in response to discrete emotions. Differences in behaviors across emotions were clearest in the 24-month-old infants, though younger infants also demonstrated some differential use of behaviors in response to discrete emotions. This is the first comprehensive study to identify differences in how infants respond with goal-directed behaviors to discrete emotions. Additionally, the inclusion of a function-based coding scheme and interpersonal paradigms may be informative for future emotion research with children and adults. Possible developmental accounts for the observed behaviors and the benefits of coding techniques emphasizing the function of social behavior over their form are discussed. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Discretization of four types of Weyl group orbit functions
International Nuclear Information System (INIS)
Hrivnák, Jiří
2013-01-01
The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented
Prediction of Water Binding to Protein Hydration Sites with a Discrete, Semiexplicit Solvent Model.
Setny, Piotr
2015-12-08
Buried water molecules are ubiquitous in protein structures and are found at the interface of most protein-ligand complexes. Determining their distribution and thermodynamic effect is a challenging yet important task, of great of practical value for the modeling of biomolecular structures and their interactions. In this study, we present a novel method aimed at the prediction of buried water molecules in protein structures and estimation of their binding free energies. It is based on a semiexplicit, discrete solvation model, which we previously introduced in the context of small molecule hydration. The method is applicable to all macromolecular structures described by a standard all-atom force field, and predicts complete solvent distribution within a single run with modest computational cost. We demonstrate that it indicates positions of buried hydration sites, including those filled by more than one water molecule, and accurately differentiates them from sterically accessible to water but void regions. The obtained estimates of water binding free energies are in fair agreement with reference results determined with the double decoupling method.
A 2+1 non-isospectral discrete integrable system and its discrete integrable coupling system
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2006-01-01
In this Letter by considering a (2+1)-dimensional discrete non-isospectral linear problem, a new (2+1)-dimensional integrable lattice hierarchy is constructed. It shows that generalization of the Blaszak-Marciniak lattice hierarchy can be obtained as a reduction. Then an extended algebraic system X-bar of X is presented, from which the integrable coupling system of the (2+1)-dimensional discrete non-isospectral Blaszak-Marciniak lattice equations are obtained
Application of an efficient Bayesian discretization method to biomedical data
Directory of Open Access Journals (Sweden)
Gopalakrishnan Vanathi
2011-07-01
Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.
Molecular dynamics of bacteriorhodopsin.
Lupo, J A; Pachter, R
1997-02-01
A model of bacteriorhodopsin (bR), with a retinal chromophore attached, has been derived for a molecular dynamics simulation. A method for determining atomic coordinates of several ill-defined strands was developed using a structure prediction algorithm based on a sequential Kalman filter technique. The completed structure was minimized using the GROMOS force field. The structure was then heated to 293 K and run for 500 ps at constant temperature. A comparison with the energy-minimized structure showed a slow increase in the all-atom RMS deviation over the first 200 ps, leveling off to approximately 2.4 A relative to the starting structure. The final structure yielded a backbone-atom RMS deviation from the crystallographic structure of 2.8 A. The residue neighbors of the chromophore atoms were followed as a function of time. The set of persistent near-residue neighbors supports the theory that differences in pKa values control access to the Schiff base proton, rather than formation of a counterion complex.
Is Discrete Mathematics the New Math of the Eighties?
Hart, Eric W.
1985-01-01
Considered are what discrete mathematics includes, some parallels and differences between new math and discrete mathematics (listed in a table), and lessons to be learned. A list of references is included. (MNS)
Comparison of discrete Hodge star operators for surfaces
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-01-01
We investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier
Supporting scalable Bayesian networks using configurable discretizer actuators
CSIR Research Space (South Africa)
Osunmakinde, I
2009-04-01
Full Text Available The authors propose a generalized model with configurable discretizer actuators as a solution to the problem of the discretization of massive numerical datasets. Their solution is based on a concurrent distribution of the actuators and uses dynamic...
Dimension Reduction and Discretization in Stochastic Problems by Regression Method
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
1996-01-01
The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ...
On some properties of the discrete Lyapunov exponent
International Nuclear Information System (INIS)
Amigo, Jose M.; Kocarev, Ljupco; Szczepanski, Janusz
2008-01-01
One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting
Breatherlike excitations in discrete lattices with noise and nonlinear damping
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus
1997-01-01
We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects...
Discretely tunable micromachined injection-locked lasers
International Nuclear Information System (INIS)
Cai, H; Yu, M B; Lo, G Q; Kwong, D L; Zhang, X M; Liu, A Q; Liu, B
2010-01-01
This paper reports a micromachined injection-locked laser (ILL) to provide tunable discrete wavelengths. It utilizes a non-continuously tunable laser as the master to lock a Fabry–Pérot semiconductor laser chip. Both lasers are integrated into a deep-etched silicon chip with dimensions of 3 mm × 3 mm × 0.8 mm. Based on the experimental results, significant improvements in the optical power and spectral purity have been achieved in the fully locked state, and optical hysteresis and bistability have also been observed in response to the changes of the output wavelength and optical power of the master laser. As a whole system, the micromachined ILL is able to provide single mode, discrete wavelength tuning, high power and direct modulation with small size and single-chip solution, making it promising for advanced optical communications such as wavelength division multiplexing optical access networks.
Discrete instability in the DNA double helix
International Nuclear Information System (INIS)
Tabi, Conrad Bertrand; Mohamadou, Alidou; Kofane, Timoleon Crepin
2009-06-01
Modulational instability (MI) is explored in the framework of the base-rotor model of DNA dynamics. We show in fact that, the helicoidal coupling introduced in the spin model of DNA reduces the system to a modified discrete sine-Gordon (sG) equation. The MI criterion is thus modified and displays interesting features because of the helicoidal coupling. This is confirmed in the numerical analysis where a critical value of the helicoidal coupling constant is derived. In the simulations, we have found that a train of pulses are generated when the lattice is subjected to MI, in agreement with analytical results obtained in a modified discrete sG equation. Also, the competitive effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. In the same way, it is shown that MI can lead to energy localization which is high for some values of the helicoidal coupling constant. (author)
Vortices trapped in discrete Josephson rings
International Nuclear Information System (INIS)
Van der Zanta, H.S.J.; Orlando, T.P.; Watanabe, Shinya; Strogatz, S.H.
1994-01-01
We report the first measurements of current- (I-V) characteristics of discrete rings of Josephson junctions. As I is increased, resonant steps appear in the I-V curve, due to phase-locking between a propagating, trapped vortex and the linear waves excited in its wake. Unexpectedly, the phase velocity of the linear waves, not the group velocity, is the physically important quantity and mode numbers outside the Brillouin zone are relevant. Our measurements show that away from the resonant steps, a single vortex can move in an environment with very little damping, making the discrete one-dimensional ring a well-defined model system for the study of ballistic and quantum vortex experiments. ((orig.))
Vortices trapped in discrete Josephson rings
Energy Technology Data Exchange (ETDEWEB)
Van der Zanta, H.S.J. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Orlando, T.P. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Watanabe, Shinya [Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Strogatz, S.H. [Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
1994-12-01
We report the first measurements of current- (I-V) characteristics of discrete rings of Josephson junctions. As I is increased, resonant steps appear in the I-V curve, due to phase-locking between a propagating, trapped vortex and the linear waves excited in its wake. Unexpectedly, the phase velocity of the linear waves, not the group velocity, is the physically important quantity and mode numbers outside the Brillouin zone are relevant. Our measurements show that away from the resonant steps, a single vortex can move in an environment with very little damping, making the discrete one-dimensional ring a well-defined model system for the study of ballistic and quantum vortex experiments. ((orig.)).
Discrete and continuous simulation theory and practice
Bandyopadhyay, Susmita
2014-01-01
When it comes to discovering glitches inherent in complex systems-be it a railway or banking, chemical production, medical, manufacturing, or inventory control system-developing a simulation of a system can identify problems with less time, effort, and disruption than it would take to employ the original. Advantageous to both academic and industrial practitioners, Discrete and Continuous Simulation: Theory and Practice offers a detailed view of simulation that is useful in several fields of study.This text concentrates on the simulation of complex systems, covering the basics in detail and exploring the diverse aspects, including continuous event simulation and optimization with simulation. It explores the connections between discrete and continuous simulation, and applies a specific focus to simulation in the supply chain and manufacturing field. It discusses the Monte Carlo simulation, which is the basic and traditional form of simulation. It addresses future trends and technologies for simulation, with par...
Juxtaposed color halftoning relying on discrete lines.
Babaei, Vahid; Hersch, Roger D
2013-02-01
Most halftoning techniques allow screen dots to overlap. They rely on the assumption that the inks are transparent, i.e., the inks do not scatter a significant portion of the light back to the air. However, many special effect inks, such as metallic inks, iridescent inks, or pigmented inks, are not transparent. In order to create halftone images, halftone dots formed by such inks should be juxtaposed, i.e., printed side by side. We propose an efficient juxtaposed color halftoning technique for placing any desired number of colorant layers side by side without overlapping. The method uses a monochrome library of screen elements made of discrete lines with rational thicknesses. Discrete line juxtaposed color halftoning is performed efficiently by multiple accesses to the screen element library.
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...
Integral and discrete inequalities and their applications
Qin, Yuming
2016-01-01
This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.
Semi-Discrete Ingham-Type Inequalities
International Nuclear Information System (INIS)
Komornik, Vilmos; Loreti, Paola
2007-01-01
One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently. Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process
Quantum RLC circuits: Charge discreteness and resonance
Energy Technology Data Exchange (ETDEWEB)
Utreras-Diaz, Constantino A. [Instituto de Fisica, Facultad de Ciencias, Universidad Austral de Chile, Campus Isla Teja s/n, Casilla 567, Valdivia (Chile)], E-mail: cutreras@uach.cl
2008-10-20
In a recent article [C.A. Utreras-Diaz, Phys. Lett. A 372 (2008) 5059], we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance inductive circuit, we obtain the Stark ladder energies in yet another way; for the circuit driven by a combination d.c. plus a.c. electromotive force (emf) we generalize earlier results by Chandia et al. [K. Chandia, J.C. Flores, E. Lazo, Phys. Lett. A 359 (2006) 693]. As a second application, we investigate the effect of electrical resistance and charge discreteness, in the resonance conditions of a series RLC quantum circuit.
Quantum RLC circuits: Charge discreteness and resonance
International Nuclear Information System (INIS)
Utreras-Diaz, Constantino A.
2008-01-01
In a recent article [C.A. Utreras-Diaz, Phys. Lett. A 372 (2008) 5059], we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance inductive circuit, we obtain the Stark ladder energies in yet another way; for the circuit driven by a combination d.c. plus a.c. electromotive force (emf) we generalize earlier results by Chandia et al. [K. Chandia, J.C. Flores, E. Lazo, Phys. Lett. A 359 (2006) 693]. As a second application, we investigate the effect of electrical resistance and charge discreteness, in the resonance conditions of a series RLC quantum circuit
Discrete approach to complex planar geometries
International Nuclear Information System (INIS)
Cupini, E.; De Matteis, A.
1974-01-01
Planar regions in Monte Carlo transport problems have been represented by a finite set of points with a corresponding region index for each. The simulation of particle free-flight reduces then to the simple operations necessary for scanning appropriate grid points to determine whether a region other than the starting one is encountered. When the complexity of the geometry is restricted to only some regions of the assembly examined, a mixed discrete-continuous philosophy may be adopted. By this approach, the lattice of a thermal reactor has been treated, discretizing only the central regions of the cell containing the fuel rods. Excellent agreement with experimental results has been obtained in the computation of cell parameters in the energy range from fission to thermalization through the 238 U resonance region. (U.S.)
Discrete event systems diagnosis and diagnosability
Sayed-Mouchaweh, Moamar
2014-01-01
Discrete Event Systems: Diagnosis and Diagnosability addresses the problem of fault diagnosis of Discrete Event Systems (DES). This book provides the basic techniques and approaches necessary for the design of an efficient fault diagnosis system for a wide range of modern engineering applications. The different techniques and approaches are classified according to several criteria such as: modeling tools (Automata, Petri nets) that is used to construct the model; the information (qualitative based on events occurrences and/or states outputs, quantitative based on signal processing and data analysis) that is needed to analyze and achieve the diagnosis; the decision structure (centralized, decentralized) that is required to achieve the diagnosis. The goal of this classification is to select the efficient method to achieve the fault diagnosis according to the application constraints. This book focuses on the centralized and decentralized event based diagnosis approaches using formal language and automata as mode...
Discrete PID Tuning Using Artificial Intelligence Techniques
Directory of Open Access Journals (Sweden)
Petr DOLEŽEL
2009-06-01
Full Text Available PID controllers are widely used in industry these days due to their useful properties such as simple tuning or robustness. While they are applicable to many control problems, they can perform poorly in some applications. Highly nonlinear system control with constrained manipulated variable can be mentioned as an example. The point of the paper is to string together convenient qualities of conventional PID control and progressive techniques based on Artificial Intelligence. Proposed control method should deal with even highly nonlinear systems. To be more specific, there is described new method of discrete PID controller tuning in this paper. This method tunes discrete PID controller parameters online through the use of genetic algorithm and neural model of controlled system in order to control successfully even highly nonlinear systems. After method description and some discussion, there is performed control simulation and comparison to one chosen conventional control method.
Discrete variable theory of triatomic photodissociation
International Nuclear Information System (INIS)
Heather, R.W.; Light, J.C.
1983-01-01
The coupled equations describing the photodissociation process are expressed in the discrete variable representation (DVR) in which the coupled equations are labeled by quadrature points rather than by internal basis functions. A large reduction in the dimensionality of the coupled equations can be realized since the spatially localized bound state nuclear wave function vanishes at most of the quadrature points, making only certain orientations of the fragments important in the region of strong interaction (small separation). The discrete variable theory of photodissociation is applied to the model dissociation of bent HCN in which the CN fragment is treated as a rigid rotor. The truncated DVR rotational distributions are compared with the exact close coupled rotational distributions, and excellent agreement with greatly reduced dimensionality of the equations is found
Lax Pairs for Discrete Integrable Equations via Darboux Transformations
International Nuclear Information System (INIS)
Cao Ce-Wen; Zhang Guang-Yao
2012-01-01
A method is developed to construct discrete Lax pairs using Darboux transformations. More kinds of Lax pairs are found for some newly appeared discrete integrable equations, including the H1, the special H3 and the Q1 models in the Adler—Bobenko—Suris list and the closely related discrete and semi-discrete pKdV, pMKdV, SG and Liouville equations. (general)
Discrete time analysis of a repairable machine
Alfa, Attahiru Sule; Castro, I. T.
2002-01-01
We consider, in discrete time, a single machine system that operates for a period of time represented by a general distribution. This machine is subject to failures during operations and the occurrence of these failures depends on how many times the machine has previously failed. Some failures are repairable and the repair times may or may not depend on the number of times the machine was previously repaired. Repair times also have a general distribution. The operating times...
Program For Parallel Discrete-Event Simulation
Beckman, Brian C.; Blume, Leo R.; Geiselman, John S.; Presley, Matthew T.; Wedel, John J., Jr.; Bellenot, Steven F.; Diloreto, Michael; Hontalas, Philip J.; Reiher, Peter L.; Weiland, Frederick P.
1991-01-01
User does not have to add any special logic to aid in synchronization. Time Warp Operating System (TWOS) computer program is special-purpose operating system designed to support parallel discrete-event simulation. Complete implementation of Time Warp mechanism. Supports only simulations and other computations designed for virtual time. Time Warp Simulator (TWSIM) subdirectory contains sequential simulation engine interface-compatible with TWOS. TWOS and TWSIM written in, and support simulations in, C programming language.
Discrete Alfven waves in the TORTUS tokamak
International Nuclear Information System (INIS)
Amagishi, Y.; Ballico, M.J.; Cross, R.C.; Donnely, I.J.
1989-01-01
Discrete Alfven Waves (DAWs) have been observed as antenna resistance peaks and as enhanced edge fields in the TORTUS tokamak during Alfven wave heating experiments. A kinetic theory code has been used to calculate the antenna loading and the structure of the DAW fields for a range of plasma current and density profiles. There is fair agreement between the measured and predicted amplitude of the DAW fields in the plasma edge when both are normalized to the same antenna power
Nuclear data preparation and discrete ordinates calculation
International Nuclear Information System (INIS)
Carmignani, B.
1980-01-01
These lectures deal with the use of the GAM-GATHER and GAM-THERMOS chains for the calculation of lattice cross sections and within use of the discrete ordinates one dimensional ANISN code for the calculation of criticality and flux distribution of the cell and of the whole reactor. As an example the codes are applied to the calculation of a PWR. Results of different approximations are compared. (author)
Discrete Ricci Flow in Higher Dimensions
2015-02-01
recently, we showed analytically that the SRF equations converged to the continuum RF equations for the neck-pinch 3- geometry [10]. In this analysis we also...Hamilton’s RF. It is the first dimensionally agnostic generalization of RF for PL geometries . We refer to our approach as simplicial Ricci flow (SRF). For a...Discrete Exterior Calculus , Regge Calculus , Piecewise Linear Complex 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18. NUMBER
Discrete mathematics course supported by CAS MATHEMATICA
Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.
2017-08-01
In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our approach, we conducted an anonymous survey. The results of the survey provide evidence that our approach contributes to high outcomes and aligns with the course aims and objectives.
"Minesweeper" and spectrum of discrete Laplacians
German, Oleg; Lakshtanov, Evgeny
2008-01-01
The paper is devoted to a problem inspired by the "Minesweeper" computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of "Minesweeper" but does not require a computer.
A variational synthesis nodal discrete ordinates method
International Nuclear Information System (INIS)
Favorite, J.A.; Stacey, W.M.
1999-01-01
A self-consistent nodal approximation method for computing discrete ordinates neutron flux distributions has been developed from a variational functional for neutron transport theory. The advantage of the new nodal method formulation is that it is self-consistent in its definition of the homogenized nodal parameters, the construction of the global nodal equations, and the reconstruction of the detailed flux distribution. The efficacy of the method is demonstrated by two-dimensional test problems
Flexible Visual Quality Inspection in Discrete Manufacturing
Petković, Tomislav; Jurić, Darko; Lončarić, Sven
2013-01-01
Most visual quality inspections in discrete manufacturing are composed of length, surface, angle or intensity measurements. Those are implemented as end-user configurable inspection tools that should not require an image processing expert to set up. Currently available software solutions providing such capability use a flowchart based programming environment, but do not fully address an inspection flowchart robustness and can require a redefinition of the flowchart if a small variation is int...
Hyponormal differential operators with discrete spectrum
Directory of Open Access Journals (Sweden)
Zameddin I. Ismailov
2010-01-01
Full Text Available In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
Shang, Barry Z; Voulgarakis, Nikolaos K; Chu, Jhih-Wei
2012-07-28
This work illustrates that fluctuating hydrodynamics (FHD) simulations can be used to capture the thermodynamic and hydrodynamic responses of molecular fluids at the nanoscale, including those associated with energy and heat transfer. Using all-atom molecular dynamics (MD) trajectories as the reference data, the atomistic coordinates of each snapshot are mapped onto mass, momentum, and energy density fields on Eulerian grids to generate a corresponding field trajectory. The molecular length-scale associated with finite molecule size is explicitly imposed during this coarse-graining by requiring that the variances of density fields scale inversely with the grid volume. From the fluctuations of field variables, the response functions and transport coefficients encoded in the all-atom MD trajectory are computed. By using the extracted fluid properties in FHD simulations, we show that the fluctuations and relaxation of hydrodynamic fields quantitatively match with those observed in the reference all-atom MD trajectory, hence establishing compatibility between the atomistic and field representations. We also show that inclusion of energy transfer in the FHD equations can more accurately capture the thermodynamic and hydrodynamic responses of molecular fluids. The results indicate that the proposed MD-to-FHD mapping with explicit consideration of finite molecule size provides a robust framework for coarse-graining the solution phase of complex molecular systems.
Physical models on discrete space and time
International Nuclear Information System (INIS)
Lorente, M.
1986-01-01
The idea of space and time quantum operators with a discrete spectrum has been proposed frequently since the discovery that some physical quantities exhibit measured values that are multiples of fundamental units. This paper first reviews a number of these physical models. They are: the method of finite elements proposed by Bender et al; the quantum field theory model on discrete space-time proposed by Yamamoto; the finite dimensional quantum mechanics approach proposed by Santhanam et al; the idea of space-time as lattices of n-simplices proposed by Kaplunovsky et al; and the theory of elementary processes proposed by Weizsaecker and his colleagues. The paper then presents a model proposed by the authors and based on the (n+1)-dimensional space-time lattice where fundamental entities interact among themselves 1 to 2n in order to build up a n-dimensional cubic lattice as a ground field where the physical interactions take place. The space-time coordinates are nothing more than the labelling of the ground field and take only discrete values. 11 references
Generalized Detectability for Discrete Event Systems
Shu, Shaolong; Lin, Feng
2011-01-01
In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our results in three aspects. (1) We extend detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong detectability. The previous algorithms are based on observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called detector. (3) We extend detectability to D-detectability. While detectability requires determining the exact state of a system, D-detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on detectability of discrete event systems becomes more applicable in solving many practical problems. PMID:21691432
Entropic Phase Maps in Discrete Quantum Gravity
Directory of Open Access Journals (Sweden)
Benjamin F. Dribus
2017-06-01
Full Text Available Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 ⊂ C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics.
New formulation of the discrete element method
Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon
2018-01-01
A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.
Inferring gene networks from discrete expression data
Zhang, L.
2013-07-18
The modeling of gene networks from transcriptional expression data is an important tool in biomedical research to reveal signaling pathways and to identify treatment targets. Current gene network modeling is primarily based on the use of Gaussian graphical models applied to continuous data, which give a closedformmarginal likelihood. In this paper,we extend network modeling to discrete data, specifically data from serial analysis of gene expression, and RNA-sequencing experiments, both of which generate counts of mRNAtranscripts in cell samples.We propose a generalized linear model to fit the discrete gene expression data and assume that the log ratios of the mean expression levels follow a Gaussian distribution.We restrict the gene network structures to decomposable graphs and derive the graphs by selecting the covariance matrix of the Gaussian distribution with the hyper-inverse Wishart priors. Furthermore, we incorporate prior network models based on gene ontology information, which avails existing biological information on the genes of interest. We conduct simulation studies to examine the performance of our discrete graphical model and apply the method to two real datasets for gene network inference. © The Author 2013. Published by Oxford University Press. All rights reserved.
Police investigations: discretion denied yet undeniably exercised
Belur, J.; Tilley, N.; Osrin, D.; Daruwalla, N.; Kumar, M.; Tiwari, V.
2014-01-01
Police investigations involve determining whether a crime has been committed, and if so what type of crime, who has committed it and whether there is the evidence to charge the perpetrators. Drawing on fieldwork in Delhi and Mumbai, this paper explores how police investigations unfolded in the specific context of women’s deaths by burning in India. In particular, it focuses on the use of discretion despite its denial by those exercising it. In India, there are distinctive statutes relating to women’s suspicious deaths, reflecting the widespread expectation that the bride’s family will pay a dowry to the groom’s family and the tensions to which this may on occasion give rise in the early years of a marriage. Often, there are conflicting claims influencing how the woman’s death is classified. These in turn affect police investigation. The nature and direction of police discretion in investigating women’s deaths by burning reflect in part the unique nature of the legislation and the particular sensitivities in relation to these types of death. They also highlight processes that are liable to be at work in any crime investigation. It was found that police officers exercised unacknowledged discretion at seven specific points in the investigative process, with potentially significant consequences for the achievement of just outcomes: first response, recording the victim’s ‘dying declaration’, inquest, registering of the ‘First Information Report’, collecting evidence, arrest and framing of the charges. PMID:26376482
Meshes optimized for discrete exterior calculus (DEC).
Energy Technology Data Exchange (ETDEWEB)
Mousley, Sarah C. [Univ. of Illinois, Urbana-Champaign, IL (United States); Deakin, Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Knupp, Patrick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-12-01
We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.
Adaptive discrete-ordinates algorithms and strategies
International Nuclear Information System (INIS)
Stone, J.C.; Adams, M.L.
2005-01-01
We present our latest algorithms and strategies for adaptively refined discrete-ordinates quadrature sets. In our basic strategy, which we apply here in two-dimensional Cartesian geometry, the spatial domain is divided into regions. Each region has its own quadrature set, which is adapted to the region's angular flux. Our algorithms add a 'test' direction to the quadrature set if the angular flux calculated at that direction differs by more than a user-specified tolerance from the angular flux interpolated from other directions. Different algorithms have different prescriptions for the method of interpolation and/or choice of test directions and/or prescriptions for quadrature weights. We discuss three different algorithms of different interpolation orders. We demonstrate through numerical results that each algorithm is capable of generating solutions with negligible angular discretization error. This includes elimination of ray effects. We demonstrate that all of our algorithms achieve a given level of error with far fewer unknowns than does a standard quadrature set applied to an entire problem. To address a potential issue with other algorithms, we present one algorithm that retains exact integration of high-order spherical-harmonics functions, no matter how much local refinement takes place. To address another potential issue, we demonstrate that all of our methods conserve partial currents across interfaces where quadrature sets change. We conclude that our approach is extremely promising for solving the long-standing problem of angular discretization error in multidimensional transport problems. (authors)
Single-crossover recombination in discrete time.
von Wangenheim, Ute; Baake, Ellen; Baake, Michael
2010-05-01
Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in discrete time, allowing only for single crossovers. While the analogous dynamics in continuous time admits a closed solution (Baake and Baake in Can J Math 55:3-41, 2003), this no longer works for discrete time. A more general model (i.e. without the restriction to single crossovers) has been studied before (Bennett in Ann Hum Genet 18:311-317, 1954; Dawson in Theor Popul Biol 58:1-20, 2000; Linear Algebra Appl 348:115-137, 2002) and was solved algorithmically by means of Haldane linearisation. Using the special formalism introduced by Baake and Baake (Can J Math 55:3-41, 2003), we obtain further insight into the single-crossover dynamics and the particular difficulties that arise in discrete time. We then transform the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation. Still, the coefficients of the second step must be determined in a recursive manner, but once this is done for a given system, they allow for an explicit solution valid for all times.
An essay on discrete foundations for physics
International Nuclear Information System (INIS)
Noyes, H.P.; McGoveran, D.O.
1988-07-01
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs
An essay on discrete foundations for physics
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.; McGoveran, D.O.
1988-07-01
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.
An essay on discrete foundations for physics
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.; McGoveran, D.O.
1988-10-05
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.
Quantum cosmology based on discrete Feynman paths
International Nuclear Information System (INIS)
Chew, Geoffrey F.
2002-01-01
Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''
An essay on discrete foundations for physics
International Nuclear Information System (INIS)
Noyes, H.P.; McGoveran, D.O.
1988-01-01
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs
Discrete phase space based on finite fields
International Nuclear Information System (INIS)
Gibbons, Kathleen S.; Hoffman, Matthew J.; Wootters, William K.
2004-01-01
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2Nx2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our NxN phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space
Discrete convolution-operators and radioactive disintegration. [Numerical solution
Energy Technology Data Exchange (ETDEWEB)
Kalla, S L; VALENTINUZZI, M E [UNIVERSIDAD NACIONAL DE TUCUMAN (ARGENTINA). FACULTAD DE CIENCIAS EXACTAS Y TECNOLOGIA
1975-08-01
The basic concepts of discrete convolution and discrete convolution-operators are briefly described. Then, using the discrete convolution - operators, the differential equations associated with the process of radioactive disintegration are numerically solved. The importance of the method is emphasized to solve numerically, differential and integral equations.
Discrete frequency identification using the HP 5451B Fourier analyser
International Nuclear Information System (INIS)
Holland, L.; Barry, P.
1977-01-01
The frequency analysis by the HP5451B discrete frequency Fourier analyser is studied. The advantages of cross correlation analysis to identify discrete frequencies in a background noise are discussed in conjuction with the elimination of aliasing and wraparound error. Discrete frequency identification is illustrated by a series of graphs giving the results of analysing 'electrical' and 'acoustical' white noise and sinusoidal signals [pt
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.
2013-01-01
on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time
A Variational Approach to Perturbed Discrete Anisotropic Equations
Directory of Open Access Journals (Sweden)
Amjad Salari
2016-01-01
Full Text Available We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.
Mittag-Leffler function for discrete fractional modelling
Directory of Open Access Journals (Sweden)
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
Applications of exterior difference systems to variations in discrete mechanics
International Nuclear Information System (INIS)
Xie Zheng; Li Hongbo
2008-01-01
In discrete mechanics, difference equations describe the fundamental physical laws and exhibit many geometric properties. Can these equations be obtained in a geometric way? Using some techniques in exterior difference systems, we investigate the discrete variational problem. As an application, we give a positive answer to the above question for the discrete Newton's, Euler-Lagrange, and Hamilton's equations
Process algebra with timing : real time and discrete time
Baeten, J.C.M.; Middelburg, C.A.; Bergstra, J.A.; Ponse, A.J.; Smolka, S.A.
2001-01-01
We present real time and discrete time versions of ACP with absolute timing and relative timing. The starting-point is a new real time version with absolute timing, called ACPsat, featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete
A Baecklund transformation between two integrable discrete hungry systems
Energy Technology Data Exchange (ETDEWEB)
Fukuda, Akiko, E-mail: j1409704@ed.kagu.tus.ac.j [Department of Mathematical Information Science, Graduate School of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Yamamoto, Yusaku [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Iwasaki, Masashi [Department of Informatics and Environmental Science, Kyoto Prefectural University, 1-5, Nakaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522 (Japan); Ishiwata, Emiko [Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Nakamura, Yoshimasa [Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)
2011-01-17
The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.
A Baecklund transformation between two integrable discrete hungry systems
International Nuclear Information System (INIS)
Fukuda, Akiko; Yamamoto, Yusaku; Iwasaki, Masashi; Ishiwata, Emiko; Nakamura, Yoshimasa
2011-01-01
The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.
Multivariable biorthogonal continuous--discrete Wilson and Racah polynomials
International Nuclear Information System (INIS)
Tratnik, M.V.
1990-01-01
Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials
Finite-dimensional reductions of the discrete Toda chain
International Nuclear Information System (INIS)
Kazakova, T G
2004-01-01
The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well-known discrete Painleve equations dP III , dP V , dP VI . Lax representations for these discrete Painleve equations are found
Process algebra with timing: Real time and discrete time
Baeten, J.C.M.; Middelburg, C.A.
1999-01-01
We present real time and discrete time versions of ACP with absolute timing and relative timing. The startingpoint is a new real time version with absolute timing, called ACPsat , featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete
Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M.A.
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate
Seslija, Marko; Scherpen, Jacquelien M.A.; van der Schaft, Arjan
2011-01-01
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate
Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation
International Nuclear Information System (INIS)
Common, Alan K; Hone, Andrew N W
2008-01-01
The Yablonskii-Vorob'ev polynomials y n (t), which are defined by a second-order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painleve equation (P II ). Here we define two-variable polynomials Y n (t, h) on a lattice with spacing h, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when h = 0. They also provide rational solutions for a particular discretization of P II , namely the so-called alternate discrete P II , and this connection leads to an expression in terms of the Umemura polynomials for the third Painleve equation (P III ). It is shown that the Baecklund transformation for the alternate discrete Painleve equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete P II , which recovers Jimbo and Miwa's Lax pair for P II in the continuum limit h → 0
Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice
International Nuclear Information System (INIS)
Kavitha, L.; Parasuraman, E.; Gopi, D.; Prabhu, A.; Vicencio, Rodrigo A.
2016-01-01
We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.
Constitutive equations for discrete electromagnetic problems over polyhedral grids
International Nuclear Information System (INIS)
Codecasa, Lorenzo; Trevisan, Francesco
2007-01-01
In this paper a novel approach is proposed for constructing discrete counterparts of constitutive equations over polyhedral grids which ensure both consistency and stability of the algebraic equations discretizing an electromagnetic field problem. The idea is to construct discrete constitutive equations preserving the thermodynamic relations for constitutive equations. In this way, consistency and stability of the discrete equations are ensured. At the base, a purely geometric condition between the primal and the dual grids has to be satisfied for a given primal polyhedral grid, by properly choosing the dual grid. Numerical experiments demonstrate that the proposed discrete constitutive equations lead to accurate approximations of the electromagnetic field
From the continuous PV to discrete Painleve equations
International Nuclear Information System (INIS)
Tokihiro, T.; Grammaticos, B.; Ramani, A.
2002-01-01
We study the discrete transformations that are associated with the auto-Baecklund of the (continuous) P V equation. We show that several two-parameter discrete Painleve equations can be obtained as contiguity relations of P V . Among them we find the asymmetric d-P II equation which is a well-known form of discrete P III . The relation between the ternary P I (previously obtained through the discrete dressing approach) and P V is also established. A new discrete Painleve equation is also derived. (author)
Exact discretization of Schrödinger equation
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2016-01-08
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
Exact discretization of Schrödinger equation
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2016-01-01
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
Discrete non-parametric kernel estimation for global sensitivity analysis
International Nuclear Information System (INIS)
Senga Kiessé, Tristan; Ventura, Anne
2016-01-01
This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output. - Highlights: • We study a discrete kernel estimation for sensitivity analysis of a model. • A discrete kernel estimator of ANOVA decomposition of the model is presented. • Sensitivity indices are calculated for discrete input parameters. • An estimator of sensitivity indices is also presented with its convergence rate. • An application is realized for improving the reliability of environmental models.
Discrete ellipsoidal statistical BGK model and Burnett equations
Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei
2018-06-01
A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.
Directory of Open Access Journals (Sweden)
Bogdan Barz
Full Text Available Amyloid β-protein (Aβ is central to the pathology of Alzheimer's disease. A 5% difference in the primary structure of the two predominant alloforms, Aβ(1-40 and Aβ(1-42, results in distinct assembly pathways and toxicity properties. Discrete molecular dynamics (DMD studies of Aβ(1-40 and Aβ(1-42 assembly resulted in alloform-specific oligomer size distributions consistent with experimental findings. Here, a large ensemble of DMD-derived Aβ(1-40 and Aβ(1-42 monomers and dimers was subjected to fully atomistic molecular dynamics (MD simulations using the OPLS-AA force field combined with two water models, SPCE and TIP3P. The resulting all-atom conformations were slightly larger, less compact, had similar turn and lower β-strand propensities than those predicted by DMD. Fully atomistic Aβ(1-40 and Aβ(1-42 monomers populated qualitatively similar free energy landscapes. In contrast, the free energy landscape of Aβ(1-42 dimers indicated a larger conformational variability in comparison to that of Aβ(1-40 dimers. Aβ(1-42 dimers were characterized by an increased flexibility in the N-terminal region D1-R5 and a larger solvent exposure of charged amino acids relative to Aβ(1-40 dimers. Of the three positively charged amino acids, R5 was the most and K16 the least involved in salt bridge formation. This result was independent of the water model, alloform, and assembly state. Overall, salt bridge propensities increased upon dimer formation. An exception was the salt bridge propensity of K28, which decreased upon formation of Aβ(1-42 dimers and was significantly lower than in Aβ(1-40 dimers. The potential relevance of the three positively charged amino acids in mediating the Aβ oligomer toxicity is discussed in the light of available experimental data.
Institute of Scientific and Technical Information of China (English)
GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun
2002-01-01
In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.
Time-delay analyzer with continuous discretization
International Nuclear Information System (INIS)
Bayatyan, G.L.; Darbinyan, K.T.; Mkrtchyan, K.K.; Stepanyan, S.S.
1988-01-01
A time-delay analyzer is described which when triggered by a start pulse of adjustable duration performs continuous discretization of the analyzed signal within nearly 22 ns time intervals, the recording in a memory unit with following slow read-out of the information to the computer and its processing. The time-delay analyzer consists of four CAMAC-VECTOR systems of unit width. With its help one can separate comparatively short, small-amplitude rare signals against the background of quasistationary noise processes. 4 refs.; 3 figs
Nonperturbative summation over 3D discrete topologies
International Nuclear Information System (INIS)
Freidel, Laurent; Louapre, David
2003-01-01
The group field theories realizing the sum over all triangulations of all topologies of 3D discrete gravity amplitudes are known to be nonuniquely Borel summable. We modify these models to construct a new group field theory which is proved to be uniquely Borel summable, defining in an unambiguous way a nonperturbative sum over topologies in the context of 3D dynamical triangulations and spin foam models. Moreover, we give some arguments to support the fact that, despite our modification, this new model is similar to the original one, and therefore could be taken as a definition of the sum over topologies of 3D quantum gravity amplitudes
Discrete expansions of continuum functions. General concepts
International Nuclear Information System (INIS)
Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.
1979-01-01
Different discrete expansions of the continuum wave functions are considered: pole expansion (according to the Mittag-Lefler theorem), Weinberg states. The general property of these groups of states is their completeness in the finite region of space. They satisfy the Schroedinger type equations and are matched with free solutions of the Schroedinger equation at the boundary. Convergence of expansions for the S matrix, the Green functions and the continuous-spectrum wave functions is studied. A new group of states possessing the best convergence is introduced
A short course in discrete mathematics
Bender, Edward A
2004-01-01
What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, seq
Compartmentalization analysis using discrete fracture network models
Energy Technology Data Exchange (ETDEWEB)
La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...
A discrete transition to advanced mathematics
Richmond, Bettina
2009-01-01
As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last thr
Construction of Discrete Time Shadow Price
International Nuclear Information System (INIS)
Rogala, Tomasz; Stettner, Lukasz
2015-01-01
In the paper expected utility from consumption over finite time horizon for discrete time markets with bid and ask prices and strictly concave utility function is considered. The notion of weak shadow price, i.e. an illiquid price, depending on the portfolio, under which the model without bid and ask price is equivalent to the model with bid and ask price is introduced. Existence and the form of weak shadow price is shown. Using weak shadow price usual (called in the paper strong) shadow price is then constructed
Rules Versus Discretion in Monetary Policy
Stanley Fischer
1988-01-01
This paper examines the case for rules rather than discretion in the conduct of monetary policy, from both historical and analytic perspectives. The paper starts with the rules of the game under the gold standard. These rules were ill-defined and not adhered to; active discretionary policy was pursued to defend the gold standard -- but the gold standard came closer to a regime of rules than the current system. The arguments for rules in general developed by Milton Friedman are described mo ap...
Newnes passive and discrete circuits pocket book
MARSTON, R M
2000-01-01
Newnes Passive and Discrete Circuits Pocket Book is aimed at all engineers, technicians, students and experimenters who can build a design directly from a circuit diagram. In a highly concise form Ray Marston presents a huge compendium of circuits that can be built as they appear, adapted or used as building blocks. The devices used have been carefully chosen for their ease of availability and reasonable price. The selection of devices has been thoroughly updated for the second edition, which has also been expanded to cover the latest ICs.The three sections of the book cover: Moder
Discrete analysis of clay layer tensile strength
International Nuclear Information System (INIS)
Le, T.N.H.; Ple, O.; Villard, P.; Gourc, J.P.
2010-01-01
The Discrete Element Method is used to investigate the tensile behaviour and cracks mechanisms of a clay material submitted to bending loading. It is the case of compacted clay liners in landfill cap cover application. Such as the soil tested in this study is plastic clay, the distinct elements model was calibrated with previous data results by taking into account cohesive properties. Various contact and cohesion laws are tested to show that the numerical model is able to reproduce the failure mechanism. Numerical results are extending to simulate a landfill cap cover and comparing to experimental large scale field bending tests achieved in a real site of storage. (authors)
Discrete time modelization of human pilot behavior
Cavalli, D.; Soulatges, D.
1975-01-01
This modelization starts from the following hypotheses: pilot's behavior is a time discrete process, he can perform only one task at a time and his operating mode depends on the considered flight subphase. Pilot's behavior was observed using an electro oculometer and a simulator cockpit. A FORTRAN program has been elaborated using two strategies. The first one is a Markovian process in which the successive instrument readings are governed by a matrix of conditional probabilities. In the second one, strategy is an heuristic process and the concepts of mental load and performance are described. The results of the two aspects have been compared with simulation data.
An Einstein equation for discrete quantum gravity
Gudder, Stan
2012-01-01
The basic framework for this article is the causal set approach to discrete quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of complex-valued functions on $Q_n$. The formalism of DQG presents us with a decoherence matrix $D_n(x,y)$, $x,y\\in Q_n$. There is a growth order in $Q_n$ and a path in $Q_n$ is a maximal chain relative to this order. We denote the set of paths in $Q_n$ by $\\Omega_n$. For...
Discrete Symmetries and Models of Flavour Mixing
International Nuclear Information System (INIS)
King, Stephen F
2015-01-01
In this talk we shall give an overview of the role of discrete symmetries, including both CP and family symmetry, in constructing unified models of quark and lepton (including especially neutrino) masses and mixing. Various different approaches to model building will be described, denoted as direct, semi-direct and indirect, and the pros and cons of each approach discussed. Particular examples based on Δ(6n 2 ) will be discussed and an A to Z of Flavour with Pati-Salam will be presented. (paper)
Generalized reciprocity principle for discrete symplectic systems
Directory of Open Access Journals (Sweden)
Julia Elyseeva
2015-12-01
Full Text Available This paper studies transformations for conjoined bases of symplectic difference systems $Y_{i+1}=\\mathcal S_{i}Y_{i}$ with the symplectic coefficient matrices $\\mathcal S_i.$ For an arbitrary symplectic transformation matrix $P_{i}$ we formulate most general sufficient conditions for $\\mathcal S_{i},\\, P_{i}$ which guarantee that $P_{i}$ preserves oscillatory properties of conjoined bases $Y_{i}.$ We present examples which show that our new results extend the applicability of the discrete transformation theory.
Stability of molecular dynamics simulations of classical systems
DEFF Research Database (Denmark)
Toxværd, Søren
2012-01-01
The existence of a shadow Hamiltonian for discrete classical dynamics, obtained by an asymptotic expansion for a discrete symplectic algorithm, is employed to determine the limit of stability for molecular dynamics (MD) simulations with respect to the time-increment h of the discrete dynamics....... The investigation is based on the stability of the shadow energy, obtained by including the first term in the asymptotic expansion, and on the exact solution of discrete dynamics for a single harmonic mode. The exact solution of discrete dynamics for a harmonic potential with frequency ω gives a criterion...... for the limit of stability h ⩽ 2/ω. Simulations of the Lennard-Jones system and the viscous Kob-Andersen system show that one can use the limit of stability of the shadow energy or the stability criterion for a harmonic mode on the spectrum of instantaneous frequencies to determine the limit of stability of MD...
Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures.
Dallaston, Michael C; Fontelos, Marco A; Tseluiko, Dmitri; Kalliadasis, Serafim
2018-01-19
The formation of iterated structures, such as satellite and subsatellite drops, filaments, and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.
Clarke, Peter; Varghese, Philip; Goldstein, David
2018-01-01
A discrete velocity method is developed for gas mixtures of diatomic molecules with both rotational and vibrational energy states. A full quantized model is described, and rotation-translation and vibration-translation energy exchanges are simulated using a Larsen-Borgnakke exchange model. Elastic and inelastic molecular interactions are modeled during every simulated collision to help produce smooth internal energy distributions. The method is verified by comparing simulations of homogeneous relaxation by our discrete velocity method to numerical solutions of the Jeans and Landau-Teller equations, and to direct simulation Monte Carlo. We compute the structure of a 1D shock using this method, and determine how the rotational energy distribution varies with spatial location in the shock and with position in velocity space.
Discrete Pathophysiology is Uncommon in Patients with Nonspecific Arm Pain.
Kortlever, Joost T P; Janssen, Stein J; Molleman, Jeroen; Hageman, Michiel G J S; Ring, David
2016-06-01
Nonspecific symptoms are common in all areas of medicine. Patients and caregivers can be frustrated when an illness cannot be reduced to a discrete pathophysiological process that corresponds with the symptoms. We therefore asked the following questions: 1) Which demographic factors and psychological comorbidities are associated with change from an initial diagnosis of nonspecific arm pain to eventual identification of discrete pathophysiology that corresponds with symptoms? 2) What is the percentage of patients eventually diagnosed with discrete pathophysiology, what are those pathologies, and do they account for the symptoms? We evaluated 634 patients with an isolated diagnosis of nonspecific upper extremity pain to see if discrete pathophysiology was diagnosed on subsequent visits to the same hand surgeon, a different hand surgeon, or any physician within our health system for the same pain. There were too few patients with discrete pathophysiology at follow-up to address the primary study question. Definite discrete pathophysiology that corresponded with the symptoms was identified in subsequent evaluations by the index surgeon in one patient (0.16% of all patients) and cured with surgery (nodular fasciitis). Subsequent doctors identified possible discrete pathophysiology in one patient and speculative pathophysiology in four patients and the index surgeon identified possible discrete pathophysiology in four patients, but the five discrete diagnoses accounted for only a fraction of the symptoms. Nonspecific diagnoses are not harmful. Prospective randomized research is merited to determine if nonspecific, descriptive diagnoses are better for patients than specific diagnoses that imply pathophysiology in the absence of discrete verifiable pathophysiology.
Magnetismo Molecular (Molecular Magentism)
Energy Technology Data Exchange (ETDEWEB)
Reis, Mario S [Universidade Federal Fluminense, Brasil; Moreira Dos Santos, Antonio F [ORNL
2010-07-01
The new synthesis processes in chemistry open a new world of research, new and surprising materials never before found in nature can now be synthesized and, as a wonderful result, observed a series of physical phenomena never before imagined. Among these are many new materials the molecular magnets, the subject of this book and magnetic properties that are often reflections of the quantum behavior of these materials. Aside from the wonderful experience of exploring something new, the theoretical models that describe the behavior these magnetic materials are, in most cases, soluble analytically, which allows us to know in detail the physical mechanisms governing these materials. Still, the academic interest in parallel this subject, these materials have a number of properties that are promising to be used in technological devices, such as in computers quantum magnetic recording, magnetocaloric effect, spintronics and many other devices. This volume will journey through the world of molecular magnets, from the structural description of these materials to state of the art research.
A Discrete Model for Color Naming
Directory of Open Access Journals (Sweden)
J. M. Boi
2007-01-01
Full Text Available The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1. Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2, and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.
A Discrete Model for Color Naming
Menegaz, G.; Le Troter, A.; Sequeira, J.; Boi, J. M.
2006-12-01
The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1). Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2), and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.
Discrete quantum spectrum of black holes
Energy Technology Data Exchange (ETDEWEB)
Lochan, Kinjalk, E-mail: kinjalk@iucaa.in; Chakraborty, Sumanta, E-mail: sumanta@iucaa.in
2016-04-10
The quantum genesis of Hawking radiation is a long-standing puzzle in black hole physics. Semi-classically one can argue that the spectrum of radiation emitted by a black hole look very much sparse unlike what is expected from a thermal object. It was demonstrated through a simple quantum model that a quantum black hole will retain a discrete profile, at least in the weak energy regime. However, it was suggested that this discreteness might be an artifact of the simplicity of eigen-spectrum of the model considered. Different quantum theories can, in principle, give rise to different complicated spectra and make the radiation from black hole dense enough in transition lines, to make them look continuous in profile. We show that such a hope from a geometry-quantized black hole is not realized as long as large enough black holes are dubbed with a classical mass area relation in any gravity theory ranging from GR, Lanczos–Lovelock to f(R) gravity. We show that the smallest frequency of emission from black hole in any quantum description, is bounded from below, to be of the order of its inverse mass. That leaves the emission with only two possibilities. It can either be non-thermal, or it can be thermal only with the temperature being much larger than 1/M.
Emotional Aging: A Discrete Emotions Perspective
Directory of Open Access Journals (Sweden)
Ute eKunzmann
2014-05-01
Full Text Available Perhaps the most important single finding in the field of emotional aging has been that the overall quality of affective experience steadily improves during adulthood and can be maintained into old age. Recent lifespan developmental theories have provided motivation- and experience-based explanations for this phenomenon. These theories suggest that, as individuals grow older, they become increasingly motivated and able to regulate their emotions, which could result in reduced negativity and enhanced positivity. The objective of this paper is to expand existing theories and empirical research on emotional aging by presenting a discrete emotions perspective. To illustrate the usefulness of this approach, we focus on a discussion of the literature examining age differences in anger and sadness. These two negative emotions have been subsumed under the singular concept of negative affect. From a discrete emotions perspective, however, they are highly distinct. Sadness is elicited by an irreversible loss and associated with low situational control, high goal adjustment tendencies, and the motivation to search for social support. The experience of anger, by contrast, is typically triggered by other individuals who intentio
Emotional aging: a discrete emotions perspective.
Kunzmann, Ute; Kappes, Cathleen; Wrosch, Carsten
2014-01-01
Perhaps the most important single finding in the field of emotional aging has been that the overall quality of affective experience steadily improves during adulthood and can be maintained into old age. Recent lifespan developmental theories have provided motivation- and experience-based explanations for this phenomenon. These theories suggest that, as individuals grow older, they become increasingly motivated and able to regulate their emotions, which could result in reduced negativity and enhanced positivity. The objective of this paper is to expand existing theories and empirical research on emotional aging by presenting a discrete emotions perspective. To illustrate the usefulness of this approach, we focus on a discussion of the literature examining age differences in anger and sadness. These two negative emotions have typically been subsumed under the singular concept of negative affect. From a discrete emotions perspective, however, they are highly distinct and show multidirectional age differences. We propose that such contrasting age differences in specific negative emotions have important implications for our understanding of long-term patterns of affective well-being across the adult lifespan.
Discretization analysis of bifurcation based nonlinear amplifiers
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Discussion of discrete D shape toroidal coil
International Nuclear Information System (INIS)
Kaiho, Katsuyuki; Ohara, Takeshi; Agatsuma, Ko; Onishi, Toshitada
1988-01-01
A novel design for a toroidal coil, called the D shape coil, was reported by J. File. The coil conductors are in pure tension and then subject to no bending moment. This leads to a smaller number of emf supports in a simpler configuration than that with the conventional toroidal coil of circular cross-section. The contours of the D shape are given as solutions of a differential equation. This equation includes the function of the magnetic field distribution in the conductor region which is inversely proportional to the winding radius. It is therefore important to use the exact magnetic field distribution. However the magnetic field distribution becomes complicated when the D shape toroidal coil is comprised of discrete coils and also depends on the D shape configuration. A theory and a computer program for designing the practical pure-tension toroidal coil are developed. Using this computer code, D shape conductors are calculated for various numbers of discrete coils and the results are compared. Electromagnetic forces in the coils are also calculated. It is shown that the hoop stress in the conductors depends only on the total ampere-turns of the coil when the contours of the D shape are similar. (author)
Discrete hierarchical organization of social group sizes.
Zhou, W-X; Sornette, D; Hill, R A; Dunbar, R I M
2005-02-22
The 'social brain hypothesis' for the evolution of large brains in primates has led to evidence for the coevolution of neocortical size and social group sizes, suggesting that there is a cognitive constraint on group size that depends, in some way, on the volume of neural material available for processing and synthesizing information on social relationships. More recently, work on both human and non-human primates has suggested that social groups are often hierarchically structured. We combine data on human grouping patterns in a comprehensive and systematic study. Using fractal analysis, we identify, with high statistical confidence, a discrete hierarchy of group sizes with a preferred scaling ratio close to three: rather than a single or a continuous spectrum of group sizes, humans spontaneously form groups of preferred sizes organized in a geometrical series approximating 3-5, 9-15, 30-45, etc. Such discrete scale invariance could be related to that identified in signatures of herding behaviour in financial markets and might reflect a hierarchical processing of social nearness by human brains.
Correlations and discreteness in nonlinear QCD evolution
International Nuclear Information System (INIS)
Armesto, N.; Milhano, J.
2006-01-01
We consider modifications of the standard nonlinear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities y=(α s N c /π)Y<10. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cutoff evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cutoff. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients
Sur, Chiranjib; Shukla, Anupam
2018-03-01
Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.
DEFF Research Database (Denmark)
Langham, Allison A; Khandelia, Himanshu; Kaznessis, Yiannis N
2006-01-01
In this work, the naturally occurring beta-hairpin antimicrobial peptide protegrin-1 (PG-1) is studied by molecular dynamics simulation in all-atom sodium dodecylsulfate and dodecylphosphocholine micelles. These simulations provide a high-resolution picture of the interactions between the peptide...
International Nuclear Information System (INIS)
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2016-01-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2018-01-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Energy Technology Data Exchange (ETDEWEB)
Mishchenko, Michael I., E-mail: michael.i.mishchenko@nasa.gov [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Dlugach, Janna M. [Main Astronomical Observatory of the National Academy of Sciences of Ukraine, 27 Zabolotny Str., 03680, Kyiv (Ukraine); Yurkin, Maxim A. [Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Institutskaya str. 3, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Bi, Lei [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Cairns, Brian [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Liu, Li [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Columbia University, 2880 Broadway, New York, NY 10025 (United States); Panetta, R. Lee [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Travis, Larry D. [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Yang, Ping [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Zakharova, Nadezhda T. [Trinnovim LLC, 2880 Broadway, New York, NY 10025 (United States)
2016-05-16
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2016-01-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of
Huang, Zhihao; Zhao, Junfei; Wang, Zimu; Meng, Fanying; Ding, Kunshan; Pan, Xiangqiang; Zhou, Nianchen; Li, Xiaopeng; Zhang, Zhengbiao; Zhu, Xiulin
2017-10-23
Orthogonal maleimide and thiol deprotections were combined with thiol-maleimide coupling to synthesize discrete oligomers/macromolecules on a gram scale with molecular weights up to 27.4 kDa (128mer, 7.9 g) using an iterative exponential growth strategy with a degree of polymerization (DP) of 2 n -1. Using the same chemistry, a "readable" sequence-defined oligomer and a discrete cyclic topology were also created. Furthermore, uniform dendrons were fabricated using sequential growth (DP=2 n -1) or double exponential dendrimer growth approaches (DP=22n -1) with significantly accelerated growth rates. A versatile, efficient, and metal-free method for construction of discrete oligomers with tailored structures and a high growth rate would greatly facilitate research into the structure-property relationships of sophisticated polymeric materials. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Modelling of discrete TDS-spectrum of hydrogen desorption
Rodchenkova, Natalia I.; Zaika, Yury V.
2015-12-01
High concentration of hydrogen in metal leads to hydrogen embrittlement. One of the methods to evaluate the hydrogen content is the method of thermal desorption spectroscopy (TDS). As the sample is heated under vacuumization, atomic hydrogen diffuses inside the bulk and is desorbed from the surface in the molecular form. The extraction curve (measured by a mass-spectrometric analyzer) is recorded. In experiments with monotonous external heating it is observed that background hydrogen fluxes from the extractor walls and fluxes from the sample cannot be reliably distinguished. Thus, the extraction curve is doubtful. Therefore, in this case experimenters use discrete TDS-spectrum: the sample is removed from the analytical part of the device for the specified time interval, and external temperature is then increased stepwise. The paper is devoted to the mathematical modelling and simulation of experimental studies. In the corresponding boundary-value problem with nonlinear dynamic boundary conditions physical- chemical processes in the bulk and on the surface are taken into account: heating of the sample, diffusion in the bulk, hydrogen capture by defects, penetration from the bulk to the surface and desorption. The model aimed to analyze the dynamics of hydrogen concentrations without preliminary artificial sample saturation. Numerical modelling allows to choose the point on the extraction curve that corresponds to the initial quantity of the surface hydrogen, to estimate the values of the activation energies of diffusion, desorption, parameters of reversible capture and hydride phase decomposition.
Modelling of discrete TDS-spectrum of hydrogen desorption
International Nuclear Information System (INIS)
Rodchenkova, Natalia I; Zaika, Yury V
2015-01-01
High concentration of hydrogen in metal leads to hydrogen embrittlement. One of the methods to evaluate the hydrogen content is the method of thermal desorption spectroscopy (TDS). As the sample is heated under vacuumization, atomic hydrogen diffuses inside the bulk and is desorbed from the surface in the molecular form. The extraction curve (measured by a mass-spectrometric analyzer) is recorded. In experiments with monotonous external heating it is observed that background hydrogen fluxes from the extractor walls and fluxes from the sample cannot be reliably distinguished. Thus, the extraction curve is doubtful. Therefore, in this case experimenters use discrete TDS-spectrum: the sample is removed from the analytical part of the device for the specified time interval, and external temperature is then increased stepwise. The paper is devoted to the mathematical modelling and simulation of experimental studies. In the corresponding boundary-value problem with nonlinear dynamic boundary conditions physical- chemical processes in the bulk and on the surface are taken into account: heating of the sample, diffusion in the bulk, hydrogen capture by defects, penetration from the bulk to the surface and desorption. The model aimed to analyze the dynamics of hydrogen concentrations without preliminary artificial sample saturation. Numerical modelling allows to choose the point on the extraction curve that corresponds to the initial quantity of the surface hydrogen, to estimate the values of the activation energies of diffusion, desorption, parameters of reversible capture and hydride phase decomposition. (paper)
A Global Network Alignment Method Using Discrete Particle Swarm Optimization.
Huang, Jiaxiang; Gong, Maoguo; Ma, Lijia
2016-10-19
Molecular interactions data increase exponentially with the advance of biotechnology. This makes it possible and necessary to comparatively analyse the different data at a network level. Global network alignment is an important network comparison approach to identify conserved subnetworks and get insight into evolutionary relationship across species. Network alignment which is analogous to subgraph isomorphism is known to be an NP-hard problem. In this paper, we introduce a novel heuristic Particle-Swarm-Optimization based Network Aligner (PSONA), which optimizes a weighted global alignment model considering both protein sequence similarity and interaction conservations. The particle statuses and status updating rules are redefined in a discrete form by using permutation. A seed-and-extend strategy is employed to guide the searching for the superior alignment. The proposed initialization method "seeds" matches with high sequence similarity into the alignment, which guarantees the functional coherence of the mapping nodes. A greedy local search method is designed as the "extension" procedure to iteratively optimize the edge conservations. PSONA is compared with several state-of-art methods on ten network pairs combined by five species. The experimental results demonstrate that the proposed aligner can map the proteins with high functional coherence and can be used as a booster to effectively refine the well-studied aligners.
Jacobian elliptic wave solutions in an anharmonic molecular crystal model
International Nuclear Information System (INIS)
Teh, C.G.R.; Lee, B.S.; Koo, W.K.
1997-07-01
Explicit Jacobian elliptic wave solutions are found in the anharmonic molecular crystal model for both the continuum limit and discrete modes. This class of wave solutions include the famous pulse-like and kink-like solitary modes. We would also like to report on the existence of some highly discrete staggered solitary wave modes not found in the continuum limit. (author). 9 refs, 1 fig
Beta oscillations define discrete perceptual cycles in the somatosensory domain.
Baumgarten, Thomas J; Schnitzler, Alfons; Lange, Joachim
2015-09-29
Whether seeing a movie, listening to a song, or feeling a breeze on the skin, we coherently experience these stimuli as continuous, seamless percepts. However, there are rare perceptual phenomena that argue against continuous perception but, instead, suggest discrete processing of sensory input. Empirical evidence supporting such a discrete mechanism, however, remains scarce and comes entirely from the visual domain. Here, we demonstrate compelling evidence for discrete perceptual sampling in the somatosensory domain. Using magnetoencephalography (MEG) and a tactile temporal discrimination task in humans, we find that oscillatory alpha- and low beta-band (8-20 Hz) cycles in primary somatosensory cortex represent neurophysiological correlates of discrete perceptual cycles. Our results agree with several theoretical concepts of discrete perceptual sampling and empirical evidence of perceptual cycles in the visual domain. Critically, these results show that discrete perceptual cycles are not domain-specific, and thus restricted to the visual domain, but extend to the somatosensory domain.
How Triage Nurses Use Discretion: a Literature Review
Directory of Open Access Journals (Sweden)
Lars Emil Fagernes Johannessen
2016-02-01
Full Text Available Discretion is quintessential for professional work. This review aims to understand how nurses use discretion when they perform urgency assessments in emergency departments with formalised triage systems—systems that are intended to reduce nurses’ use of discretion. Because little research has dealt explicitly with this topic, this review addresses the discretionary aspects of triage by reinterpreting qualitative studies of how triage nurses perform urgency assessments. The review shows (a how inexhaustive guidelines and a hectic work environment are factors that necessitate nurses’ use of discretion and (b how nurses reason within this discretionary space by relying on their experience and intuition, judging patients according to criteria such as appropriateness and believability, and creating urgency ratings together with their patients. The review also offers a synthesis of the findings’ discretionary aspects and suggests a new interactionist dimension of discretion.Keywords: Triage, discretion, emergency department, meta-ethnography, review, decision-making
Discrete-Time Nonlinear Control of VSC-HVDC System
Directory of Open Access Journals (Sweden)
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
A note on inconsistent families of discrete multivariate distributions
Ghosh, Sugata; Dutta, Subhajit; Genton, Marc G.
2017-01-01
We construct a d-dimensional discrete multivariate distribution for which any proper subset of its components belongs to a specific family of distributions. However, the joint d-dimensional distribution fails to belong to that family and in other words, it is ‘inconsistent’ with the distribution of these subsets. We also address preservation of this ‘inconsistency’ property for the symmetric Binomial distribution, and some discrete distributions arising from the multivariate discrete normal distribution.
Identification of parameters of discrete-continuous models
International Nuclear Information System (INIS)
Cekus, Dawid; Warys, Pawel
2015-01-01
In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible
A note on inconsistent families of discrete multivariate distributions
Ghosh, Sugata
2017-07-05
We construct a d-dimensional discrete multivariate distribution for which any proper subset of its components belongs to a specific family of distributions. However, the joint d-dimensional distribution fails to belong to that family and in other words, it is ‘inconsistent’ with the distribution of these subsets. We also address preservation of this ‘inconsistency’ property for the symmetric Binomial distribution, and some discrete distributions arising from the multivariate discrete normal distribution.
Search Parameter Optimization for Discrete, Bayesian, and Continuous Search Algorithms
2017-09-01
NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CONTINUOUS SEARCH ALGORITHMS by...to 09-22-2017 4. TITLE AND SUBTITLE SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CON- TINUOUS SEARCH ALGORITHMS 5. FUNDING NUMBERS 6...simple search and rescue acts to prosecuting aerial/surface/submersible targets on mission. This research looks at varying the known discrete and
Network Science Research Laboratory (NSRL) Discrete Event Toolkit
2016-01-01
ARL-TR-7579 ● JAN 2016 US Army Research Laboratory Network Science Research Laboratory (NSRL) Discrete Event Toolkit by...Laboratory (NSRL) Discrete Event Toolkit by Theron Trout and Andrew J Toth Computational and Information Sciences Directorate, ARL...Research Laboratory (NSRL) Discrete Event Toolkit 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Theron Trout
Identification of parameters of discrete-continuous models
Energy Technology Data Exchange (ETDEWEB)
Cekus, Dawid, E-mail: cekus@imipkm.pcz.pl; Warys, Pawel, E-mail: warys@imipkm.pcz.pl [Institute of Mechanics and Machine Design Foundations, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa (Poland)
2015-03-10
In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.
Reflectionless discrete Schr\\"odinger operators are spectrally atypical
VandenBoom, Tom
2017-01-01
We prove that, if an isospectral torus contains a discrete Schr\\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schr\\"odinger operator. We also show that the only reflectionless discrete Schr\\"odinger operators having zero, one, or two spectral gaps are periodic.
Reflectionless Discrete Schrödinger Operators are Spectrally Atypical
VandenBoom, Tom
2017-12-01
We prove that, if an isospectral torus contains a discrete Schrödinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schrödinger operator. We also show that the only reflectionless discrete Schrödinger operators having zero, one, or two spectral gaps are periodic.
Discrete ambiguities in CP-violating asymmetries in B decays
International Nuclear Information System (INIS)
London, David
1998-01-01
The CP-angles α, β and γ can be extracted from CP-violating asymmetries in the B system, but only up to discrete ambiguities. These discrete ambiguities make it difficult to determine with certainty whether or not new physics is present. I show that, if the condition α+β+γ=π is imposed, there remains a twofold ambiguity in the CP-angle set (α,β,γ), and I discuss ways to cleanly resolve this final discrete ambiguity
A hierarchy of Liouville integrable discrete Hamiltonian equations
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
Lax pairs for ultra-discrete Painleve cellular automata
International Nuclear Information System (INIS)
Joshi, N; Nijhoff, F W; Ormerod, C
2004-01-01
Ultra-discrete versions of the discrete Painleve equations are well known. However, evidence for their integrability has so far been restricted. In this letter, we show that their Lax pairs can be constructed and, furthermore, that compatibility conditions of the result yield the ultra-discrete Painleve equation. For conciseness, we restrict our attention to a new d-P III . (letter to the editor)
Chaos of discrete dynamical systems in complete metric spaces
International Nuclear Information System (INIS)
Shi Yuming; Chen Guanrong
2004-01-01
This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces
Dynamics and Thermodynamics of Molecular Machines
DEFF Research Database (Denmark)
Golubeva, Natalia
2014-01-01
to their microscopic size, molecular motors are governed by principles fundamentally different from those describing the operation of man-made motors such as car engines. In this dissertation the dynamic and thermodynamic properties of molecular machines are studied using the tools of nonequilibrium statistical......Molecular machines, or molecular motors, are small biophysical devices that perform a variety of essential metabolic processes such as DNA replication, protein synthesis and intracellular transport. Typically, these machines operate by converting chemical energy into motion and mechanical work. Due...... mechanics. The first part focuses on noninteracting molecular machines described by a paradigmatic continuum model with the aim of comparing and contrasting such a description to the one offered by the widely used discrete models. Many molecular motors, for example, kinesin involved in cellular cargo...
Molecular separation method and apparatus
International Nuclear Information System (INIS)
Villa-Aleman, E.
1996-01-01
A method and apparatus are disclosed for separating a gaseous mixture of chemically identical but physically different molecules based on their polarities. The gaseous mixture of molecules is introduced in discrete quantities into the proximal end of a porous glass molecular sieve. The molecular sieve is exposed to microwaves to excite the molecules to a higher energy state from a lower energy state, those having a higher dipole moment being excited more than those with a lower energy state. The temperature of the sieve kept cold by a flow of liquid nitrogen through a cooling jacket so that the heat generated by the molecules colliding with the material is transferred away from the material. The molecules thus alternate between a higher energy state and a lower one, with the portion of molecules having the higher dipole moment favored over the others. The former portion can then be extracted separately from the distal end of the molecular sieve. 2 figs
National Research Council Canada - National Science Library
Provan, Drew; Gribben, John
2010-01-01
... The molecular basis of hemophilia, 219 Paul LF Giangrande 4 The genetics of acute myeloid leukemias, 42 Carolyn J Owen & Jude Fitzgibbon 19 The molecular basis of von Willebrand disease, 233 Luciano Baronc...
Towards Molecular Dynamics Simulations of Chiral Room-Temperature Ionic Liquids
Czech Academy of Sciences Publication Activity Database
Lísal, Martin; Chval, Z.; Storch, Jan; Izák, Pavel
2014-01-01
Roč. 189, SI (2014), s. 85-94 ISSN 0167-7322 R&D Projects: GA ČR(CZ) GAP106/12/0569; GA MŠk LH12020 Institutional support: RVO:67985858 Keywords : chiral room-temperature ionic liquid * molecular dynamics simulation * non-polarizable fully flexible all-atom force field Subject RIV: CI - Industrial Chemistry, Chemical Engineering Impact factor: 2.515, year: 2014
Stabilizing the discrete vortex of topological charge S=2
International Nuclear Information System (INIS)
Kevrekidis, P.G.; Frantzeskakis, D.J.
2005-01-01
We study the instability of the discrete vortex with topological charge S=2 in a prototypical lattice model and observe its mediation through the central lattice site. Motivated by this finding, we analyze the model with the central site being inert. We identify analytically and observe numerically the existence of a range of linearly stable discrete vortices with S=2 in the latter model. The range of stability is comparable to that of the recently observed experimentally S=1 discrete vortex, suggesting the potential for observation of such higher charge discrete vortices
Mapping of uncertainty relations between continuous and discrete time.
Chiuchiù, Davide; Pigolotti, Simone
2018-03-01
Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.
Discretization-induced delays and their role in the dynamics
International Nuclear Information System (INIS)
Ramani, A; Grammaticos, B; Satsuma, J; Willox, R
2008-01-01
We show that a discretization of a continuous system may entail 'hidden' delays and thus introduce instabilities. In this case, while the continuous system has an attractive fixed point, the instabilities present in the equivalent discrete one may lead to the appearance of a limit cycle. We explain that it is possible, thanks to the proper staggering of the discrete variables, to eliminate the hidden delay. However, in general, other instabilities may appear in the discrete system which can even lead to chaotic behaviour