Computer Simulation of WaterMediated Adhesion Between Phospholipid Bilayer and Solid Support Functionalized with SelfAssembled Monolayers


 Helena Pitts
 3 years ago
 Views:
Transcription
1 Biointerphases (2012) 7:57 DOI /s ARTICLE Computer Simulation of WaterMeiate Ahesion Between Phospholipi Bilayer an Soli Support Functionalize with SelfAssemble Monolayers Alexaner Pertsin Michael Grunze Receive: 17 May 2012 / Accepte: 16 August 2012 / Publishe online: 28 August 2012 The Author(s) This article is publishe with open access at Springerlink.com Abstract An attempt is mae to estimate, via computer simulation of the force istance relation, the free energy of ahesion between a phosphatiylethanolamine bilayer an an alkanethiolate selfassemble monolayer (SAM) in aqueous meium. The simulations are performe using the gran canonical Monte Carlo technique an atomistic force fiels. The bilayer ahesion free energy is preicte to be 22 ± 3 mj/m 2 ( 1.4 ± 0.2 kcal/mol) on a hyrophilic carboxylterminate SAM an 1 ± 1 mj/m 2 ( 0.06 ± 0.06 kcal/mol) on a hyrophobic methylterminate SAM. In the last two ecaes, the watermeiate interaction of lipi bilayers with various surfaces has receive much attention [1]. This is explaine, in particular, by everincreasing practical interest in planar bilayer membranes supporte on soli substrates. For biologists an biophysicists, the supporte lipi bilayers (SLBs) provie a goo moel system for stuying the membrane structure an properties because of a better stability of SLBs with respect to chemical manipulation an estructive effects of surfacesensitive characterization techniques. For physicists an physicochemists, SLBs are of interest mainly as a means for biofunctionalization of inorganic solis an polymeric materials. A practical outcome of the associate research is the evelopment of new biosensors, which combine the small thickness an high electrical resistivity of SLBs with their ability to serve as a matrix for incorporating receptors an, simultaneously, to suppress nonspecific ligan bining [1]. A. Pertsin (&) M. Grunze Angewante Physikalische Chemie, Universität Heielberg, Im Neuenheimer Fel 253, Heielberg, Germany A critical parameter that governs the stability an other properties of SLBs is the free energy of ahesion between the bilayer an substrate, W. In a general case, W can be represente as the sum of two basic components. One component is ue to irect bilayer substrate interactions, while the other arises from socalle hyration forces. These latter are associate with a thin aqueous film that is usually present between the bilayer an substrate. (It is this film that maintains the lateral fluiity of the bilayer.) In principle, W can be etermine experimentally by the surface force apparatus (SFA) or atomic force microscopy (AFM) an relate techniques. A thorough inspection of the literature has however reveale only one relevant stuy, as recently reporte by Anerson et al. [2] from the Israelachvili group for zwitterionic phospholipi bilayers (DMPC) supporte on silica glass substrates. The lack of experimental ata on the bilayersubstrate ahesion energy attracts attention to computer simulations as a potential means of aequately moeling SFA experiments base on realistic force fiels. An avantage of computer simulations is the possibility of partitioning W into iniviual physical components corresponing to the iniviual components of the intermolecular interaction energy. The knowlege of the physical components of W offers a clearer insight into the mechanism of the bilayer substrate ahesion. By now, the number of computer simulations of SLBs is very limite. Of the eight publishe simulation stuies [3 10], only three [3 5] were base on a realistic atomistic escription. The others were concerne with oversimplifie coarsegraine [6 8] an highly coarsegraine [9, 10] moels, which are harly capable of quantitatively escribing watermeiate bilayer substrate interactions. Of particular interest is the atomistic simulation stuy by Heine et al. [3] who mae a first attempt to quantify the
2 Page 2 of 6 Biointerphases (2012) 7:57 ahesion energy between a lipi bilayer an aquartz substrate in aqueous meia. Although the simulation correctly preicte the equilibrium separation between the bilayer an substrate, the calculate ahesion energies prove to be about two orers of magnitue higher than the experimental values measure by Anerson et al. [2] ( mj/m 2, epening on the metho of bilayer preparation). It is worth noting that the abovecite computer simulations of SLBs were all performe using the molecular ynamics (MD) technique an close statistical ensembles (NVT an NP N T), where the number of particles in the confine system remaine constant. By contrast, a real SLB stuie in an SFA experiment represents an open confine system, where water sanwiche between the bilayer an substrate is allowe to exchange molecules with a surrouning bulk water reservoir. The relevant statistical escription is provie by the gran canonical (lvt) or isostress (lp N T) ensembles. In our previous simulations of the watermeiate interaction between two ientical phospholipi bilayers [11, 12], the problem of moeling an open system was solve by resorting to a gran canonical Monte Carlo (GCMC) technique involving special expeients for enhancing sampling efficiency [13]. The aim was to unerstan the physical nature of forces responsible for the shortrange interbilayer repulsion. In the present work, our GCMC simulations are extene to asymmetric systems, where one bilayer is replace by a soli substrate. Unlike the previous stuies [11, 12], now the interest is concentrate on separations where one can expect bilayer substrate attraction responsible for ahesion. The specific lipi consiere in the present work is ilauroylphosphatiylethanolamine (DLPE) stuie in our previous simulations [11, 12]. As a substrate, we use a gol support functionalize by carboxyl an methylterminate alkanethiolate selfassemble monolayers (hereafter, OSAM an CSAM) of the general formula X(CH 2 ) n S (X = COOH an CH 3, n = 12 an 13, respectively). This choice is natural as far as aqueous meium is concerne, where the water affinity of the substrate may play a ecisive role in the bilayer substrate ahesion. As a preliminary stage of this work, we have recently simulate watermeiate ahesion between the O an CSAMs both in symmetric an asymmetric combinations (i.e., between like SAMs an between unlike SAMs, respectively) [14]. The calculate free energies of ahesion prove to be in acceptable agreement with the available experimental ata extracte from AFM measurements of force istance relations. The behavior of the two symmetric an one asymmetric systems with increasing confinement was quite ifferent. The symmetric system boune by the hyrophilic OSAMs kept confine water at all separations trie, incluing separations in the region of repulsive pressures. The system confine by two hyrophobic CSAMs showe a capillary evaporation occurring at a fairly large separation in the attractive region. As a consequence, the ahesion energy was mainly etermine by the irect interaction of bare SAMs. A capillary evaporation was also observe in the asymmetric OSAM/water/CSAM system. In this case, however, the evaporation was incomplete. The remaining water molecules were all asorbe on the hyrophilic OSAM, while the hyrophobic CSAM was separate from the rest of the system by a thin vapor layer. These observations have provie a goo basis for a comparative analysis of the behavior of DLPE/water/SAM systems. The moel system use in the present simulations reflects the configuration of an SFA experiment, as schematically epicte in Fig. 1. The system elements shown in black are explicitly present in the system, while those shown in gray are simulate implicitly. As in our previous stuies [11, 12] the outer (upper) phospholipi monolayer was represente in a meanfiel manner as a flat structureless surface interacting with the carbon atoms of the lower monolayer through a (3 9) inverse power potential. The position of this surface correspons to the miplane of the bilayer, as shown by the ashe line in Fig. 1. The parameters of the (3 9) potential were calibrate so as to fit atomistic force fiel results for the interaction energy of two DLPE monolayers facing each other with their hyrophobic sies. The inter an intramolecular energies of DLPE were calculate using the AMBERbase force fiel refine by Smonyrew an Berkowitz [15]. The methyl an methylene groups were treate in the uniteatom approximation, while the hyrogen atoms of the amino group were treate explicitly. The DLPE molecules were regare as flexible but subject to bonlength constraints. These latter were Fig. 1 Configuration of the simulation moel. The parts simulate explicitly an implicitly are shown in black an gray, respectively
3 Biointerphases (2012) 7:57 Page 3 of 6 implemente using the rotational isplacement proceure suggeste in our early paper [16]. The gol support was represente by a twoimensional hexagonal lattice of force sites corresponing to the (111) plane of the gol monocrystal. The interaction of gol with water was neglecte. The alkane chains were escribe with an allatom moel, with the atom atom potentials calibrate by Williams [17] by fitting the equilibrium structure an lattice energy of hyrocarbon crystals to the relevant experimental ata. The potential parameters of sulfur were the same as use by Mar an Klein [18] in their MD simulations of an alkanethiolate SAM, while the interactions involving the COOH group were treate using the respective potentials from the OPLSAA force fiel [19]. As with DLPE, the conformation of the SAM molecules was subject to bonlength constraints. In calculations of the intermolecular interaction energy, each molecule bearing Coulombic charges was represente as a set of electrically neutral groups. At short separations between the group centers, the electrostatic interaction energy was calculate irectly as the sum of charge charge interactions, while at large separations the ipole ipole group group approximation was use. The cutoff istances for the charge charge an ipole ipole contributions were 20 an 100 Å, respectively. The Lennar Jones potentials escribing the exchange repulsion an ispersion interactions were cut off at a istance of 15 Å. The bulk water reservoir surrouning the SLB in Fig. 1 was treate implicitly by equating the chemical potential of confine water to that of bulk water [20, 21], as etermine in separate GCMC simulations of the latter. The fluctuations of the number of confine water molecules were simulate through repeate attempts to create or estruct a water molecule in the confine region. The water water interactions were escribe with the TIP4P force fiel [22], while the mixe water DLPE an water SAM interaction parameters were calculate using geometric mean combination rules. The substrate (SAM) sie of the simulation box was constructe base on an orthorhombic unit cell with two symmetrically istinct alkanethiolate molecules an perios a = 3c, b = c 3 where c = 4.08 Å is the lattice pffiffi constant of gol. The starting arrangement of the molecules in the unit cell was taken the same as foun in our early work [23] by global energy minimization. The simulation box was compose of 18 unit cells (3 unit cells along x axis an 6 unit cells along y), so that the number of alkanethiolate molecules in the substrate sie of the simulation box was 36 an the lateral imensions of the simulation box were L x = 3a = Å, L y = 6b = 42.4 Å. The starting configuration of the lipi sie of the simulation box was built up proceeing from the crystalstate bilayer configuration, as observe in the DLPE acetic aci crystal [11]. To make the lipi an substrate sies of the system commensurable, the crystalstate bilayer configuration was slightly stretche along the x axis an compresse along the y axis so as to fit the lateral imensions of the simulation box. The area per lipi molecule in the resulting configuration prove to be 48.7 Å 2, which is close to a semiempirical estimate of 51.2 Å 2 reporte by Nagle an Wiener [24] for fluiphase DLPE bilayers at 308 K. The GCMC simulation proceure use was iscusse in etail elsewhere [11, 12]. In brief, the simulations were performe with a fixe number of the bilayer an substrate molecules, so that the system was actually treate as a semigran canonical ensemble. A total of five types of ranom moves were attempte: insertion, eletion, an translationalrotational (hereafter isplacement) moves of water plus conformational an isplacement moves of DLPE an SAM molecules. To improve the acceptance probability of insertion an eletion moves, the Swensen Wang filtering [25] an an orientational bias proceure [26] were use. The former rejecte an improbable insertion or eletion of a ranomly selecte water molecule base on its position an a computationally cheep preictor of the associate energy. The latter i the same with respect to molecular orientation. The attempts to insert a water molecule were mae over the whole volume treate explicitly. The key quantity evaluate in our GCMC simulations was the normal pressure, p. It was calculate in the force form (as oppose to the virial form ) by summation of the zcomponents of the forces exerte on the DLPE bilayer by the SAM substrate an water. The total pressure p was represente as the sum two components, p ¼ p þ p h, where p was associate with irect bilayer substrate interactions an p h was the socalle hyration (solvation) pressure [14] ue to the forces exerte on the bilayer by water molecules. (It is worth noting in this context that the hyration pressure p h is frequently use to mean the total pressure p operating between the substrates. Here we prefer to follow the efinition given by Evans an Markoni [27], where p h is just a component of p.) The irect pressure p was further partitione into contributions from electrostatic, ispersion, an exchange repulsion (steric) forces, p ¼ p elst þ p isp þ p rep, by collecting the forces associate with the respective terms of the intermolecular interaction potentials. The ahesion free energy was calculate by integrating the pressureseparation relation p(h) from the equilibrium separation, h 0, as efine by the conition ph ð 0 Þ ¼ 0, to the largest separation trie, h max, where the magnitue of p was within the respective statistical error. All the simulations were performe at a temperature of 308 K.
4 Page 4 of 6 Biointerphases (2012) 7:57 Consiering a fairly slow convergence of pressure [14], we ha to use very long GCMC runs an to check the reproucibility of the calculate values of pressure by comparing the results of inepenent runs iffering in the initial structure an/or the sequence of ranom numbers. The length of a GCMC run was passes, each comprising N 0 moves, where N 0 is the initial number of water molecules in a given pass. The first half of the run serve to equilibrate the system, while the ensemble averages were calculate in the secon half. For each particular separation h, 5 7 inepenent GCMC runs were performe an the calculate quantities were average out. The calculation error was estimate as the average absolute eviation from the mean. Typical curves emonstrating the convergence of pressure in the course of five inepenent GCMC runs are presente in Fig. 2. We first consier the case of the hyrophilic OSAM substrate. The calculations of the pressureseparation relation p(h) were performe in orer of increasing confinement starting from h max = 43.5 Å, where the magnitue of p i not excee the respective average eviation, D p. The highest confinement trie for at h = 33 Å, which correspone to strongly repulsive bilayer substrate interaction. The calculate p(h) is shown in Fig. 3a, where positive an negative pressures correspon to repulsion an attraction, respectively. The curve shows a well efine minimum at h = 36 Å with a epth of about 0.7 kbar. The equilibrium separation is at h 0 & 34.3 Å. The hyration egree at the separation nearest to h 0 (h = 34.5 Å) is 6.6. The integration of p(h) from 34.3 to 43.5 Å results in the ahesion free energy W =2.2 ± 0.3 kbar Å =  22 ± 3 mj/m 2, which is close to the values calculate for the OSAM/water/OSAM an OSAM/water/CSAM systems (26 ± 4 an 25 ± 3 mj/m 2, respectively) [14]. The istribution of pressure over its iniviual components at the separation of strongest attraction (36 Å) is Fig. 2 Convergence of pressure in the course of five inepenent GCMC runs. The ata refer to the DLPE/water/OSAM system at h = 36 Å Fig. 3 Pressureseparation relations for DLPE bilayer supporte on OSAM (a) an CSAM (b) shown in Fig. 4a. It can be seen that the factor responsible for ahesive attraction is the irect bilayer substrate interaction p, which is in turn etermine by the interplay between the attractive p elst strongly repulsive p rep an p isp, on one han, an, on the other. It is worth noting that the force fiel use in our simulations involves no explicit terms responsible for hyrogen boning. The latter is escribe by the electrostatic interaction of protononor an protonacceptor groups, an hence the contribution to p ue to formation of hyrogen bons between the bilayer an substrate enters into p elst, while the contribution to pressure from hyrogen bons forme by water with the bilayer an substrate is a part of p h. As seen from Fig. 4a, the hyration forces play an important role in the total force balance: Being comparable in magnitue with p, the repulsive p h substantially weakens the watermeiate ahesion between the bilayer an substrate. The replacement of the hyrophilic OSAM substrate by the hyrophobic CSAM reuces the ahesive strength to values comparable with the calculation error (Fig. 3b). The minimum of the p(h) curve occurs somewhere between 37 an 38 Å an has a epth of about 0.1 ± 0.1 kbar. The equilibrium separation h 0 is at h = 36.8 Å. The hyration egree at the separation nearest to h 0 (h = 37 Å) is 7.2. The istribution of pressure over its components (Fig. 4b) is qualitatively similar to that foun in the DLPE/water/ OSAM system, except for the lack of p elst because of the absence of electrostatic terms in the Williams potentials [17]. The ahesion free energy W calculate from the p(h) curve in Fig. 3b is 1 ± 1 mj/m 2. The corresponing
5 Biointerphases (2012) 7:57 Fig. 4 Distribution of pressure over its physical components for DLPE supporte on OSAM (a) an CSAM (b) at separations corresponing to the minimum of the pressureseparation curve. Note that the pressure scales in a an b are ifferent experimental value of W is not available because the attempts to prepare an SLB by asorption of small unilamellar vesicles (SUV) onto CSAM faile [28, 29]: The SUV asorption le to formation of a supporte lipi monolayer (SLM) with the hyrophobic tails irecte towar the hyrophobic SAM substrate. The associate ahesion energy has not been measure experimentally but it harly iffers significantly from the value of 88 ± 35 mj/m2 foun in AFM experiments with the CSAM/water/CSAM system [30]. That is, the contact of the hyrophobic CSAM substrate with the hyrophobic lipi tails is 1 2 orers of magnitue more favorable in ahesion energy compare to the contact with the hyrophilic lipi heas, as moele by our simulation of the DLPE/water/CSAM system. It is very likely therefore that the ifference in ahesion energy is the main factor that etermines the preference of SLM over SLB on eposition of SUVs on CSAM. As the confinement was increase, both of the DLPE/ water/sam systems showe a monotonous ecrease in the ensembleaverage number of water molecules, hn i. In this respect, they were similar to the symmetric OSAM/ water/osam system but iffere from the asymmetric OSAM/water/CSAM an symmetric CSAM/water/CSAM ones, where the function hn i(h) showe a iscontinuity associate with capillary evaporation [14]. The lack of capillary evaporation in the DLPE/water/SAM systems is not surprising in view of a high water affinity of the DLPE bilayer ue to an easy accessibility of its protonacceptor an protononor groups to water molecules. A eep penetration of water into bilayer can be Page 5 of 6 Fig. 5 Snapshot of the DLPE/water/OSAM system at h = 36 A. O, N, an P atoms of DLPE are shown in re, blue, an purple, respectively; S an O atoms of SAM are shown in green an re; water O atoms are shown in turquoise Fig. 6 Snapshot of the DLPE/water/CSAM system at h = 37 A appreciate from snapshots of the DLPE/water/SAM systems in Figs. 5 an 6. In conclusion, this work represents a first attempt to simulate an SLB as an open system, where confine water is allowe to exchange molecules with surrouning bulk water so as to sustain the chemical equilibrium with the latter. Compare to the previous GCMC simulations concerne with the shortrange repulsion between phospholipi bilayers [11, 12] similar simulations of SLBs in the region responsible for ahesion are more emaning an inexact because of much smaller magnitues of attractive pressure. This is particularly true of systems where the bilayer substrate ahesion energy is less than 1 mj/m2.
6 Page 6 of 6 Biointerphases (2012) 7:57 Unfortunately, the experimental ata on the ahesion forces operating in SLBs are limite by single systems [2, 31] so that our simulation results cannot be irectly compare with experiment. Nevertheless, the acceptable agreement of our previous results for the SAM/water/SAM systems [14] with the experimental ahesion energies provies a reason to hope that the approach suggeste in this an previous [14] works will be useful in preicting an interpreting the bilayer substrate ahesion strength. Acknowlegment This work was supporte by the Deutsche Forschungsgemeinschaft through grant GR 625/601. Open Access This article is istribute uner the terms of the Creative Commons Attribution License which permits any use, istribution, an reprouction in any meium, provie the original author(s) an the source are creite. References 1. Sackmann ES (1996) Science 271: Anerson TH, Min Y, Weirich KL, Zeng H, Fygenson D, Israelachvili JN (2009) Langmuir 25: Heine DR, Rammohan AR, Balakrishnan J (2007) Molec Simul 33: Tarek M, Tu K, Klein ML, Tobias DJ (1999) Biophys J 77: Roark M, Feller SE (2008) Langmuir 24: Xing C, Faller R (2008) J Phys Chem B 112: Xing C, Faller R (2009) J Chem Phys 131: Xing C, Ollila OHS, Vattulainen I, Faller R (2009) Soft Matter 5: Hoopes MI, Deserno M, Longo ML, Faller R (2008) J Chem Phys 129: Ró_zycki B, Weikl TR, Lipowsky R (2008) Phys Rev Lett 100: Pertsin A, Platonov D, Grunze M (2005) J Chem Phys 122: Pertsin A, Grunze M (2011) Curr Opin Colloi Interface Sci 16: Shelley JC, Patey GN (1994) J Chem Phys 100: Pertsin A, Grunze M (2012) J Chem Phys 137: Smonyrev AM, Berkowitz ML (1999) J Comput Chem 20: Pertsin AJ, Hahn J, Grossmann HP (1994) J Comput Chem 15: Williams DE (1967) J Chem Phys 47: Mar W, Klein ML (1994) Langmuir 10: Jorgensen WL, Maxwell DS, TiraoRives J (1996) J Am Chem Soc 118: Frenkel D, Smit B (2002) Unerstaning molecular simulation: from algorithms to applications, 2n en. Acaemic Press, San Diego 21. Allen MP, Tilesley DJ (1987) Computer Simulation of Liquis. Clarenon Press, Oxfor 22. Jorgensen WL, Chanrasekhar J, Maura JD, Impey RW, Klein ML (1983) J Chem Phys 79: Pertsin AJ, Grunze M (1994) Langmuir 10: Nagle JF, Wiener MC (1988) Biochim Biophys Acta 942: Swensen RH, Wang JS (1987) Phys Rev Lett 58: Shelley JC, Patey GN (1995) J Chem Phys 102: Evans R, Marconi UMB (1987) J Chem Phys 86: Lingler S, Rubinstein I, Knoll W, Offenhäusser A (1997) Langmuir 13: Keller CA, Kasemo B (1998) Biophys J 75: Clear SC, Nealey PF (1999) J Colloi Interface Sci 213: Valtiner M, Donalson SH Jr, Gebbie MA, Israelachvili JN (2012) J Am Chem Soc 134:
Model for Dopant and Impurity Segregation During Vapor Phase Growth
Mat. Res. Soc. Symp. Proc. Vol. 648, P3.11.17 2001 Materials Research Society Moel for Dopant an Impurity Segregation During Vapor Phase Growth Craig B. Arnol an Michael J. Aziz Division of Engineering
More informationThermal conductivity of graded composites: Numerical simulations and an effective medium approximation
JOURNAL OF MATERIALS SCIENCE 34 (999)5497 5503 Thermal conuctivity of grae composites: Numerical simulations an an effective meium approximation P. M. HUI Department of Physics, The Chinese University
More informationensembles When working with density operators, we can use this connection to define a generalized Bloch vector: v x Tr x, v y Tr y
Ph195a lecture notes, 1/3/01 Density operators for spin 1 ensembles So far in our iscussion of spin 1 systems, we have restricte our attention to the case of pure states an Hamiltonian evolution. Toay
More informationAPPROXIMATE SOLUTION FOR TRANSIENT HEAT TRANSFER IN STATIC TURBULENT HE II. B. Baudouy. CEA/Saclay, DSM/DAPNIA/STCM GifsurYvette Cedex, France
APPROXIMAE SOLUION FOR RANSIEN HEA RANSFER IN SAIC URBULEN HE II B. Bauouy CEA/Saclay, DSM/DAPNIA/SCM 91191 GifsurYvette Ceex, France ABSRAC Analytical solution in one imension of the heat iffusion equation
More informationChapter 4. Electrostatics of Macroscopic Media
Chapter 4. Electrostatics of Macroscopic Meia 4.1 Multipole Expansion Approximate potentials at large istances 3 x' x' (x') x x' x x Fig 4.1 We consier the potential in the farfiel region (see Fig. 4.1
More informationTHE VAN KAMPEN EXPANSION FOR LINKED DUFFING LINEAR OSCILLATORS EXCITED BY COLORED NOISE
Journal of Soun an Vibration (1996) 191(3), 397 414 THE VAN KAMPEN EXPANSION FOR LINKED DUFFING LINEAR OSCILLATORS EXCITED BY COLORED NOISE E. M. WEINSTEIN Galaxy Scientific Corporation, 2500 English Creek
More information1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity
AP Physics Multiple Choice Practice Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity. A soli conucting sphere is given a positive charge Q.
More informationSimulation of Angle Beam Ultrasonic Testing with a Personal Computer
Key Engineering Materials Online: 485 I: 669795, Vols. 773, pp 3833 oi:.48/www.scientific.net/kem.773.38 4 rans ech ublications, witzerlan Citation & Copyright (to be inserte by the publisher imulation
More informationThe Coupling between the Hydration and Double Layer Interactions
7584 Langmuir 00, 18, 75847593 The Coupling between the Hyration an ouble Layer Interactions Eli Ruckenstein* an Marian Manciu epartment of Chemical Engineering, State University of New York at Buffalo,
More informationarxiv: v2 [condmat.statmech] 11 Nov 2016
Noname manuscript No. (will be inserte by the eitor) Scaling properties of the number of ranom sequential asorption iterations neee to generate saturate ranom packing arxiv:607.06668v2 [conmat.statmech]
More informationProf. Dr. Ibraheem Nasser electric_charhe 9/22/2017 ELECTRIC CHARGE
ELECTRIC CHARGE Introuction: Orinary matter consists of atoms. Each atom consists of a nucleus, consisting of protons an neutrons, surroune by a number of electrons. In electricity, the electric charge
More informationOptimization of Geometries by Energy Minimization
Optimization of Geometries by Energy Minimization by Tracy P. Hamilton Department of Chemistry University of Alabama at Birmingham Birmingham, AL 3594140 hamilton@uab.eu Copyright Tracy P. Hamilton, 1997.
More information'HVLJQ &RQVLGHUDWLRQ LQ 0DWHULDO 6HOHFWLRQ 'HVLJQ 6HQVLWLYLW\,1752'8&7,21
Large amping in a structural material may be either esirable or unesirable, epening on the engineering application at han. For example, amping is a esirable property to the esigner concerne with limiting
More informationPoS(RAD COR 2007)030. Threejet DIS final states from k dependent parton showers. F. Hautmann University of Oxford
OUTP8P Threejet DIS final states from k epenent parton showers University of Oxfor Email: hautmann@thphys.ox.ac.uk H. Jung DESY Email: jung@mail.esy.e Experimental measurements of angular correlations
More informationCracktip stress evaluation of multiscale Griffith crack subjected to
Cracktip stress evaluation of multiscale Griffith crack subjecte to tensile loaing by using periynamics XiaoWei Jiang, Hai Wang* School of Aeronautics an Astronautics, Shanghai Jiao Tong University,
More informationPrep 1. Oregon State University PH 213 Spring Term Suggested finish date: Monday, April 9
Oregon State University PH 213 Spring Term 2018 Prep 1 Suggeste finish ate: Monay, April 9 The formats (type, length, scope) of these Prep problems have been purposely create to closely parallel those
More information3D FEM Modeling of fiber/matrix interface debonding in UD composites including surface effects
IOP Conference Series: Materials Science an Engineering 3D FEM Moeling of fiber/matrix interface eboning in UD composites incluing surface effects To cite this article: A Pupurs an J Varna 2012 IOP Conf.
More informationTransmission Line Matrix (TLM) network analogues of reversible trapping processes Part B: scaling and consistency
Transmission Line Matrix (TLM network analogues of reversible trapping processes Part B: scaling an consistency Donar e Cogan * ANC Eucation, 308310.A. De Mel Mawatha, Colombo 3, Sri Lanka * onarecogan@gmail.com
More informationA Modification of the JarqueBera Test. for Normality
Int. J. Contemp. Math. Sciences, Vol. 8, 01, no. 17, 8485 HIKARI Lt, www.mhikari.com http://x.oi.org/10.1988/ijcms.01.9106 A Moification of the JarqueBera Test for Normality Moawa ElFallah Ab ElSalam
More informationLecture 2 Lagrangian formulation of classical mechanics Mechanics
Lecture Lagrangian formulation of classical mechanics 70.00 Mechanics Principle of stationary action MATHGA To specify a motion uniquely in classical mechanics, it suffices to give, at some time t 0,
More information6. Friction and viscosity in gasses
IR2 6. Friction an viscosity in gasses 6.1 Introuction Similar to fluis, also for laminar flowing gases Newtons s friction law hols true (see experiment IR1). Using Newton s law the viscosity of air uner
More informationarxiv: v1 [hepex] 4 Sep 2018 Simone Ragoni, for the ALICE Collaboration
Prouction of pions, kaons an protons in Xe Xe collisions at s =. ev arxiv:09.0v [hepex] Sep 0, for the ALICE Collaboration Università i Bologna an INFN (Bologna) Email: simone.ragoni@cern.ch In late
More informationPCCP PAPER. 1 Introduction. A. Nenning,* A. K. Opitz, T. M. Huber and J. Fleig. View Article Online View Journal View Issue
PAPER View Article Online View Journal View Issue Cite this: Phys. Chem. Chem. Phys., 2014, 16, 22321 Receive 4th June 2014, Accepte 3r September 2014 DOI: 10.1039/c4cp02467b www.rsc.org/pccp 1 Introuction
More informationApproaches for Predicting Collection Efficiency of Fibrous Filters
Volume 5, Issue, Summer006 Approaches for Preicting Collection Efficiency of Fibrous Filters Q. Wang, B. Maze, H. Vahei Tafreshi, an B. Poureyhimi Nonwovens Cooperative esearch Center, North Carolina State
More informationSensors & Transducers 2015 by IFSA Publishing, S. L.
Sensors & Transucers, Vol. 184, Issue 1, January 15, pp. 5359 Sensors & Transucers 15 by IFSA Publishing, S. L. http://www.sensorsportal.com Noninvasive an Locally Resolve Measurement of Soun Velocity
More informationSpectral Flow, the Magnus Force, and the. JosephsonAnderson Relation
Spectral Flow, the Magnus Force, an the arxiv:conmat/9602094v1 16 Feb 1996 JosephsonAnerson Relation P. Ao Department of Theoretical Physics Umeå University, S901 87, Umeå, SWEDEN October 18, 2018 Abstract
More informationBohr Model of the Hydrogen Atom
Class 2 page 1 Bohr Moel of the Hyrogen Atom The Bohr Moel of the hyrogen atom assumes that the atom consists of one electron orbiting a positively charge nucleus. Although it oes NOT o a goo job of escribing
More informationElectroacoustic and Dielectric Dispersion of Concentrated Colloidal Suspensions
IEEE Transactions on Dielectrics an Electrical Insulation Vol. 13, No. 3; June 26 657 Electroacoustic an Dielectric Dispersion of Concentrate Colloial Suspensions S. hualli, M. L. Jiménez,. V. Delgao Department
More informationCritical Size and Particle Growth
Critical Size an article Growth rof. Sotiris E. ratsinis article Technology Laboratory Department of Mechanical an rocess Engineering, ETH Zürich, Switzerlan www.ptl.ethz.ch 1 NucleationConensation A
More informationMath 342 Partial Differential Equations «Viktor Grigoryan
Math 342 Partial Differential Equations «Viktor Grigoryan 6 Wave equation: solution In this lecture we will solve the wave equation on the entire real line x R. This correspons to a string of infinite
More informationTransition Metals. dblock
Transition Metals The transition metals are block metals. Sometimes the term is use to refer to all block elements (all of which are metals), though more strictly it inclues those that are in the transition
More informationinflow outflow Part I. Regular tasks for MAE598/494 Task 1
MAE 494/598, Fall 2016 Project #1 (Regular tasks = 20 points) Har copy of report is ue at the start of class on the ue ate. The rules on collaboration will be release separately. Please always follow the
More informationSurvey Sampling. 1 Designbased Inference. Kosuke Imai Department of Politics, Princeton University. February 19, 2013
Survey Sampling Kosuke Imai Department of Politics, Princeton University February 19, 2013 Survey sampling is one of the most commonly use ata collection methos for social scientists. We begin by escribing
More informationExtinction, σ/area. Energy (ev) D = 20 nm. t = 1.5 t 0. t = t 0
Extinction, σ/area 1.5 1.0 t = t 0 t = 0.7 t 0 t = t 0 t = 1.3 t 0 t = 1.5 t 0 0.7 0.9 1.1 Energy (ev) = 20 nm t 1.3 Supplementary Figure 1: Plasmon epenence on isk thickness. We show classical calculations
More informationLeastSquares Regression on Sparse Spaces
LeastSquares Regression on Sparse Spaces Yuri Grinberg, Mahi Milani Far, Joelle Pineau School of Computer Science McGill University Montreal, Canaa {ygrinb,mmilan1,jpineau}@cs.mcgill.ca 1 Introuction
More informationIn the usual geometric derivation of Bragg s Law one assumes that crystalline
Diffraction Principles In the usual geometric erivation of ragg s Law one assumes that crystalline arrays of atoms iffract Xrays just as the regularly etche lines of a grating iffract light. While this
More informationTimeofArrival Estimation in NonLineOfSight Environments
2 Conference on Information Sciences an Systems, The Johns Hopkins University, March 2, 2 TimeofArrival Estimation in NonLineOfSight Environments Sinan Gezici, Hisashi Kobayashi an H. Vincent Poor
More informationEstimation of hardness by nanoindentation of rough surfaces
Journal of MATERIALS RESEARCH Welcome Comments Help Estimation of harness by nanoinentation of rough surfaces M. S. Bobji an S. K. Biswas Department of Mechanical Engineering, Inian Institute of Science,
More informationThe total derivative. Chapter Lagrangian and Eulerian approaches
Chapter 5 The total erivative 51 Lagrangian an Eulerian approaches The representation of a flui through scalar or vector fiels means that each physical quantity uner consieration is escribe as a function
More informationDot trajectories in the superposition of random screens: analysis and synthesis
1472 J. Opt. Soc. Am. A/ Vol. 21, No. 8/ August 2004 Isaac Amiror Dot trajectories in the superposition of ranom screens: analysis an synthesis Isaac Amiror Laboratoire e Systèmes Périphériques, Ecole
More information05 The Continuum Limit and the Wave Equation
Utah State University DigitalCommons@USU Founations of Wave Phenomena Physics, Department of 112004 05 The Continuum Limit an the Wave Equation Charles G. Torre Department of Physics, Utah State University,
More informationA SIMPLE ENGINEERING MODEL FOR SPRINKLER SPRAY INTERACTION WITH FIRE PRODUCTS
International Journal on Engineering PerformanceBase Fire Coes, Volume 4, Number 3, p.953, A SIMPLE ENGINEERING MOEL FOR SPRINKLER SPRAY INTERACTION WITH FIRE PROCTS V. Novozhilov School of Mechanical
More informationOn the Surprising Behavior of Distance Metrics in High Dimensional Space
On the Surprising Behavior of Distance Metrics in High Dimensional Space Charu C. Aggarwal, Alexaner Hinneburg 2, an Daniel A. Keim 2 IBM T. J. Watson Research Center Yortown Heights, NY 0598, USA. charu@watson.ibm.com
More informationarxiv:condmat/ v1 12 Oct 2005
Creation an estruction of a spin gap in weakly couple quarterfille laers B. Eegger,, H.G. Evertz, an R.M. Noack Institut für Theoretische Physik, Technische Universität Graz, A8 Graz, Austria Institut
More informationA Simple Model for the Calculation of Plasma Impedance in Atmospheric Radio Frequency Discharges
Plasma Science an Technology, Vol.16, No.1, Oct. 214 A Simple Moel for the Calculation of Plasma Impeance in Atmospheric Raio Frequency Discharges GE Lei ( ) an ZHANG Yuantao ( ) Shanong Provincial Key
More informationSemiclassical analysis of longwavelength multiphoton processes: The Rydberg atom
PHYSICAL REVIEW A 69, 063409 (2004) Semiclassical analysis of longwavelength multiphoton processes: The Ryberg atom Luz V. VelaArevalo* an Ronal F. Fox Center for Nonlinear Sciences an School of Physics,
More informationMULTISCALE FRICTION MODELING FOR SHEET METAL FORMING
MULTISCALE FRICTION MODELING FOR SHEET METAL FORMING Authors J. HOL 1, M.V. CID ALFARO 2, M.B. DE ROOIJ 3 AND T. MEINDERS 4 1 Materials innovation institute (M2i) 2 Corus Research Centre 3 University of
More informationFormulation of statistical mechanics for chaotic systems
PRAMANA c Inian Acaemy of Sciences Vol. 72, No. 2 journal of February 29 physics pp. 315 323 Formulation of statistical mechanics for chaotic systems VISHNU M BANNUR 1, an RAMESH BABU THAYYULLATHIL 2 1
More informationChapter 2 Lagrangian Modeling
Chapter 2 Lagrangian Moeling The basic laws of physics are use to moel every system whether it is electrical, mechanical, hyraulic, or any other energy omain. In mechanics, Newton s laws of motion provie
More informationEvaporating droplets tracking by holographic high speed video in turbulent flow
Evaporating roplets tracking by holographic high spee vieo in turbulent flow Loïc Méès 1*, Thibaut Tronchin 1, Nathalie Grosjean 1, JeanLouis Marié 1 an Corinne Fournier 1: Laboratoire e Mécanique es
More informationP. A. Martin b) Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom
Timeharmonic torsional waves in a composite cyliner with an imperfect interface J. R. Berger a) Division of Engineering, Colorao School of Mines, Golen, Colorao 80401 P. A. Martin b) Department of Mathematics,
More informationImpurities in inelastic Maxwell models
Impurities in inelastic Maxwell moels Vicente Garzó Departamento e Física, Universia e Extremaura, E671Baajoz, Spain Abstract. Transport properties of impurities immerse in a granular gas unergoing homogenous
More informationwater adding dye partial mixing homogenization time
iffusion iffusion is a process of mass transport that involves the movement of one atomic species into another. It occurs by ranom atomic jumps from one position to another an takes place in the gaseous,
More informationRFSS: Lecture 4 Alpha Decay
RFSS: Lecture 4 Alpha Decay Reaings Nuclear an Raiochemistry: Chapter 3 Moern Nuclear Chemistry: Chapter 7 Energetics of Alpha Decay Geiger Nuttall base theory Theory of Alpha Decay Hinrance Factors Different
More informationGeneralization of the persistent random walk to dimensions greater than 1
PHYSICAL REVIEW E VOLUME 58, NUMBER 6 DECEMBER 1998 Generalization of the persistent ranom walk to imensions greater than 1 Marián Boguñá, Josep M. Porrà, an Jaume Masoliver Departament e Física Fonamental,
More informationModeling the effects of polydispersity on the viscosity of noncolloidal hard sphere suspensions. Paul M. Mwasame, Norman J. Wagner, Antony N.
Submitte to the Journal of Rheology Moeling the effects of polyispersity on the viscosity of noncolloial har sphere suspensions Paul M. Mwasame, Norman J. Wagner, Antony N. Beris a) epartment of Chemical
More informationADIT DEBRIS PROJECTION DUE TO AN EXPLOSION IN AN UNDERGROUND AMMUNITION STORAGE MAGAZINE
ADIT DEBRIS PROJECTION DUE TO AN EXPLOSION IN AN UNDERGROUND AMMUNITION STORAGE MAGAZINE Froe Opsvik, Knut Bråtveit Holm an Svein Rollvik Forsvarets forskningsinstitutt, FFI Norwegian Defence Research
More informationThe influence of the equivalent hydraulic diameter on the pressure drop prediction of annular test section
IOP Conference Series: Materials Science an Engineering PAPER OPEN ACCESS The influence of the equivalent hyraulic iameter on the pressure rop preiction of annular test section To cite this article: A
More informationSchrödinger s equation.
Physics 342 Lecture 5 Schröinger s Equation Lecture 5 Physics 342 Quantum Mechanics I Wenesay, February 3r, 2010 Toay we iscuss Schröinger s equation an show that it supports the basic interpretation of
More informationOn colourblind distinguishing colour pallets in regular graphs
J Comb Optim (2014 28:348 357 DOI 10.1007/s108780129556x On colourblin istinguishing colour pallets in regular graphs Jakub Przybyło Publishe online: 25 October 2012 The Author(s 2012. This article
More informationCONTROL CHARTS FOR VARIABLES
UNIT CONTOL CHATS FO VAIABLES Structure.1 Introuction Objectives. Control Chart Technique.3 Control Charts for Variables.4 Control Chart for Mean(Chart).5 ange Chart (Chart).6 Stanar Deviation Chart
More informationDrug Delivery to the Lungs (DDL2017), Vibha Puri, et al.
Effect of Air Jet Micronization on Particle Properties an the Correlation of Interparticle Interactions by Atomic Force Microscopy with Surface Forces by Inverse Gas Chromatography Vibha Puri, 1 Jageep
More informationA note on asymptotic formulae for onedimensional network flow problems Carlos F. Daganzo and Karen R. Smilowitz
A note on asymptotic formulae for oneimensional network flow problems Carlos F. Daganzo an Karen R. Smilowitz (to appear in Annals of Operations Research) Abstract This note evelops asymptotic formulae
More informationExpected Value of Partial Perfect Information
Expecte Value of Partial Perfect Information Mike Giles 1, Takashi Goa 2, Howar Thom 3 Wei Fang 1, Zhenru Wang 1 1 Mathematical Institute, University of Oxfor 2 School of Engineering, University of Tokyo
More informationKinetics of radiationless energy transfer from upper excited states
1 August 1997 Ž Chemical Physics Letters 74 1997 171 176 Kinetics of raiationless energy transfer from upper excite states EN Bounov 1, MN BerberanSantos, JMG Martinho Centro e QuımicaFısica Molecular,
More informationThe effect of nonvertical shear on turbulence in a stably stratified medium
The effect of nonvertical shear on turbulence in a stably stratifie meium Frank G. Jacobitz an Sutanu Sarkar Citation: Physics of Fluis (1994present) 10, 1158 (1998); oi: 10.1063/1.869640 View online:
More informationNumber of wireless sensors needed to detect a wildfire
Number of wireless sensors neee to etect a wilfire Pablo I. Fierens Instituto Tecnológico e Buenos Aires (ITBA) Physics an Mathematics Department Av. Maero 399, Buenos Aires, (C1106ACD) Argentina pfierens@itba.eu.ar
More informationQubit channels that achieve capacity with two states
Qubit channels that achieve capacity with two states Dominic W. Berry Department of Physics, The University of Queenslan, Brisbane, Queenslan 4072, Australia Receive 22 December 2004; publishe 22 March
More informationThe PressSchechter mass function
The PressSchechter mass function To state the obvious: It is important to relate our theories to what we can observe. We have looke at linear perturbation theory, an we have consiere a simple moel for
More informationSpecific ion effects on the interaction of. hydrophobic and hydrophilic self assembled
Supporting Information Specific ion effects on the interaction of hydrophobic and hydrophilic self assembled monolayers T. RiosCarvajal*, N. R. Pedersen, N. Bovet, S.L.S. Stipp, T. Hassenkam. NanoScience
More informationHomework 7 Due 18 November at 6:00 pm
Homework 7 Due 18 November at 6:00 pm 1. Maxwell s Equations Quasistatics o a An air core, N turn, cylinrical solenoi of length an raius a, carries a current I Io cos t. a. Using Ampere s Law, etermine
More informationθ x = f ( x,t) could be written as
9. Higher orer PDEs as systems of firstorer PDEs. Hyperbolic systems. For PDEs, as for ODEs, we may reuce the orer by efining new epenent variables. For example, in the case of the wave equation, (1)
More informationA Review of Multiple Try MCMC algorithms for Signal Processing
A Review of Multiple Try MCMC algorithms for Signal Processing Luca Martino Image Processing Lab., Universitat e València (Spain) Universia Carlos III e Mari, Leganes (Spain) Abstract Many applications
More informationSelffocusing and soliton formation in media with anisotropic nonlocal material response
EUROPHYSICS LETTERS 20 November 1996 Europhys. Lett., 36 (6), pp. 419424 (1996) Selffocusing an soliton formation in meia with anisotropic nonlocal material response A. A. Zoulya 1, D. Z. Anerson 1,
More informationAdsorption of H 2 O, NH 3, CO, NO 2, and NO on graphene: A firstprinciples study
Asorption of H 2 O, NH 3, CO, NO 2, an NO on graphene: A firstprinciples stuy O. Leenaerts,* B. Partoens, an F. M. Peeters Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B2020 Antwerpen,
More informationConstruction of the Electronic Radial Wave Functions and Probability Distributions of Hydrogenlike Systems
Construction of the Electronic Raial Wave Functions an Probability Distributions of Hyrogenlike Systems Thomas S. Kuntzleman, Department of Chemistry Spring Arbor University, Spring Arbor MI 498 tkuntzle@arbor.eu
More informationChapter 2 Governing Equations
Chapter 2 Governing Equations In the present an the subsequent chapters, we shall, either irectly or inirectly, be concerne with the bounarylayer flow of an incompressible viscous flui without any involvement
More informationA USERFRIENDLY TOOL FOR SIMULATING THE TIMEDEPENDENT FIELD DISTRIBUTION IN PE INSULATION ON THE BASIS OF A PHYSICAL APPROACH
A USERFRIENLY TOOL FOR SIMULATING THE TIMEEPENENT FIEL ISTRIBUTION IN PE INSULATION ON THE BASIS OF A PHYSICAL APPROACH Séverine LE ROY, Laboratoire Plasma et Conversion Energie, (France), severine.leroy@laplace.univtlse.fr
More informationInfluence of Radiation on Product Yields in a Film Boiling Reactor
R&D NOTES Influence of Raiation on Prouct Yiels in a Film Boiling Reactor C. Thomas Aveisian, Wing Tsang, Terence Daviovits, an Jonah R. Allaben Sibley School of Mechanical an Aerospace Engineering, Cornell
More informationarxiv: v1 [heplat] 19 Nov 2013
HUEP13/69 SFB/CPP1398 DESY 13225 Applicability of QuasiMonte Carlo for lattice systems arxiv:1311.4726v1 [heplat] 19 ov 2013, a,b Tobias Hartung, c Karl Jansen, b Hernan Leovey, Anreas Griewank
More informationTo understand how scrubbers work, we must first define some terms.
SRUBBERS FOR PARTIE OETION Backgroun To unerstan how scrubbers work, we must first efine some terms. Single roplet efficiency, η, is similar to single fiber efficiency. It is the fraction of particles
More informationAsymptotics of a Small Liquid Drop on a Cone and Plate Rheometer
Asymptotics of a Small Liqui Drop on a Cone an Plate Rheometer Vincent Cregan, Stephen B.G. O Brien, an Sean McKee Abstract A cone an a plate rheometer is a laboratory apparatus use to measure the viscosity
More informationInfluence of weight initialization on multilayer perceptron performance
Influence of weight initialization on multilayer perceptron performance M. Karouia (1,2) T. Denœux (1) R. Lengellé (1) (1) Université e Compiègne U.R.A. CNRS 817 Heuiasyc BP 649  F66 Compiègne ceex 
More informationStudy on aeroacoustic structural interactions in fanducted system
Stuy on aeroacoustic structural interactions in fanucte system Yankei CHIANG 1 ; Yatsze CHOY ; Li CHENG 3 ; Shiukeung TANG 4 1,, 3 Department of Mechanical Engineering, The Hong Kong Polytechnic University,
More informationAnalysis of Biochemical Equilibria Relevant to the Immune Response: Finding the Dissociation Constants
Bull Math Biol 202) 74:7 206 DOI 0.007/s538029762 ORIGINAL ARTICLE Analysis of Biochemical Equilibria Relevant to the Immune Response: Fining the Dissociation Constants L.J. Cummings R. PerezCastillejos
More informationSYNCHRONOUS SEQUENTIAL CIRCUITS
CHAPTER SYNCHRONOUS SEUENTIAL CIRCUITS Registers an counters, two very common synchronous sequential circuits, are introuce in this chapter. Register is a igital circuit for storing information. Contents
More informationCollective optical effect in complement lefthanded material
Collective optical effect in complement lefthane material S.C. Wu, C.F. Chen, W. C. Chao, W.J. Huang an H. L. Chen, National Nano Device Laboratories, 10011 TaHsueh Roa, Hsinchu, Taiwan R.O.C A.C.
More informationQuantum mechanical approaches to the virial
Quantum mechanical approaches to the virial S.LeBohec Department of Physics an Astronomy, University of Utah, Salt Lae City, UT 84112, USA Date: June 30 th 2015 In this note, we approach the virial from
More informationInteraction force in a vertical dust chain inside a glass box
Interaction force in a vertical ust chain insie a glass box Jie Kong, Ke Qiao, Lorin S. Matthews an Truell W. Hye Center for Astrophysics, Space Physics, an Engineering Research (CASPER) Baylor University
More informationA Hybrid Approach Based on the Genetic Algorithm and Monte Carlo Method to Optimize the 3D Radiant Furnaces
Int J Avance Design an Manufacturing Technology, Vol. 8/ o. 3/ September  2015 67 A Hybri Approach Base on the Genetic Algorithm an Monte Carlo Metho to Optimize the 3D Raiant Furnaces B. Kamkari* Young
More informationSwitching Time Optimization in Discretized Hybrid Dynamical Systems
Switching Time Optimization in Discretize Hybri Dynamical Systems Kathrin Flaßkamp, To Murphey, an Sina OberBlöbaum Abstract Switching time optimization (STO) arises in systems that have a finite set
More information3.2 Shot peening  modeling 3 PROCEEDINGS
3.2 Shot peening  moeling 3 PROCEEDINGS Computer assiste coverage simulation FrançoisXavier Abaie a, b a FROHN, Germany, fx.abaie@frohn.com. b PEENING ACCESSORIES, Switzerlan, info@peening.ch Keywors:
More information6 General properties of an autonomous system of two first order ODE
6 General properties of an autonomous system of two first orer ODE Here we embark on stuying the autonomous system of two first orer ifferential equations of the form ẋ 1 = f 1 (, x 2 ), ẋ 2 = f 2 (, x
More informationThe Principle of Least Action
Chapter 7. The Principle of Least Action 7.1 Force Methos vs. Energy Methos We have so far stuie two istinct ways of analyzing physics problems: force methos, basically consisting of the application of
More informationarxiv:physics/ v2 [physics.edph] 23 Sep 2003
Mass reistribution in variable mass systems Célia A. e Sousa an Vítor H. Rorigues Departamento e Física a Universiae e Coimbra, P3004516 Coimbra, Portugal arxiv:physics/0211075v2 [physics.eph] 23 Sep
More informationqq 1 1 q (a) q (b) 2q (c)
1... Multiple Choice uestions with One Correct Choice A hollow metal sphere of raius 5 cm is charge such that the potential on its surface to 1 V. The potential at the centre of the sphere is (a) zero
More informationTable of Common Derivatives By David Abraham
Prouct an Quotient Rules: Table of Common Derivatives By Davi Abraham [ f ( g( ] = [ f ( ] g( + f ( [ g( ] f ( = g( [ f ( ] g( g( f ( [ g( ] Trigonometric Functions: sin( = cos( cos( = sin( tan( = sec
More informationVertical shear plus horizontal stretching as a route to mixing
Vertical shear plus horizontal stretching as a route to mixing Peter H. Haynes Department of Applie Mathematics an Theoretical Physics, University of Cambrige, UK Abstract. The combine effect of vertical
More informationKNN Particle Filters for Dynamic Hybrid Bayesian Networks
KNN Particle Filters for Dynamic Hybri Bayesian Networs H. D. Chen an K. C. Chang Dept. of Systems Engineering an Operations Research George Mason University MS 4A6, 4400 University Dr. Fairfax, VA 22030
More informationIPA Derivatives for MaketoStock ProductionInventory Systems With Backorders Under the (R,r) Policy
IPA Derivatives for MaketoStock ProuctionInventory Systems With Backorers Uner the (Rr) Policy Yihong Fan a Benamin Melame b Yao Zhao c Yorai Wari Abstract This paper aresses Infinitesimal Perturbation
More information