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Physical Units, Constants and Conversion Factors

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Physical Units, Constants and Conversion Factors Here we regroup the values of the most useful physical and chemical constants used in the book. Also some practical combinations of such constants are provided. Units are expressed in the International System (SI), and conversion to the older CGS system is also given. For most quantities and units, the practical definitions currently used in the context of biophysics are also shown. © Springer International Publishing Switzerland 2016 609 F. Cleri, The Physics of Living Systems, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-3-319-30647-6 610 Physical units, constants and conversion factors Basic physical units (boldface indicates SI fundamental units) SI cgs Biophysics Length (L) meter (m) centimeter (cm) Angstrom (Å) 1 0.01 m 10−10 m Time (T) second (s) second (s) 1 µs=10−6 s 1 1 1ps=10−12 s Mass (M) kilogram (kg) gram (g) Dalton (Da) −27 1 0.001 kg 1/NAv = 1.66 · 10 kg Frequency (T−1) s−1 Hz 1 1 Velocity (L/T) m/s cm/s µm/s 1 0.01 m/s 10−6 m/s Acceleration (L/T2) m/s2 cm/s2 µm/s2 1 0.01 m/s2 10−6 m/s2 Force (ML/T2) newton (N) dyne (dy) pN 1kg· m/s2 10−5 N 10−12 N Energy, work, heat joule (J) erg kB T (at T = 300 K) (ML2/T2) 1kg· m2/s2 10−7 J 4.114 pN · nm 0.239 cal 0.239 · 10−7 cal 25.7 meV 1C· 1V 1 mol ATP = 30.5 kJ = 7.3 kcal/mol Power (ML2/T3) watt (W) erg/s ATP/s 1kg· m2/s3 =1J/s 10−7 J/s 0.316 eV/s Pressure (M/LT2) pascal (Pa) atm Blood osmolarity 1 N/m2 101325˙ Pa ∼ 300 mmol/kg 1 bar = 105 Pa ∼300 Pa = 3 · 10−3 atm Electric current (A) ampere (A) e.s.u. Transmembrane 1 2.998 · 109 A current ∼1-2 mA/cm2 Electric charge (A/T) coulomb (C) statCoulomb (stC) 1A·s 2.998 · 109 C Electric volt (V) statCoulomb (stC) Neuron action potential potential (ML2/T3A) 1W/A 2.998 · 109 C ∼ 100 mV Electrical ohm () statOhm (st) Cell membrane (with K+ resistance (ML2/T3A2) 1 V/A 1.11265 · 10−12 and Na+ channels) 1-2 k · µm2 Temperature (K) kelvin (K) celsius (◦C) 1 1 Physical units, constants and conversion factors 611 Useful physical constants and their combinations 23 −1 Avogadro’s number, NAv = 6.0221409 × 10 mol = 1 (12 ) = . × −27 Atomic mass unit, mu 12 m C 1 66053904 10 kg −23 −5 Boltzmann’s constant, kB = 1.3806485 × 10 J/K (joule/kelvin degree) = 8.617×10 eV/K Planck’s constant, h = 6.62607 × 10−34 J s = 4.132 eV/fs, = h/2π Stefan-Boltzmann’s constant, σ = 5.670367 × 10−8 W/(m2K4) Gas constant, R = 8.31446 J/(K· mol) = 1.987 cal/(K· mol) = NAv · kB Molar volume at STP Vm = 22.414 litre/mol Speed of light, c = 2.99792458 × 108 m/s Elementary charge, e = 1.60217662 × 10−19 C (coulomb) −12 Vacuum dielectric constant, ε0 = 8.854 · 10 F/m (faraday/metre) 9 2 −2 Coulomb’s constant, Kc = 1/(4πε0) = 8.9875 × 10 Nm C Faraday’s constant, F = 96485.309 C/mol 2 −10 mu c = 1.4924 × 10 J = 931.494 MeV 2 −28 Kce = 2.3071 × 10 Jm=1.44eVnm c = 3.1615 × 1026 J m = 197.33 eVnm RT = kB T × NAv = 2.479 kJ/mol (at 300 K) h/kB T = 0.16 ps (at 300 K) Useful conversion factors (with some old-fashioned units) To convert from: To: Multiply by: radian degree arc 57.29578 angstrom nanometer 0.1 light-year metre (m) 9.461 × 1015 cm3 litre 0.001 eV joule (J) 1.6021 × 10−19 eV (wavelength) cm−1 8,065.73 eV (wavelength) nanometer 1,239.84 teraHertz (THz = 1012Hz) meV (wavelength) 4.13567 standard atmosphere kilopascal (kPa) 101.325 bar kilopascal (kPa) 100 millimeter of mercury (at 0 ◦C) kilopascal (kPa) 0.1333224 millimeter of water (at 4 ◦C) pascal (Pa) 9.80665 pound/sq.inch (lb/in2, psi) pascal (Pa) 6,900 centipoise (viscosity) pascal-second (Pa s) 0.001 horse-power (hP) watt (W) 746 kilowatt-hour (kWh) megajoule (MJ) 3.6 calorie joule (J) 4.184 eV kcal/mole 23.0609 gauss tesla (T) 0.0001 weber/sq.metre tesla (T) 1 ampere-hour coulomb (C) 3,600 Index A ATP, adenosine triphosphate, 78, 113, 188, Accretion mechanism, 496 206, 209, 221, 240, 264, 276, 357, Acetylation, 107 430 Actin, 193, 207, 261 Autocatalysis, 507 monomer (G-actin), 226 Autocatalytic reaction, 80 polymerisation, 226 Avalon explosion, 90 polymerisation speed, 227 Average curvature, surface, 486 treadmilling effect, 228 Avogadro’s number, 11 Action potentia Axoplasm, 271 Hodgkin-Huxley experiment, 280 Action potential, 262, 275, 278 in muscle, 442 B plants, 303 Bacterial DNA, 71 post-synaptic, 291 Ballot theorem, 179 propagation speed, 282 Bartel and Szostak experiment, 80 Basal metabolic rate, 138 subthreshold, 285 Bending modulus wave-like propagation, 284 of a rmembrane, 325 Active transport, 264 of a rod, 324, 326 Adiabatic transformation, 14 Bilateral symmetry, 505 Adipocytes, 147 Binomial distribution, 66 Adiposomes, 147 Biodiversity, 554 ADP, adenosine diphosphate, 113, 215, 430 abundance, 563 Albedo, Earth surface, 39 richness, 563 Allometry, 529 Bio-geochemical cycle, 557 Amino acid, 105 Biomass, 555 Amphiphilic molecule, 169, 337 Biomass, upper bound for a species, 561 Anaerobic glycolysis, 134 Biosphere, 30 Ancient Greek medial school, 96 Biosynthesis Antiporter, ion channel, 134 clay hypothesis, 89 Apex predator, 555 iron-sulphur hypothesis, 89 Aquaporin, see ion channel Biot number, 143 Archimedean tiling, 488 Biphasic material, 387 Argentavis, 538 Biphasic model, human tissues, 390 Arrhenius law, of biodiversity, 563 Bistable oscillator, 439 Asakura and Oosawa experiment, 169 Black body, 41 Aspect ratio, 484 Body plan, 90, 505 © Springer International Publishing Switzerland 2016 613 F. Cleri, The Physics of Living Systems, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-3-319-30647-6 614 Index Boiling point, 55 Chromatin, 101, 356 Boltzmann Chromosome, 101, 356 constant, 17 Chronaxy, 278 entropy definition, 19 Cilium, 236 entropy equation, 62 Clausius, irreversible transformation, 18 kinetic theory of gas, 25 Clausius, thermodynamic entropy, 23 Boltzmann factor, 216, 345 Claverie and Rault, see mimivirus Bond number, 481 Clay hypothesis, see biosynthesis Bone size scaling, 537 Clock-and-wavefront model, 511 Brain plasticity, 292 Closed ecosystem, see ecology Brain-blood barrier, 188 Closed system, 20 Brittle, material, 374 Codon, 105 Brown fat, 147 Coenzymes, 151 Brownian motion Cohesin, 356 and membrane diffusion, 180 Cohesin, motor protein, 357 early experiments, 178 Colloid, 169 Einstein’s equations, 205 Competition, between species, 550 rectified, 216 Condensin, 356 Smoluchowski problem, 179 Condensin, motor protein, 357 Bulk modulus, 371 Conductance, neuron membrane, 269 Buoyancy force, 537 Constant, vector field, 50 Constitutive relation, 370 Contour length, 174 C Cortical tension, see membrane Calvin’s cycle, see photosynthesis Cost of transport, 541 Cambrian explosion, 90 Coupled oscillators, 513 Cantilever, 444 Creatine phosphate, 146 Capillarity, 478 Creep, 377 meniscus, 479 Crescentin, bacterial protein, 351 Capillarity length, 481 Cross bridges, sarcomere, 425 Carbohydrates, 153 Crowding agents, 172 furanose, 154 Cryptochrome, 257 monosaccharide, 153 Curl, see rotor pyranose, 154 Current summation, synaptic, 293 Carbon cycle, 558 Cyclic machine, 207, 213 Cardiac index, 139 ratchet, 216 Carnot, cyclic thermal engine, 18 Cytoskeleton, 244 Carrying capacity, 546 actin, 193 Catalyser, see enzyme centromere, 193 Catalytic efficiency, enzyme, 234 microtubules, 193 Cell cycle, 354 spectrin, 195 Cell nucleus, 337 Cellulose, 397 Central Dogma, 100 D Centromere, 101 Damping coefficient, aerodynamic, 448 Chaotic system, see deterministic chaos Debye-Huckel approximation, 175 Chemical potential, 27 Debye length, 175 Chemiosmotic theory, 120 Debye repulsion, screening, 173 Chlamydomonas, unicellular alga, 189, 255 Deformation (elastic) energy, 416 Chlorophyll, 476 Dendritic spines, 292 Cholesterol, 199 Depletion force, 169 Chondrocyte, 386 Depolarisation, membrane, 270 Chromatid, 101 Deterministic chaos, 547 Index 615 butterfly effect, 548 closed ecosystem, 556 critical bifurcation, 548 food chain, 555 loss of information, 548 mobile ecosystem, 556 Lyapunov exponent, 548 trophic level, 555 Lyapunov time, 548 Ecosystem Diastole, heart contraction, 296 producers versus consumers, 555 Diffusion Ectoderm, 505 across membrane, 176 Edema, tissue, 187 Diffusion coefficient, 177, 191, 205 Elastic compliance, 409 Diffusion equation, 180 Elastic constant, 409 Dinosaurs Elastic energy, storage, 535 extinction, 95, 539 Elastic moduli running speed, 458 bulk modulus, 411 Diodora aspera, gastropod, 191 Lamé parameters, 410 Diploblastic, body plan, 505 Poisson’s ratio, 414 Dipole moment, 167 shear modulus, 412 Dirac delta function, 45 Young’s modulus, 412 Divergence angle, 515 Elastic modulus, 370 Divergence, of a vector, 49 Electric permittivity, relative, 312 DNA Electrocardiogram, 300 exon, 77, 103 Endoderm, 505 Franklin and Wilkins x-ray diffraction, Endoergic, reaction, 69 97 Endoplasmic reticulum, 337 grooves, major and minor, 100 Energy accumulation rate, 543 intron, 77, 103 Energy barrier, 213 methylation, 107, 108 Energy budget, 543 mismatch, 99 Energy surface, 213 Nirenberg and Khorana genetic code, 97 England’s theory, maximum dissipation, 82 nucleoside, 99 Enthalpy, 27 nucleotide, 98 Entropic force, see generalised force Watson and Crick model, 97 Entropy Drag coefficient, 206 information, 36 Drag force negative, 36 in rotation, 240 Environmental pressure, 561 Stokes coefficient, 239 Enzymatic cycles, 124 Drosophila melanogaster, fruit fly, 257, 260, Enzyme, 126 428, 510 Epigenetic modification, 106 Ductile, material, 374 Equation of continuity, 180 Dulong and Petit, specific heat, 22 Equilibrium constant, 127 Dutch famine, 1944, 108 Equilibrium, statistical postulate, 12 Dynamic range, neuron, 295 Equipartition of energy,
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  • Arxiv:2012.01639V4 [Cond-Mat.Soft] 29 Jun 2021 T =Kbt/Ε, Where Kb and T Are the Boltzmann Constant and the Temperature of System, Respectively

    Arxiv:2012.01639V4 [Cond-Mat.Soft] 29 Jun 2021 T =Kbt/Ε, Where Kb and T Are the Boltzmann Constant and the Temperature of System, Respectively

    Self-Assembly of Isostatic Self-Dual Colloidal Crystals Qun-Li Lei,1, 2, ∗ Wei Zheng,1, 2, ∗ Feng Tang,1 Xiangang Wan,1 Ran Ni,2, y and Yuqiang Ma1, z 1National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China 2School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore Self-dual structures whose dual counterparts are themselves possess unique hidden symmetry, beyond the description of classical spatial symmetry groups. Here we propose a strategy based on a nematic monolayer of attractive half-cylindrical colloids to self-assemble these exotic structures. This system can be seen as a 2D system of semi-disks. By using Monte Carlo simulations, we discover two isostatic self-dual crystals, i.e., an unreported crystal with pmg space-group symmetry and the twisted Kagome crystal. For the pmg crystal approaching the critical point, we find the double degeneracy of the full phononic spectrum at the self-dual point, and the merging of two tilted Weyl nodes into one critically-tilted Dirac node. The latter is `accidentally' located on the high-symmetry line. The formation of this unconventional Dirac node is due to the emergence of the critical flat bands at the self-dual point, which are linear combinations of finite-frequency floppy modes. These modes can be understood as mechanically-coupled self-dual rhomb chains vibrating in some unique uncoupled ways. Our work paves the way for designing and fabricating self-dual materials with exotic mechanical or phononic properties.