Skip to main content

Thermodynamics of Irreversible Particle Creation Phenomena and Its Cosmological Consequence

  • Chapter
  • First Online:
Thermo-Mechanics Applications and Engineering Technology

Abstract

The study of particle creation phenomena at the expense of the gravitational field is of great research interest. It might solve the cosmological puzzle singlehandedly, without the need for either dark energy or modified theory of gravity. In the early universe, it serves the purpose of reheating which gave way to escape from inflationary phase to the hot Big Bang model. In the late universe, it instigates late-time cosmic acceleration, without affecting standard Big Bang Nucleosynthesis (BBN), Cosmic Microwave Background Radiation (CMBR), or Structure Formation. In this chapter, we briefly review the present status of cosmic evolution, develop the thermodynamics for irreversible particle creation phenomena, and study its consequences at the early as well as at the late universe.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abramo LRW, Finelli F (2003) Cosmological dynamics of the tachyon with an inverse power-law potential. Phys Lett B 575:165

    Google Scholar 

  • Achterberg A, Hurley K et al (2008) The Search for Muon Neutrinos from Northern Hemisphere Gamma-Ray Bursts with AMANDA, The IceCube collaboration, and The IPN collaboration. Astrophys J 674:357

    Google Scholar 

  • Aguirregabiria JM, Lazkoz R (2004) Tracking solutions in tachyon cosmology. Phys Rev D 69:123502

    Google Scholar 

  • Agullo I, Parker L (2011) Non-Gaussianities and the stimulated creation of quanta in the inflationary universe. Phys Rev D 83:063526

    Google Scholar 

  • Alam U, Sahni V (2002) Supernova constraints on braneworld dark energy. astro-ph/0209443

    Google Scholar 

  • Albrecht A, Steinhardt PJ (1982) Cosmology for grand unified theories with radiatively induced symmetry breaking. Phys Rev Lett 48:1220

    Google Scholar 

  • ANTARES Collaboration (2012) Measurement of atmospheric neutrino oscillations with the ANTARES neutrino telescope. Phys Lett B 714:224

    Google Scholar 

  • Armend´ariz-Pic´on C, Damour T, Mukhanov V (1999) k-Inflation. Phys Lett B 458:209

    Google Scholar 

  • Armend´ariz-Pic´on C, Mukhanov V, Steinhardt PJ (2000) Dynamical solution to the problem of a small cosmological constant and late-time cosmic acceleration. Phys Rev Lett 85:4438

    Google Scholar 

  • Armend´ariz-Pic´on C, Mukhanov V, Steinhardt PJ (2001) Essentials of k-essence. Phys Rev D 63:103510

    Google Scholar 

  • Bagla JS, Jassal HK, Padmanabhan T (2003) Cosmology with tachyon field as dark energy. Phys Rev D 67:063504

    Google Scholar 

  • Bahamonde S, Odintsov SD, Oikonomouand VK, Wright M (2016) Correspondence of F(R) gravity singularities in Jordan and Einstein frames. Annals Phys 373:96

    Google Scholar 

  • Banerjee N, Majumder B (2016) A question mark on the equivalence of Einstein and Jordan frames. Phys Lett B 754:129

    Google Scholar 

  • Banerjee A, Santos NO (1983) Anisotropic cosmological model with viscous fluid. J Math Phys 24(11):2689

    Google Scholar 

  • Banerjee A, Santos NO (1984) Spatially homogeneous cosmological models. Gen Rel Grav 16:217

    Google Scholar 

  • Banerjee A, Sanyal AK (1986) Homogeneous anisotropic cosmologiacl models with viscous fluid and magnetic field. Gen Rel Grav 18:1251

    Google Scholar 

  • Banerjee A, Sanyal AK (1988) Irrotational Bianchi Type-V Viscous Fluid Cosmology with Heat Flux. Gen Rel Grav 20:103

    Google Scholar 

  • Banerjee A, Duttachoudhury SB, Sanyal AK (1985) Bianchi Type I cosmological Model with a Viscous Fluid. J Math Phys 26:3010

    Google Scholar 

  • Banerjee A, Duttachoudhury SB, Sanyal AK (1986) Bianchi type-II cosmological model with viscous fluid. Gen Rel Grav 18:461

    Google Scholar 

  • Bardeen JM (1980) Gauge-invariant cosmological perturbations. Phys Rev D 22:1882

    Google Scholar 

  • Barrow JD (1990) Graduated inflationary universes. Phys Lett B 235:40

    Google Scholar 

  • Barrow JD (1995) Slow-roll inflation in scalar-tensor theories. Phys Rev D 51:2729

    Google Scholar 

  • Barrow JD, Saich P (1990) The behaviour of intermediate inflationary universes. Phys Lett B 249:406

    Google Scholar 

  • Bassett BA, Tsujikawa S, Wands D (2006) Inflation dynamics and reheating. Rev Mod Phys 78:537

    Google Scholar 

  • Belinskii VA, Khalatnikov IM (1975) Influence of viscosity on the character of cosmological evolution. Sov Phys JETP 42(2):205

    Google Scholar 

  • Bento MC, Bertolami O, Sen AA (2002) Generalized chaplygin gas, accelerated expansion and dark energy matter unification. Phys Rev D 66:043507

    Google Scholar 

  • Bergmann PG (1968) Comments on scalar tensor theory. Int J Theor Phys 1:25

    Google Scholar 

  • Bertotti B, Less L, Tortora P (2003) A test of general relativity with radio links with the Cassini spacecraft. Nature 425:374

    Google Scholar 

  • Bhadra A, Sarkar K, Datta DP, Nandi KK (2007) Brans–Dicke theory: Jordan versus Einstein frame. Mod Phys Lett A 22:367

    Google Scholar 

  • Bilic N, Tupper GB, Viollier RD (2002) Dark matter, dark energy and the chaplygin gas. astro-ph/0207423

    Google Scholar 

  • Birrell ND, Davies PCW (1982) Quantum fields in curved space. Cambridge University Press, Cambridge

    Google Scholar 

  • Brans C, Dicke RH (1961) Mach’s principle and a relativistic theory of gravitation. Phys Rev 124:925

    Google Scholar 

  • Brax P, Bruck C, Davis AC, Khoury J, Weltman A (2004) Detecting dark energy in orbit: the cosmological chameleon. Phys Rev D 70:123518

    Google Scholar 

  • Brax P, Bruck C, Mota DF, Nunes NJ, Winther HA (2010) Chameleons with field dependent couplings. Phys Rev D 82:083503

    Google Scholar 

  • Briscese F, Elizalde E, Nojiri S, Odintsov SD (2007) Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity. Phys Lett B 646:105

    Google Scholar 

  • Brooker DJ, Odintsov SD, Woodard RP (2016) Precision predictions for the primordial power spectra from f (R) models of inflation. Nucl Phys B 911:318

    Google Scholar 

  • Cadarni N, Fabri R (1978) Production of entropy and viscous damping of anisotropy in homogeneous cosmological models - Bianchi type-I spaces. IL, Nuovo Cimento 44B:228

    Google Scholar 

  • Caldwell RR (2002) A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state. Phys Lett B 545:23

    Google Scholar 

  • Caldwell RR, Dave R, Steinhardt PJ (1998) Cosmological imprint of an energy component with general equation of state. Phys Rev Lett 80:1582

    Google Scholar 

  • Caldwell RR, Kamionkowski M, Weinberg NN (2003) Phantom energy and cosmic doomsday. Phys Rev Lett 91:071301

    Google Scholar 

  • Calvao MO, Lima JAS, Waga I (1992) On the thermodynamics of matter creation in cosmology. Phys Lett A 162:223

    Google Scholar 

  • Capozziello S, De Laurentis M (2011) Extended theories of gravity. Phys Rep 509:167

    Google Scholar 

  • Capozziello S, Nojiri S, Odintsov SD, Troisi A (2006) Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase. Phys Lett B 639:135

    Google Scholar 

  • Capozziello S, Martin-Moruno P, Rubano C (2010) Physical non-equivalence of the Jordan and Einstein frames. Phys Lett B 689:117

    Google Scholar 

  • Carroll SM, Sawicki I, Silvestri A, Trodden M (2006) Modified-source gravity and cosmological structure formation. New J Phys 8:323

    Google Scholar 

  • Chiba T, Okabe T, Yamaguchi M (2000) Kinetically driven quintessence. Phys Rev D 62:023511

    Google Scholar 

  • Choudhury TR, Padmanabhan T (2005) Cosmological parameters from supernova observations: a critical comparison of three data sets. Astron Astrophys 429:807

    Google Scholar 

  • Copeland EJ, Garousi MR, Sami M, Tsujikawa S (2005) What is needed of a tachyon if it is to be the dark energy? Phys Rev D 71:043003

    Google Scholar 

  • Debnath S, Sanyal AK (2011) Can particle creation phenomena replace dark energy? Class Quan Grav 28:145015

    Google Scholar 

  • Dick R (1998) Inequivalence of Jordan and Einstein frame: what is the low energy gravity In. string theory? Gen Rel Grav 30:435

    Google Scholar 

  • Dicke RH (1962a) Mach’s principle and invariance under transformation of units. Phys Rev 125:2163

    Google Scholar 

  • Dicke RH (1962b) Implications for cosmology of stellar and galactic evolution rates. Rev Mod Phys 34:110

    Google Scholar 

  • Dodelson S (2003) Modern Cosmology. Academic Press, San Francisco

    Google Scholar 

  • Dvali G, Turner MS (2003) Dark Energy as a modification of the Friedmann equation. astro-ph/0301510

    Google Scholar 

  • Dvali G, Gabadadze G, Porrati M (2000) 4D gravity on a brane in 5D Minkowski space. Phys Lett B 485:208

    Google Scholar 

  • Elizalde E, Nojiri S, Odintsov SD (2004) Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up. Phys Rev D 70:043539

    Google Scholar 

  • Ellis GFR (1971) Relativistic Cosmology, Rendicontidella Scuola Internazionale de Fisica “Enrico Fermi” XL VII, Corso

    Google Scholar 

  • Faraoni V, Gunzig E (1999) Einstein frame or Jordan frame? Int J Theor Phys 38:217

    Google Scholar 

  • Faraoni V, Gunzig E, Nardone P (1999) Conformal transformations in classical gravitational theories and in cosmology. Fund Cosmic Phys 20:121

    Google Scholar 

  • Flanagan EE (2004) Palatini form of 1/R gravity. Phys Rev Lett 92:071101

    Google Scholar 

  • Freedman WL et al (2001) Final results from the hubble space telescope key project to measure the hubble constant. Astrophys J 553:47

    Google Scholar 

  • Friedmann A (1922) On the curvature of space. Z Phys 10:377

    Google Scholar 

  • Friedmann A (1924) On the possibility of a world with constant negative curvature of space. Z Phys 21:326

    Google Scholar 

  • Frieman J, Hill C, Stebbins A, Waga I (1995) Cosmology with ultra-light pseudo-nambu-goldstone bosons. Phys Rev Lett 75:2077

    Google Scholar 

  • Garriga J, Mukhanov V (1999) Perturbations in k-inflation. Phys Lett B 458:219

    Google Scholar 

  • Gasperini M, Veneziano G (1993) Inflation deflation and frame-independence in string cosmology. Mod Phys Lett A 8:3701

    Google Scholar 

  • Gasperini M, Veneziano G (1994) Dilaton production in string cosmology. Phys Rev D 50:2519

    Google Scholar 

  • Gibbons GW (2002) Cosmological evolution of the rolling tachyon. Phys Lett B 537:1

    Google Scholar 

  • Gubser SS, Khoury J (2004) Scalar self-interactions loosen constraints from fifth force searches. Phys Rev D 70:104001

    Google Scholar 

  • Gunzig E, Geheniau J, Prigogine I (1987) Entropy and Cosmology. Nature 330:621

    Google Scholar 

  • Guo ZK, Zhang YZ (2004) Cosmological scaling solutions of multiple tachyon fields with inverse square potentials. JCAP 0408:010

    Google Scholar 

  • Guth AH (1981) Inflationary universe: a possible solution to the horizon and flatness problems. Phys Rev D 23:347

    Google Scholar 

  • Haouat S, Chekireb R (2011) On the creation of scalar particles in a flat Robertson-Walker spacetime. Mod Phys Lett A 26:2639

    Google Scholar 

  • Haouat S, Chekireb R (2012) Effect of electromagnetic fields on the creation of scalar particles in a flat Robertson–Walker space-time. EPJC 72:2034

    Google Scholar 

  • Hawking SW (1974) Black hole explosions? Nature 248:30

    Google Scholar 

  • Hawking SW (1975) Particle creation by black holes. Comm Math Phys 43:199

    Google Scholar 

  • Hawking SW, Ellis GFR (1973) The large-scale structure of space-time. Cambridge University Press

    Google Scholar 

  • Heller M, Suszycki L (1974) Dust-filled viscous universes. Acta Phys Pol B 5:345

    Google Scholar 

  • Heller M, Limek ZK, Suszycki L (1973) Imperfect fluid Friedmannian cosmology. Astrophys Space Sci 20:205

    Google Scholar 

  • Hubble EP (1929) A relation between distance and radial velocity among extra-galactic nebulae. Proc Natl Acad Sci 15:168

    Google Scholar 

  • Islam JN (2002) An introduction to mathematical cosmology. Cambridge University Press

    Google Scholar 

  • Ito Y, Nojiri S (2009) Gauss-Bonnet chameleon mechanism of dark energy. Phys Rev D 79:103008

    Google Scholar 

  • Jackiw R (2000) A particle field theorist’s lectures on supersymmetric, non-abelian fluid mechanics and d-branes. arXiv: physics/0010042

    Google Scholar 

  • Kamenshchik AY, Moschella U, Pasquier V (2001) An alternative to quintessence. Phys Lett B 511:265

    Google Scholar 

  • Kearns E, Kajita T, Totsuka Y (1999) Detecting massive neutrinos. Scientific American

    Google Scholar 

  • Khoury J, Weltman A (2004) Chameleon cosmology. Phys Rev D 69:044026

    Google Scholar 

  • Komatsu E et al (2011) Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation. Astrophys J Suppl Series 192:18

    Google Scholar 

  • La D, Steinhardt PJ (1989) Extended inflationary cosmology. Phys Rev Lett 62:376

    Google Scholar 

  • Landau LD, Lifshitz EM (1959) Fluid mechanics pergamon press

    Google Scholar 

  • Lemaître G (1927) Ann Sci Soc Brussels (in French) 47A:41

    Google Scholar 

  • Lemaître G (1931) Translated in English. Monthly Not Royal Astrono Soc 91:483

    Google Scholar 

  • Lima JAS, Germano ASM, Abramo LRW (1996) FRW-type cosmologies with adiabatic matter creation. Phys Rev D 53:4287

    Google Scholar 

  • Lima JAS, Silva FE, Santos RC (2008) Accelerating cold dark matter cosmology (ΩΛ≡ 0). Class Quan Grav 25:205006

    Google Scholar 

  • Linde AD (1982) A new inflationary universe scenario a possible solution of the horizon, flatness homogeneity, isotropy and primordial monopole problems. Phys Lett B 108:389

    Google Scholar 

  • Linde AD (1983) Chaotic Inflation. Phys Lett B 129:177

    Google Scholar 

  • Magnano G, Sokolowski LM (1994) On physical equivalence between nonlinear gravity. Theories and a general relativistic self gravitating scalar field. Phys Rev D 50:50395059

    Google Scholar 

  • Mathiazhagan C, Johri VB (1984) An inflationary universe in Brans-Dicke theory: a hopeful sign of theoretical estimation of the gravitational constant. Class Quant Grav 1:L29

    Google Scholar 

  • Misner CW (1984) Neutrino viscosity and the isotropy of primordial blackbody radiation (1967) Phys Rev lett 19:533

    Google Scholar 

  • Mukhanov VF, Winitzki S (2007) Introduction to quantum fields in gravity. Cambridge: Cambridge University Press

    Google Scholar 

  • Mukhanov VF, Feldman HA, Brandenberger RH (1992) Theory of cosmological perturbations. Phys Rep 215:203

    Google Scholar 

  • Murphy GL (1973) Big-bang model without singularities. Phys Rev D 8(12):4231

    Google Scholar 

  • Narlikar JV (1983) Introduction to cosmology. Cambridge University Press

    Google Scholar 

  • NESTOR collaboration (1994) NESTOR: a neutrino particle astrophysics underwater laboratory for the Mediterranean Author links open overlay panel. Nucl Phys B 35:294

    Google Scholar 

  • Nightingale JD (1973) Independent investigations concerning bulk viscosity in relativistic homogeneous isotropic cosmologies. Astrphys J 185:105

    Google Scholar 

  • Nojiri S, Odintsov SD (2006) Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe. Phys Rev D 74:086005

    Google Scholar 

  • Nojiri S, Odintsov SD (2011) Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models. Phys Rep 505:59

    Google Scholar 

  • Nosengo N (2012) Gran Sasso: Chamber of physics. Nature 485:435

    Google Scholar 

  • Padmanabhan T (2002) Accelerated expansion of the universe driven by tachyonic matter. Phys Rev D 66:021301

    Google Scholar 

  • Papastamatiou J, Parker L (1979) Asymmetric creation of matter and antimatter in the expanding universe. Phys Rev D 19:2283

    Google Scholar 

  • Parker L (1968) Particle creation in expanding universes. Phys Rev Lett 21:562

    Google Scholar 

  • Parker L (1969) Quantized fields and particle creation in expanding universes. I. Phys Rev 183:1057

    Google Scholar 

  • Parker L (1971) Quantized fields and particle creation in expanding universes. II. Phys Rev D 3:346

    Google Scholar 

  • Peebles PJE (1980) The large scale structure of the universe. Princeton University Press

    Google Scholar 

  • Peebles PJE (1993) Principles of physical cosmology. Princeton University Press

    Google Scholar 

  • Peebles PJE, Ratra B (1988) Cosmology with a time-variable cosmological ‘constant’. Ap J Lett 325:L17

    Google Scholar 

  • Penzias AA, Wilson RW (1965) A measurement of excess antenna temperature at 4080 Mc/s. Astrophys J 142:419

    Google Scholar 

  • Perlmutter S et al (1999) Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys J 517:565

    Google Scholar 

  • Planck collaboration (2014) Planck 2013 results-I. Overview of products and scientific results.Astron Astrophys 571:A1

    Google Scholar 

  • Planck collaboration P. A. R. Ade (2016) Planck 2015 results-XIII. Cosmological parameters. Astron Astrophys 594:A20

    Google Scholar 

  • Prigogine I (1989) Thermodynamics and cosmology. Int J Theor Phys 28:927

    Google Scholar 

  • Prigogine I, Geheniau J, Gunzig E, Nardone P (1989) Thermodynamics and cosmology. Gen Rel Grav 21:767

    Google Scholar 

  • Ratra B, Peebles PJE (1988) Cosmological consequences of a rolling homogeneous scalar field. Phys Rev D 37:3406

    Google Scholar 

  • Reiss AG et al (2011) A 3% Solution: determination of the hubble constant with the hubble space telescope and wide field camera 3. Astrophys J 730:119

    Google Scholar 

  • Ribeiro MB, Sanyal AK (1987) Bianchi VI0 viscous fluid cosmology with magnetic field. J Math Phys 28:657

    Google Scholar 

  • Riess AG et al (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116:1009

    Google Scholar 

  • Sachs RK, Wolfe AM (1967) Perturbations of a cosmological model and angular variations of the microwave background. Astrophys J 147:73

    Google Scholar 

  • Sahni V, Shtanov Y (2003) Braneworld models of dark energy. JCAP 0311:014

    Google Scholar 

  • Sanyal AK (2007) If Gauss-Bonnet interaction plays the role of dark energy. Phys Lett B 645:1

    Google Scholar 

  • Sanyal AK (2008) Intermediate inflation or late time acceleration? Adv High Energy Phys 2008:630414

    Google Scholar 

  • Sanyal AK (2009a) Smooth crossing of ωΛ = −1 line in a single scalar field model. Adv High Energy Phys 2009:612063

    Google Scholar 

  • Sanyal AK (2009b) Transient crossing of phantom divide line ωΛ = −1 under Gauss-Bonnet interaction. Gen Rel Grav 41:1511

    Google Scholar 

  • Sen A (2002a) Rolling Tachyon. JHEP 0204:048

    Google Scholar 

  • Sen A (2002b) Tachyon Matter. JHEP 0207:065

    Google Scholar 

  • Sk N, Sanyal AK (2017) Why scalar-tensor equivalent theories are not physically equivalent? IJMPD 26:1750162

    Google Scholar 

  • Soussa ME, Woodard RP (2004) The force of gravity from a lagrangian containing inverse powers of the ricci scalar. Gen Rel Grav 36:855

    Google Scholar 

  • Spergel DN et al (2007) Wilkinson Microwave Anisotropy Probe (WMAP) Three year results: implications for cosmology. Astrophys J suppl 170:377

    Google Scholar 

  • Spindel P (1981) Mass formula in a cosmogenesis model. Phys Lett 107:361

    Google Scholar 

  • Starobinsky AA (1980) A new type of isotropic cosmological models without singularity. Phys Lett B 91:99

    Google Scholar 

  • Steigman G, Santos RC, Lima JAS (2009) An accelerating cosmology without dark energy. J Cosmol Astropart Phys JCAP06:33

    Google Scholar 

  • Steinhardt PJ, Accetta FS (1990) Hyperextended inflation. Phys Rev Lett 64:2740

    Google Scholar 

  • Treciokas R, Ellis GFR (1971) Isotropic solutions of the Einstein-Boltzmann equations. Comm Math Phys 23:1

    Google Scholar 

  • Tsujikawa S, Tamaki T, Tavakol R (2009) Chameleon scalar fields in relativistic gravitational backgrounds. JCAP 0905:020

    Google Scholar 

  • Vollick DN (2003) 1/R curvature corrections as the source of the cosmological acceleration. Phys Rev D 68:063510

    Google Scholar 

  • Vollick DN (2004) On the viability of the Palatini form of 1/R gravity. Class Quant Grav 21:3813

    Google Scholar 

  • Wagner RV (1970) Scalar-tensor theory and gravitational waves. Phys Rev D 1:3209

    Google Scholar 

  • Weinberg S (1971) Entropy generation and the survival of protogalaxies in an expanding universe. Astrophys J 168:175

    Google Scholar 

  • Weinberg S (1972) Gravitation and cosmology. Wiley, New York

    Google Scholar 

  • Zimdahl W, Pavón D (1993) Cosmology with adiabatic matter creation. Phys Lett A 176:57

    Google Scholar 

  • Zimdahl W, Triginer J, Pavón D (1996) Collisional equilibrium, particle production, and the inflationary universe. Phys Rev D 54:6101

    Google Scholar 

  • Zlatev I, Wang LM, Steinhardt PJ (1999) Quintessence, cosmic coincidence, and the cosmological constant. Phys Rev Lett 82:896

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abhik Kumar Sanyal .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sanyal, A.K., Debnath, S. (2018). Thermodynamics of Irreversible Particle Creation Phenomena and Its Cosmological Consequence. In: Driss, Z., Necib, B., Zhang, HC. (eds) Thermo-Mechanics Applications and Engineering Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-70957-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70957-4_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70956-7

  • Online ISBN: 978-3-319-70957-4

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics