## Research Interests

- Mathematical modeling of earthquake fault mechanics
- Dynamic rupture along and crossing with a material interface
- Earthquake energy estimation based on inversion analyses
- Determination mechanisms of rupture velocity
- Unilateral rupture along very long reverse faults
- Slip/stress heterogeneity and foreshock-mainshock-aftershock sequences
- Source time functions based on a stochastic differential equation
- Seismicity data analysis
- Objective threshold determination of a matched-filter technique for seismic event detection based on the extreme value theory and an information criterion
- Seismic event-pair detection by similarity thresholding.
- Laboratory seismology
- Elastodynamics and rheorogy of sand after strong vibration or water injection
- Dynamic opening/shear rupture in a photoelastic medium

## Academic Positions & Education

- Assistant professor, Apr. 2015 -- present
- Department of Physical Science, College of Science and Engineering, Ritsumeikan University, Japan
- Teaching Earth Science/Laboratory Works in Earth Science
- Postdoctoral fellow, Oct. 2013 -- Mar. 2015
- Mega Quake Risk Management Project / Faculty of Engineering, Information and Systems, Tsukuba University, Japan
- PhD course, Apr. 2009 -- Sep. 2013
- Earthquake Research Institute / Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Japan
- supervised by Teruo Yamashita and Nobuki Kame
- Internship, Jul. 2011 -- Aug. 2011
- School of Engineering and Applied Science, Harvard University, U.S.
- research assistant of James R. Rice
- Master's course, Apr. 2007 -- Mar. 2009
- Earthquake Research Institute / Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Japan
- supervised by Teruo Yamashita
- Undergraduate course, Apr. 2003 -- Mar. 2007
- Department of Mathematics, Faculty of Science, Tokyo University of Science, Japan
- supervised by Keiichi Kato

## Publications

### Submitted manuscripts

- Ohara, K., Yagi, Y., Yamashita, S., Okuwaki, R., Hirano, S., & Fukahata, Y. (under review)
- Complex evolution of the 2016 Kaikoura earthquake revealed by teleseismic body waves
- submitted to
*Geophys. J. int.* *EarthArXiv*, doi:10.31223/X55936

### Peer-reviewed journal papers

- Hirano, S., Kawakata, H. & Doi, I. (2022)
- A matched-filter technique with an objective threshold
*Scientific Reports*,**12**:25839, doi:10.1038/s41598-022-25839-2- 大嵜雅人, 吉光奈奈, 平野史朗, 福山英一 (EN: Osaki, M., Yoshimitsu, N., Hirano, S., & Fukuyama, E.) (2022)
- 注水による誘発地震発生場を模擬した寒天ゲルを用いた光弾性実験手法 (EN: Photoelastic experimental approach using agar gel to simulate a stress field of fluid injection induced earthquakes)
*地震 第2輯 (Zisin: Journal of Seismological Society of Japan)*,**75**:83--91, doi:10.4294/zisin.2021-17 (Japanese text with English abstract.)- Hirano, S. (2022)
- Source time functions of earthquakes based on a stochastic differential equation
*Scientific Reports*,**12**:3936, doi:10.1038/s41598-022-07873-2- Numerical results in an ascii format:
*OSF*: Open Science Framework, doi:10.17605/OSF.IO/VUXJ6 - Nakayama, M., Kawakata, H., Hirano, S., & Doi, I. (2021)
- Development of a laboratory monitoring system for elastic waves transmitted through sand under dry and saturated conditions
*Earth Planet Space*,**73**(25), doi:10.1186/s40623-020-01346-4- Hirano, S., & Itou, H. (2020)
- Parameter interdependence of dynamic self-similar crack with distance-weakening friction
*Geophys. J. Int.*,**223**(3):1584--1596, doi:10.1093/gji/ggaa392-
## Erratum

eq. (7) must be $L(x) = \displaystyle \log\left|\frac{1-x}{1+x}\right|$ (absolute value symbol was missing)

$\Delta \sigma_b$ in eqs.(C1)(C5)(C6)(C7) and next line to eq.(C9) must be $\sigma_b$.

- Okuwaki, R., Hirano, S., Yagi, Y., & Shimizu, K. (2020)
- Inchworm-like source evolution through a geometrically complex fault fueled persistent supershear rupture during the 2018 Palu Indonesia earthquake
*Earth Planet. Sci. Lett.*,**547**(2020):116449, doi:10.1016/j.epsl.2020.116449*EarthArXiv Preprints*, doi:10.31223/osf.io/j4cas*OSF*: Open Science Framework, doi:10.17605/OSF.IO/8AZ3G- Hirano, S. (2019)
- Modeling of unilateral rupture along very-long reverse faults
*J. Geophys. Res.*,**124**(1):1057--1071, doi:10.1029/2018JB016511.- Okuwaki, R., Kasahara, A., Yagi, Y., Hirano, S. & Fukahata, Y. (2019)
- Backprojection to image slip
*Geophys. J. Int.*,**216**(3):1529--1537, doi:10.1093/gji/ggy505.- Tamaribuchi, K., Yagi, Y., Enescu, B. & Hirano, S. (2018)
- Characteristics of foreshock and aftershock activity inferred from the JMA earthquake catalog improved by automatic processing
*Earth Planet Space*,**70**:90, doi:10.1186/s40623-018-0866-9.- Hirano, S. & Yagi, Y. (2017)
- Dependence of seismic and radiated energy on shorter wavelength components
*Geophys. J. Int.*,**209**(3):1585--1592, doi:10.1093/gji/ggx108.- Hirano, S. & Yamashita, T. (2016)
- Modeling of interfacial dynamic slip pulses with slip-weakening friction
*Bull. Seism. Soc. Am.***106**(4):1628--1636, doi: 10.1785/0120150208.## Erratum

$\displaystyle \frac{1}{1+S}$ in eqs. (19)(20)(22) must be $\displaystyle - \frac{1}{1+S}$ (minus sign was missing)

- Self archive of a pre-copyedit version
- Hirano, S. & Yamashita, T. (2015)
- Dynamic anti-plane rupture propagation crossing a material interface: modelling with BIEM
*Geophys. J. Int.***200**(2):1220--1233, doi:10.1093/gji/ggu471.## Erratum

eq. (26) must be $\Psi_l(X) = \displaystyle \sqrt{X^2-\beta_l^{-2}} \arctan{\frac{\eta_l}{\sqrt{X^2-\beta_l^{-2}}}} - \eta_l$ (subscript $l$ of $\beta$ was missing)

- Okuwaki, R., Yagi, Y. & Hirano, S. (2014)
- Relationship between High-frequency Radiation and Asperity Ruptures, Revealed by Hybrid Back-projection with a Non-planar Fault Model
*Scientific Reports,***4**:7120, doi:10.1038/srep07120.- Yagi, Y., Okuwaki, R., Enescu, B., Hirano, S., Yamagami, Y., Endo, S. & Komoro, T. (2014)
- Rupture process of the 2014 Iquique Chile earthquake in relation with the foreshock activity
*Geophys. Res. Lett.,***41**(12):4201--4206, doi: 10.1002/2014GL060274.- Hirano, S. & Yamashita, T. (2011)
- Analysis of the static stress field around faults lying along and intersecting a bimaterial interface
*Geophys. J. Int.***187**(3):1460--1478, doi:10.1111/j.1365-246X.2011.05202.x.

### Peer-reviewed proceeding papers

- Hirano, S. (accepted)
- Résumé: Energy estimation of earthquake faulting processes
*Singularity and asymptotic behavior of solutions for partial differential equations with conservation law: RIMS Kôkyûroku Bessatsu.*- Self archive of a pre-copyedit version
- Hirano, S. (2020)
- Friction vs. damage: dynamic self-similar crack growth revisited
- In: Itou, H. et al. (eds)
*Mathematical Analysis of Continuum Mechanics and Industrial Applications III. CoMFoS18*. Mathematics for Industry, Springer, doi:10.1007/978-981-15-6062-0_12 - Self archive of a pre-copyedit version
- Nakayama, M., Kawakata, H., Hirano, S., Doi, I., & Takahashi, N. (2018)
- Propagation characteristics of elastic waves transmitted through sand soils under dry and saturated conditions
*Progress in Acoustic Emission XIX, Jpn. Soc. Non-Destructive Inspection*, 163--167.- Hirano, S. (2018)
- Integral representation and its applications in earthquake mechanics: a review
- In: van Meurs, P. et al. (eds)
*Mathematical Analysis of Continuum Mechanics and Industrial Applications II. CoMFoS 2016*. Mathematics for Industry, vol 30. Springer, Singapore, doi:10.1007/978-981-10-6283-4_9. - Self archive of a pre-copyedit version
- Hirano, S. (2017)
- Propagation velocity of pulse-like rupture along earthquake faults
- In: Itou, H. et al. (eds)
*Mathematical Analysis of Continuum Mechanics and Industrial Applications*. Mathematics for Industry, vol 26. Springer, Singapore, doi:10.1007/978-981-10-2633-1_10. - Self archive of a pre-copyedit version

### Book

- Itou, H., Hirano, S., Kimura, M., Kovtunenko, V.A., & Khludnev, A.M. (Eds.) (2020)
*Mathematical Analysis of Continuum Mechanics and Industrial Applications III. CoMFoS18*. Mathematics for Industry, Springer, doi:10.1007/978-981-15-6062-0

### Misc.

- Hirano, S., & Okuwaki, R. (2020)
- Note on “Backprojection to image slip”
*OSF*: Open Science Framework, doi:10.17605/OSF.IO/PB7HK- Endo, S., Nakao, A., Hirano, S. & Yagi, Y. (2017)
- The 2013 Sea of Okhotsk deep earthquake: A complex rupture within the Ringwoodite stability zone
*Earth Evol. Sci.*,**11**:23--30.- 桑野修, 平野史朗, 藤田哲史, 日下部哲也, 小寺祐貴, 亀伸樹, 中谷正生, 安藤亮輔 (2011)
- 寒天（アガロースゲル）を用いた断層の動的破壊実験
- 日本地震学会ニュースレター Vol.22 No.6, 表紙

## International Conferences

- Hirano, S.
- Statistics and variability of source time functions based on a stochastic differential equation
- American Geophysical Union 2021 Fall Meeting, New Orleans and Online, December, 2021
- Okuwaki, R., Yagi, Y., Shimizu, K., Fukahata, Y., Hirano, S., Hicks, S.P., Craig, T.J., Fan, W., Goes, S.D.B., and Wright, T.J.
- Accounting epistemic uncertainty in finite-fault inversion: development of a potency-density tensor approach to investigate complex earthquake rupture processes
- American Geophysical Union 2021 Fall Meeting, New Orleans and Online, December, 2021 (Oral, Invited)
- Hirano, S.
- Various inverse problems in seismology: seismic tomography, hypocenter location, earthquake source kinematics, and Earth's crustal stress.
- Control and inverse problems on waves, oscillations and flows - Mathematical analysis and computational methods -, Online, September, 2021 (Oral)
- Hirano, S.
- Theoretical properties of source time functions based on a stochastic differential equation
- Joint Scientific Assembly IAGA-IASPEI 2021, Online, August 26, 2021 (Flash talk & Poster)
- Okuwaki, R., Hirano, S., Yagi, Y., & Shimizu, K.
- Source evolution through a geometrically complex fault system controls supershear rupture during the 2018 Palu earthquake
- FRINGE 2021 (Advances in the Science and Applications of SAR Interferometry and Sentinel-1 InSAR), Online, May 31--June 04, 2021 (Oral)
- Hirano, S., & Itou, H.
- Dynamic antiplane self-similar crack with distance-weakening friction: an analytical solution for source parameter estimation
- American Geophysical Union 2020 Fall Meeting, Online, December 16, 2020 (Flash talk & Poster)
- Go to the poster page.
- Hirano, S.
- An empirical PDE for slip along earthquake faults
- The Second Russia-Japan Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications" - 20th Conference of Continuum Mechanics Focusing on Singularities (CoMFoS20), Online, December 15, 2020 (Oral)
- Hirano, S.
- A nonlinear integro-differential equation for earthquake faulting
- RIMS Workshop on Analysis of inverse problems through partial differential equations and related topics, Kyoto, Japan, January 09, 2020 (Oral)
- Hirano, S.
- An observation-based differential equation of spatio-temporal slip distribution
- American Geophysical Union 2019 Fall Meeting, San Francisco, U.S., December 13, 2019 (Poster)
- Kakutani, T., Kawakata, H., & Hirano, S.
- Seismic response change of a sand soil after strong motion, revealed by a transmission laboratory experiment
- American Geophysical Union 2019 Fall Meeting, San Francisco, U.S., December 11, 2019 (Poster)
- Nakayama, M., Kawakata, H., Hirano, S., & Doi, I.
- Propagation characteristic changes of elastic waves transmitted through a sand soil in water injection and drainage processes
- American Geophysical Union 2019 Fall Meeting, San Francisco, U.S., December 10, 2019 (Poster)
- Hirano, S.
- Dynamic growth of a self-similar anti-plane crack during earthquakes
- Russia-Japan Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications", Novosibirsk, Russia, November 12, 2019 (Oral)
- Hirano, S.
- Energy dissipation during dynamic antiplane self-similar crack growth
- CoMFoS19:Mathematical Analysis of Continuum Mechanics and Industrial Applications, Kanazawa, Japan, July 15, 2019 (Oral)
- Hirano, S.
- Analytical solution of dynamic self-similar crack growth under distance-weakening friction
- Numerical Modeling of Earthquake Motions: Waves and Ruptures, Smolenice, Slovakia, July 01--03, 2019 (Poster)
- Hirano, S., Kawakata, H., & Doi, I.
- Foreshock activity detection by a threshold-free matched-filter technique
- Japan Geoscience Union Meeting, Chiba, Japan, May 26, 2019 (Oral)
- Hirano, S.
- Aftershocks and the GR law due to a heterogeneous slip model
- American Geophysical Union 2018 Fall Meeting, Washington D.C., U.S., December 14, 2018 (Oral)
- Nakayama, M., Kawakata, H., Hirano, S., Doi, I., & Takahashi, N.
- 24-hours broadband measurements of elastic waves transmitted through sand soils under dry and saturated conditions to investigate differences in propagation characteristics
- American Geophysical Union 2018 Fall Meeting, Washington D.C., U.S., December 10, 2018 (Poster)
- Nakayama, M., Kawakata, H., Hirano, S., Doi, I., & Takahashi, N.
- Propagation characteristics of elastic waves transmitted through sand soils under dry and saturated conditions
- 24th International Acoustic Emission Symposium, Sapporo, Japan, November 07, 2018 (Oral)
- Hirano, S., Toyomoto, Y., Kawakata, H., & Doi, I.
- Application of Extreme Value Theory to a Matched-Filter Analysis
- 10th ACES International Workshop, Awaji Island, Japan, September 27, 2018 (Poster)
- Hirano, S.
- Friction vs. damage: dynamic self-similar crack growth revisited
- CoMFoS18:Mathematical Analysis of Continuum Mechanics and Industrial Applications, Kyoto, Japan, June 13, 2018 (Oral)
- Hirano, S., Toyomoto, Y., Kawakata, H. & Doi, I.
- Objective matched-filter analysis for dertecting small events
- International Symposium on Earthquake Forecast / 5th International Workshop on Earthquake Preparation Process, ~Observation, Validation, Modeling, Forecasting~, Chiba, Japan, May 25, 2018 (Poster)
- Wakamatsu, S., Kawakata, H. & Hirano, S.
- Observed seismic and infrasonic signals around the Hakone volcano -Discussion based on a finite-difference calculation-
- American Geophysical Union 2017 Fall Meeting, New Orleans, U.S., December 15, 2017 (Poster)
- Hirano, S.
- Mathematical modeling and numerical simulation of unilateral dynamic rupture propagation along very-long reverse faults
- American Geophysical Union 2017 Fall Meeting, New Orleans, U.S., December 14, 2017 (Poster)
- Nakayama, M., Kawakata, H., Hirano, S., Doi, I. & Takahashi, N.
- Improvement in transmission experiment of elastic waves through partially saturated porous sand soil
- American Geophysical Union 2017 Fall Meeting, New Orleans, U.S., December 14, 2017 (Poster)
- Yoneda, N., Kawakata, H., Hirano, S., Yoshimitsu, N. & Takahashi, N.
- Extraction of AE events to estimate their b values under a triaxial compressive condition ~Examination using continuous broadband records~
- American Geophysical Union 2017 Fall Meeting, New Orleans, U.S., December 14, 2017 (Poster)
- Hirano, S.
- Unilateral dynamic rupture propagation along earthquake faults
- CoMFoS17:Mathematical Analysis of Continuum Mechanics and Industrial Applications, OIST, Japan, September 21, 2017 (Oral)
- Hirano, S.
- Energy estimation of earthquake faulting based on a wavefield inversion
- RIMS workshop on "Singularity and asymptotic behavior of solutions for partial differential equations with conservation law", Kyoto, Japan, June 08, 2017 (Oral)
- Hirano, S.
- Integral equation for mechanics of earthquakes
- RIMS workshop on "Inverse problems for partial differential equations and related areas", Kyoto, Japan, January 26, 2017 (Oral)
- Nakayama, M., Kawakata, H., Hirano, S., Doi, I., & Takahashi, N.
- Transmission experiment of elastic waves with short wavelengths through a highly porous sand soil during water injection
- American Geophysical Union 2016 Fall Meeting, San Francisco, U.S., December 15, 2016 (Poster)
- Toyomoto, Y., Kawakata, H., Hirano, S. & Doi, I.
- Foreshock search over a long duration using a method of setting appropriate criteria
- American Geophysical Union 2016 Fall Meeting, San Francisco, U.S., December 15, 2016 (Poster)
- Tsujimura, Y., Kawakata, H., Fukuyama, E., Yamashita, F., Xu, S., Mizoguchi, K, Takizawa, S. & Hirano, S.
- Spatio-temporal foreshock activity during stick-slip experiments of large rock samples
- American Geophysical Union 2016 Fall Meeting, San Francisco, U.S., December 13, 2016 (Poster)
- Hirano, S., Yamashita, T. & Hatano, T.
- Behavior of pulse-like rupture with velocity-time-dependent friction from a granular layer model
- American Geophysical Union 2016 Fall Meeting, San Francisco, U.S., December 12, 2016 (Oral)
- Hirano, S.
- Integral representation and its applications of the mechanics of earthquakes
- CoMFoS16:Mathematical Analysis of Continuum Mechanics and Industrial Applications, Kyushu University, Japan, October 23, 2016 (Oral)
- Hirano, S. & Yamashita, T.
- Propagation velocity of pulse-like rupture with a time-weakening friction law
- American Geophysical Union 2015 Fall Meeting, San Francisco, U.S., December 18, 2015 (Poster)
- Iwata, K., Kawakata, H., Hirano, S., & Doi, I.
- Estimation of Seismic Attenuation beneath Tateyama Volcano, Central Japan by Using Peak Delay
- American Geophysical Union 2015 Fall Meeting, San Francisco, U.S., December 17, 2015 (Poster)
- Imahori, A., Kawakata, H., Hirano, S., Yoshimitsu, N., & Takahashi, N.
- Travel Times of Later Phases for Transmitting Waves through a Fracturing Westerly Granite Sample under a Triaxial Compressive Condition
- American Geophysical Union 2015 Fall Meeting, San Francisco, U.S., December 16, 2015 (Poster)
- Hirano, S.
- Propagation velocity of pulse-like rupture along earthquake fault
- CoMFoS15:Mathematical Analysis of Continuum Mechanics and Industrial Applications, Kyushu University, Japan, November 16, 2015 (Oral)
- Hirano, S. & Yagi, Y.
- Dependence of seismic energy on higher wavenumber components
- American Geophysical Union 2014 Fall Meeting, San Francisco, U.S., December 19, 2014 (Poster)
- Yagi, Y., Okuwaki, R., Enescu, B. & Hirano, S.
- Rupture process of the 2014 Iquique Chile earthquake in relation with the foreshock activity
- American Geophysical Union 2014 Fall Meeting, San Francisco, U.S., December 17, 2014 (Poster)
- Okuwaki, R., Yagi, Y. & Hirano, S.
- Relationship between High-frequency Radiation and Asperity Rupture，Revealed by Hybrid Back-projection with Non-planer Fault
- Seismological Society of America Annual Meeting, Anchorage, U.S., May 01, 2014 (Poster)
- Hirano, S. & Yamashita, T.
- BIEM Simulation for Anti-Plane Dynamic Rupture Propagation across a Bimaterial Interface
- Seismological Society of America Annual Meeting, Anchorage, U.S., April 30, 2014 (Oral)
- Hirano, S.
- An integral representation and numerical simulation of dynamic earthquake faulting occurring in a two-layered medium
- Conference on Diffusion in Heterogeneous Media and Related Topics, Tokyo, Japan, March 06, 2014 (Oral)
- Hirano, S. & Yamashita, T.
- Off Fault Stress Distribution around Dynamic Slip Pulse on a Bimaterial Interface
- The 7th ACES International Workshop, Otaru, Japan, October 04, 2010 (Poster)
- Hirano, S. & Yamashita, T.
- Theoretical analysis of static mode-II crack in two-layered medium - interfacial fault and intersecting fault
- Workshop -Earthquake Source Dynamics: Data and Data-constrained Numerical Modeling, Smolenice Castle, Slovakia, June 28, 2010 (Poster)
- Hirano, S. & Yamashita, T.
- Mathematical and numerical analysis of non-planar static mode-II crack in a two-layered medium
- American Geophysical Union 2009 Fall meeting, San Francisco, U.S., December 17, 2009 (Poster)
- Hirano, S. & Yamashita, T.
- Mathematical and numerical analyses of arbitrarily oriented static mode-II crack in a two-layered medium
- The 7th General Assembly of Asian Seismological Commission and The 2008 Fall meeting of Seismological Society of Japan, Tsukuba, Japan, November 27, 2008 (Poster)

## Award & Grants

- Mar. 2019
- The Young Scientist Award of Seismological Society of Japan for
*Extention of Mathematical Seismology* - Apr. 2022 -- Mar. 2025
- Growth and termination of dynamic rupture revealed by a stochastic fault model
- The JSPS Grant-in-Aid for Scientific Research(C) Program No. 22K03782
- Principal Investigator
- Apr. 2022 -- Mar. 2025
- Elastodynamics for strongly heterogeneous material: experiment, numerical simulation, and theory
- The JSPS Grant-in-Aid for Scientific Research(B) Program No. 22H01336
- Co-Investigator (PI: Kawakata, H., Ritsumeikan Uviv.)
- Apr. 2021 -- Mar. 2024
- Understanding the physics of foreshocks based on dense seismic observation and seismicity model
- The JSPS Grant-in-Aid for Scientific Research(B) Program No. 21H01191
- Co-Investigator (PI: Naoi, M., Kyoto Univ.)
- Apr. 2018 -- Mar. 2022
- SDE modeling for diversity and heterogeneity of earthquake ruptures
- The JSPS Grant-in-Aid for Early-Career Scientists Program No. 18K13637
- Principal Investigator
- Apr. 2017 -- Mar. 2021
- Mathematical modeling and analysis of discontinuous phenomena in continuum body
- The JSPS Grant-in-Aid for Scientific Research(B) Program No. 17H02857
- Co-Investigator (PI: Kimura, M., Kanazawa Univ.)

### Award

### Grants

## Contributions

- Journal Reviewer
- Bulletin of Seismological Society of America
- Computers and Mathematics with Applications
- Earth Planets Space
- European Journal of Environmental and Civil Engineering
- Geophysical Journal International
- Journal of Geophysical Research: Solid Earth
- Journal of Japan Association for Earthquake Engineering
- Tectonophysics
- Grant Reviewer
- Israel Science Foundation
- Conference Management
- Program committee for The 10th International Congress on Industrial and Applied Mathematics. Waseda University, Tokyo, Japan, August 20-25, 2023
- Organizing committee for CoMFoS18:Mathematical Analysis of Continuum Mechanics and Industrial Applications, Kyoto, Japan, June 13--15, 2018
- Projects
- Earthquake and Volcano Hazards Observation and Research Program (Co-investigator, 2015-)
- Mega Quake Risk Management project at University of Tsukuba (Postdoctoral fellow, 2013-2014)
- AE measurements in deep South African gold mines: Phase II - monitoring of rock mass damage by underground cavities and prediction of rockbursts (Research assistant, 2009-2011)

## Scientific Societies

- Geophysics
- American Geophysical Union
- Seismological Society of America
- Japan Geoscience Union
- Seismological Society of Japan
- Applied Mathematics
- The Japan Society for Industrial and Applied Mathematics (secretary of a research group Mathematical Aspects of Continuum Mechanics)