Qiita Teams that are logged in
You are not logged in to any team

Log in to Qiita Team
Community
OrganizationEventAdvent CalendarQiitadon (β)
Service
Qiita JobsQiita ZineQiita Blog
3
Help us understand the problem. What are the problem?
@kaizen_nagoya

計算物理学 Rubin H. Landau 参考文献・docker登録。docker(52)

計算物理学 Rubin H. Landau , Manuel Jos´e P´aez Mej´ia
51JDSZN5Z6L._SX329_BO1,204,203,200_.jpg
https://www.amazon.co.jp/dp/product/4254130864/

http://www.physics.orst.edu/`rubin/CPbook/PROGS

Computational Physics problem solving with computers 2nd Contents(目次)
https://www.researchgate.net/publication/204752438_Computational_Physics_Problem_Solving_with_Computers_2nd

実行

3分類。

1)PythonCodes
2)HPCodes
3)Animations

2) HPCodes

7 モンテカルロ法の応用

7.10 手法:フォンノイマンの棄却法 pond.c

docker/ubuntu
# cd /home/cp/HCPcodes
# clang pond.c -o pond
pond.c:19:1: warning: type specifier missing, defaults to 'int' [-Wimplicit-int]
main()  {
^
1 warning generated.
# ./pond
data stored in pond.dat
# cat pond.dat
1   4.000000
2   4.000000
...
998 3.130261
999 3.131131
1000    3.132000

19 ハイパフォーマンス・コンピューティング:プロファイリングとチューニング

高効率計算:横顔と調律

19.3 チューニング前のプログラム tune.f
19.5 基本的な最適化 tune1.f
19.6 ベクトルチューニング tune2.f
19.7 RISC上でのベクトルコード tune3.f
19.8 スーパースカラーチューニング tune4.f

docker/ubuntu
# cd /home/cp/HPCodes
# gfortran tune1.f -o tune1
# gfortran tune2.f -o tune2
# gfortran tune3.f95 -o tune3
# gfortran tune4.f95 -o tune4
# ./tune1
  1   1.00000   0.30350   1.00000
  2   0.92179   0.05728   0.95690
  3   0.91720   0.01562   0.96664
  4   0.91691   0.00402   0.96348
  5   0.91688   0.00116   0.96414
  6   0.91688   0.00031   0.96391
  7   0.91688   0.00009   0.96397
  8   0.91688   0.00002   0.96395
  9   0.91688   0.00001   0.96395
 10   0.91688   0.00000   0.96395
 11   0.91688   0.00000   0.96395
# ./tune2
  1   1.00000   0.30350   1.00000
  2   0.92179   0.05728   0.95690
  3   0.91720   0.01562   0.96664
  4   0.91691   0.00402   0.96348
  5   0.91688   0.00116   0.96414
  6   0.91688   0.00031   0.96391
  7   0.91688   0.00009   0.96397
  8   0.91688   0.00002   0.96395
  9   0.91688   0.00001   0.96395
 10   0.91688   0.00000   0.96395
 11   0.91688   0.00000   0.96395
# ./tune3
  1   1.00000   0.30350   1.00000
  2   0.92179   0.05728   0.95690
  3   0.91720   0.01562   0.96664
  4   0.91691   0.00402   0.96348
  5   0.91688   0.00116   0.96414
  6   0.91688   0.00031   0.96391
  7   0.91688   0.00009   0.96397
  8   0.91688   0.00002   0.96395
  9   0.91688   0.00001   0.96395
 10   0.91688   0.00000   0.96395
 11   0.91688   0.00000   0.96395
# ./tune4
  1   1.30000   0.43195   1.00000
  2   0.25846   0.25262   0.91802
  3   0.91078   0.12232   0.98690
  4   0.60074   0.07103   0.96267
  5   0.78326   0.03775   0.97875
  6   0.68699   0.02114   0.97091
  7   0.74112   0.01151   0.97550
  8   0.71171   0.00637   0.97306
  9   0.72800   0.00349   0.97443
 10   0.71908   0.00192   0.97368
 11   0.72400   0.00106   0.97409
 12   0.72129   0.00058   0.97387
 13   0.72278   0.00032   0.97399
 14   0.72196   0.00018   0.97393
 15   0.72241   0.00010   0.97396

25 静電ポテンシャル

25.6 格子上の解 laplace.c(.f)

docker/ubuntu
# cd /home/cp/HPCodes
# gcc laplace.c -o laplacec
# ./laplacec
data stored in laplace.dat
# cp laplace.dat laplacec.dat
# gfortran laplace.f -o laplacef
# ./laplacef
Note: The following floating-point exceptions are signalling: IEEE_DENORMAL
STOP data saved in laplace.dat
# cp laplace.dat laplacef.dat
# cat laplacec.dat
100.000000
0.000000
...
100.000000
49.927579
30.090184
20.722835
..
100.000000
69.620142
49.710342
37.238386


source code

https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/index.html
次の3分類

Python Codes
https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/PythonCodes/

High Performance Computing (HPC) Codes
https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/HPCodes/

Animations
https://physics.oregonstate.edu/~landaur/Books/CPbook/Codes/Animations/

Contents 3rd edition

Preface ii 1. ComputationalScienceBasics1 1
1.1 Software Needed to Use This eBook 1
1.2 Using The Features of This eBook 4
1.3 Computational Physics and Computational Science 7
1.4 Viewing the Subjects to be Covered 8
1.5 Making Computers Obey; Languages (Theory) 11
1.6 Programming Warmup 14
1.7 Computer Number Representations (Theory) 21
1.8 Problem: Summing Series 29
2. Errors&UncertaintiesinComputations2 32
2.1 Types of Errors (Theory) 32
2.2 Errors in Spherical Bessel Functions (Problem) 37
2.3 Experimental Error Investigation (Problem) 40
3. VisualizationTools3 45
3.1 Data Visualization (General) 46
3.2 Python Matplotlib, Visual (VPython) Packages 46
3.3 Using Packages in Python Programs 47
3.4 Matplotlib for 2-D Graphs in Python 48
3.5 2-D Plots with Visual (VPython) 54
3.6 Animations with Visual (VPython) 56
3.7 Gnuplot: Reliable 2-D and 3-D Plots 57
3.8 Texturing and 3-D Imaging 65
3.9 Grace/ACE: Superb 2-D Graphs for Unix/Linux 65
4. PythonObject-OrientedPrograms:Impedance&Batons4 71
4.1 Unit I. Basic Objects: Complex Impedance 71
4.2 Complex Numbers (Math) 72
4.3 Resistance Becomes Impedance (Theory) 73
4.4 Abstract Data Structures, Objects (CS) 74
4.5 Python’s Built-in Complex Number Type 80
4.6 Complex Currents (Solution) 80
4.7 OOP Worked Examples 81
4.8 Subclasses and Class Inheritance 85
4.9 Unit II. Advanced Objects: Baton Projectiles⊙ 85
4.10 Trajectory of a Thrown Baton (Problem) 86
4.11 OOP Design Concepts (CS) 88
4.12 Multiple Classes and Multiple Inheritances 89
4.13 Multiple Inheritances, Classes in One File 92
4.14 Multiple Inheritance, Separate Files 93
4.15 OOP Example: Superposition of Motions 101
4.16 Newton’s Laws of Motion (Theory) 101
4.17 OOP Class Structure (Method) 102
4.18 Python Implementation 102
5. MonteCarloSimulations(Nonthermal)5 104
5.1 Unit I. Deterministic Randomness 104
5.2 Random Sequences (Theory) 104
5.3 Unit II. Monte Carlo Applications 109
5.4 A Random Walk (Problem) 109
5.5 Radioactive Decay (Problem) 112
5.6 Decay Implementation and Visualization 115
6. Integration6 116
6.1 Integrating a Spectrum (Problem) 116
6.2 Quadrature as Box Counting (Math) 116
6.3 Experimentation 125
6.4 Higher-Order Rules (Algorithm) 125
6.5 Monte Carlo Integration by Stone Throwing 126
6.6 High-Dimensional Integration (Problem) 128
6.7 Integrating Rapidly Varying Functions (Problem) 129
6.8 Nonuniform Assessment ⊙ 132
7. Differentiation&Searching7 135
7.1 Unit I. Numerical Differentiation 135
7.2 Forward Difference (Algorithm) 136
7.3 Central Difference (Algorithm) 136
7.4 Extrapolated Difference (Method) 137
7.5 Error Analysis (Assessment) 138
7.6 Second Derivatives (Problem) 139
7.7 Unit II. Trial-and-Error Searching 140
7.8 Quantum States in a Square Well (Problem) 140
7.9 Trial-and-Error Roots via Bisection Algorithm 140
7.10 Newton–Raphson Searching (Improved Algorithm) 142
8. MatrixEquationSolutions;DataFitting8 146
8.1 Unit I. Systems of Equations, Matrix Computing 146
8.2 Two Masses on a String 147
8.3 Classes of Matrix Problems (Maths) 150
8.4 Numerical Python and Python Matrix Library 155
8.5 Unit II. Data Fitting 162
8.6 Fitting Exponential Decay (Problem) 167
8.7 Least-Squares Fitting (Method) 170
9. DifferentialEquationApplications9 178
9.1 Unit I. Free Nonlinear Oscillations 178
9.2 Nonlinear Oscillators (Models) 179
9.3 Types of Differential Equations (Math) 180
9.4 Dynamic Form for ODEs (Theory) 181
9.5 ODE Algorithms 183
9.6 Solution for Nonlinear Oscillations (Assessment) 191
9.7 Extensions: Nonlinear Resonances, Beats, Friction 192
9.8 Extension: Time-Dependent Forces 194
9.9 Unit II. Binding A Quantum Particle 194
9.10 Theory: Quantum Eigenvalue Problem 195
9.11 Algorithm: Eigenvalues via ODE Solver + Search 196
9.12 Explorations 202
9.13 Unit III. Scattering, Projectiles & Orbits 203
9.14 Problem 1: Classical Chaotic Scattering 203
9.15 Problem 2: Balls Falling Out of the Sky 206
9.16 Theory: Projectile Motion with Drag 207
9.17 Problem 3: Planetary Motion 208
10.Fourier Analysis: Signals and Filters 10 211
10.1 Unit I. Fourier Analysis of Nonlinear Oscillations 211
10.2 Fourier Series (Math) 212
10.3 Exercise: Summation of Fourier Series 214
10.4 Fourier Transforms (Theory) 215
10.5 Unit II. Filtering Noisy Signals 223
10.6 Noise Reduction via Autocorrelation (Theory) 224
10.7 Filtering with Transforms (Theory) 227
10.8 Unit III. Fast Fourier Transform Algorithm (FFT) ⊙ 231
10.9 FFT Implementation 234
10.10 FFT Assessment 234
11.Wavelet Analysis & Data Compression 11 238
11.1 Unit I. Wavelet Basics 238
11.2 Wave Packets and Uncertainty Principle (Theory) 240
11.3 Short-Time Fourier Transforms (Math) 241
11.4 The Wavelet Transform 242
11.5 Unit II. Discrete Wavelet Transforms, MRA⊙ 246
12.Discrete & Continuous Nonlinear Dynamics 12 259
12.1 Unit I. Bug Population Dynamics (Discrete) 259
12.2 The Logistic Map (Model) 259
12.3 Properties of Nonlinear Maps (Theory) 260
12.4 Mapping Implementation 262
12.5 Bifurcation Diagram 263
12.6 Logistic Map Random Numbers (Exploration)· 265
12.7 Other Maps (Exploration) 266
12.8 Signals of Chaos: Lyapunov Coefficients ⊙ 266
12.9 Unit I Quiz 268
12.10 Unit II. Pendulums Become Chaotic 270
12.11 Chaotic Pendulum ODE 270
12.12 Visualization: Phase Space Orbits 273
12.13 Exploration: Bifurcations of Chaotic Pendulums 279
12.14 Alternate Problem: The Double Pendulum 280
12.15 Assessment: Fourier/Wavelet Analysis of Chaos 282
12.16 Exploration: Alternate Phase Space Plots 283
12.17 Further Explorations 283
12.18 Unit III. Coupled Predator–Prey Models ⊙ 284
12.19 Lotka–Volterra Model 285
13.Fractals & Statistical Growth 13 290
13.1 Fractional Dimension (Math) 290
13.2 The Sierpin ́ski Gasket (Problem 1) 291
13.3 Beautiful Plants (Problem 2) 293
13.4 Ballistic Deposition (Problem 3) 296
13.5 Length of British Coastline (Problem 4) 298
13.6 Correlated Growth, Forests, Films (Problem 5) 301
13.7 Globular Cluster (Problem 6) 301
13.8 Fractals in Bifurcation Plot (Problem 7) 305
13.9 Fractals from Cellular Automata 305
13.10 Perlin Noise Adds Realism ⊙ 307
13.11 Quiz 311
14.HPC Hardware, Tuning, Parallel Computing 14 312
14.1 Unit I. High-Performance Computers (CS) 312
14.2 Memory Hierarchy 313
14.3 The Central Processing Unit 316
14.4 CPU Design: Reduced Instruction Set Computer 316
14.5 CPU Design: Multiple-Core Processors 317
14.6 CPU Design: Vector Processor 318
14.7 Unit II. Parallel Computing 319
14.8 Parallel Semantics (Theory) 319
14.9 Distributed Memory Programming 321
14.10 Parallel Performance 322
14.11 Parallelization Strategy 324
14.12 Practical Aspects of MIMD Message Passing 325
14.13 Example of a Supercomputer: IBM Blue Gene/L 327
14.14 Towards Exascale Computing via Multinode-Multicore-GPU Com-
puters 329
14.15 Unit III. HPC Program Optimization 331
14.16 Programming for the Data Cache (Method) 340
14.17 Practical Tips for Multicore, GPU Programming 342
15.Thermodynamic Simulations, Quantum Path Integration 15 345
15.1 Unit I. Magnets via the Metropolis Algorithm 345
15.2 An Ising Chain (Model) 345
15.3 Statistical Mechanics (Theory) 347
15.4 Metropolis Algorithm 348
15.5 Unit II. Magnets via Wang–Landau Sampling ⊙ 354
15.6 Wang–Landau Sampling 356
15.7 Unit III. Feynman Path Integrals ⊙ 361
15.8 Feynman’s Space-Time Propagation (Theory) 361
15.9 Exploration: Quantum Bouncer’s Paths ⊙ 370
16.Simulating Matter with Molecular Dynamics 16 374
16.1 Molecular Dynamics (Theory) 374
16.2 Verlet and Velocity-Verlet Algorithms 380
16.3 1-D Implementation and Exercise 381
16.4 Trajectory Analysis 384
16.5 Quiz 384
17.PDEs for Electrostatics & Heat Flow 17 386
17.1 PDE Generalities 386
17.2 Unit I. Electrostatic Potentials 387
17.3 Fourier Series Solution of a PDE 388
17.4 Solution: Finite-Difference Method 391
17.5 Assessment via Surface Plot 394
17.6 Alternate Capacitor Problems 395
17.7 Implementation and Assessment 397
17.8 Electric Field Visualization (Exploration) 398
17.9 Laplace Quiz 398
17.10 Unit II. Finite-Element Method ⊙ 399
17.11 Electric Field from Charge Density (Problem) 399
17.12 Analytic Solution 400
17.13 Finite-Element (Not Difference) Methods 400
17.14 FEM Implementation and Exercises 404
17.15 Exploration 406
17.16 Unit III. Heat Flow via Time-Steps (Leapfrogs) 406
17.17 The Parabolic Heat Equation (Theory) 407
17.18 Assessment and Visualization 412
17.19 Improved Heat Flow: Crank–Nicolson Method 413
18.PDE Waves: String, Quantum Packet, E&M 18 418
18.1 Unit I. Vibrating String 418
18.2 The Hyperbolic Wave Equation (Theory) 418
18.3 Waves with Friction (Extension) 424
18.4 Waves for Variable Tension and Density (Extension) 425
18.5 Unit II. Quantum Wave Packets 429
18.6 Time-Dependent Schro ̈dinger Equation (Theory) 429
18.7 Algorithm for the 2-D Schro ̈dinger Equation 433
18.8 Unit III. E&M Waves, Finite-Difference t Domain ⊙ 435
18.9 Maxwell’s Equations 435
18.10 FDTD Algorithm 436
19.Solitons & Computational Fluid Dynamics 19 443
19.1 Unit I. Advection, Shocks, Russell’s Soliton 443
19.2 Theory: Continuity and Advection Equations 444
19.3 Theory: Shock Waves via Burgers’ Equation 445
19.4 Including Dispersion 448
19.5 Shallow-Water Solitons; the KdeV Equation 449
19.6 Unit II. River Hydrodynamics 453
19.7 Hydrodynamics, the Navier–Stokes Equation (Theory) 453
19.8 2-D Flow over a Beam 459
19.9 Theory: Vorticity Form of Navier–Stokes Equation 459
20.Integral Equations in Quantum Mechanics 20 468
20.1 Unit I. Bound States of Nonlocal Potentials 468
20.2 Momentum-Space Schro ̈dinger Equation (Theory) 469
20.3 Unit II. Nonlocal Potential Scattering ⊙ 473
20.4 Lippmann–Schwinger Equation (Theory) 473
A. Glossary A 479
B. Installing Python, Matplotlib, NumPy B 485
C. Software Directories E 486
D. Compression via DWT with Thresholding F 489
D.1 More on Thresholding 491
D.2 Wavelet Implementation and Assessment 492
Bibliography 493
Index 503

Bibliography

[Abar 93] ABARBANEL, H. D. I., M. I. RABINOVICH, AND M. M. SUSHCHIK (1993), Introduction to Nonlinear Dynamics for Physicists, World Scientific, Singapore. 283
[A&S 72] ABRAMOWITZ, M., AND I. A. STEGUN (1972), Handbook of Mathematical Functions, 10th Ed. U.S. Govt. Printing Office, Washington. 122
[Add 02] ADDISON, P. S. (2002). The Illustrated Wavelet Transform Handbook, Institute of Physics Publishing, Bristol and Philadelphia. 239, 244, 247
[ALCMD] MORRIS, J., D. TURNER, AND K.-M. HO AL_CMD, Ames Laboratory Classical Molecular Dynamics. http://codeblue.umich.edu/hoomd-blue/.
[A&T 87] ALLAN, M. P. AND J. P. TILDESLEY (1987), Computer Simulations of Liquids, Oxford Science Publications, Oxford, UK. 374
[Amd 67] AMDAHL, G., Validity of the Single-Processor Approach to Achieving Large-Scale Computing Capabilities, Proc. AFIPS., 483 (1967). 374
[Anc 02] ANCONA, M. G. (2002), Computational Methods for Applied Science & Engineer ing, Rinton Press, Princeton, NJ. 323
[A&W 01] ARFKEN, G. B.. AND H. J. WEBER (2001). Mathematical Methods for Physicists, Harcourt/Academic Press, San Diego. 410
[Argy 91] ARGYRIS, J., M. HAASE, AND J. C. HEINRICH (1991), Comput. Meth. Appl. Mech. Eng., 86. 1. 240, 386
[Arm 91] ARMIN, B., AND H. SHLOMO, EDS. (1991), Fractals and Disordered Systems, Springer-Verlag, Berlin.
[Ask 77] ASKAR, A., AND A. S. CAKMAK (1977), J. Chem. Phys. 68, 2794. 290
[Bai 05] BAILEY, M. OSU Chroma Depth Scientific Visualization Gallery,
http://web.engr.oregonstate.edu/~mjb/chromadepth/. 430, 433
[Bana 99] BANACLOCHE, J. G., (1999), A Quantum Bouncing Ball, Am. J. Phys. 67, 776 782. 65
[Bars 93] BARNSLEY, M. E. AND L. P. HURD, (1993), Fractal Image Compression, A. K. Peters, UK. 370
[Becker 54] BECKER, R. A., (1954), Introduction to Theoretical Mechanics, McGraw-Hill, New York. 294, 305
[Berry] BERRYMAN, A. A., Predator-Prey Dynamics, http://classes.entom.wsu.edu/543/. 427
[B&R 02] BEVINGTON, P. R., AND D. K. ROBINSON (2002), Data Reduction and Error Analysis for the Physical Sciences, 3rd Ed., McGraw-Hill, New York.
[Bin 01] BINDER, K. AND D. W. HEERMANN, (2001) Monte Carlo Methods, Springer Verlag, Berlin. 163, 170, 171
[Bleh 90] BLEHER, S., C. GREBOGI, AND E. OTT (1990), Bifurcations in Chaotic Scattering, Physica D. 46, 87.
[Burde 74] BUNDE, A. AND S. HAVLIN (EDS) (1991), Fractals and Disordered Systems, Springer, Berlin. 203
[Burg 74] BURGERS, J. M., (1974), The Non-Linear Diffusion Equation; Asymptotic Solutions and Starristical Problems, Reidel, Boston. 291 1
[B&H 95] BRIGGS, W. L., AND V. E. HENSON (1995), The DFT, An Owner's Manual, SLAM, Philadelphia. 445
[C&P 85] R. CAR AND M. PARRINELLO (1985), Phys. Rev. Lett. 55, 2471. 216
[C&P 88] CARRIER, G. E., AND C. E. PEARSON (1988), Partial Differential Equations, Academic Press, San Diego. 374
[C&S 10] CHABAY, R. W. AND SHERWOOD, B. A. (2010), Matter and Interactions, 3rd Edition, Wiley, New York.
[C&L 81] CHRISTIANSEN, P. L., AND P. S. LOMDAHL (1981), Physica 2D, 482. ii
[C&O 78] CHRISTIANSEN, P. L., AND O. H. OLSEN (1978), Phys. Lett. 68A, 185; (1979),
Physica Scripta 20, 531. (CSE) Computing in Science & Engineering,
http://www.computer.org/portal/web/cise/home.
[CPUG] CPUG, Computational Physics degree program for Undergraduates, Oregon State University, science. http://oregonstate.edu/rubin/CPUG. 2, 312
[C&N 47] CRANK, J., AND P. NICOLSON (1946), Procd. Cambridge Phil. Soc. 43, 50. 10
[Chrom] ChromaDepth Technologies CHROMADEPTH TECHNOLOGIES
http://www.chromatek.com/. 413
[Clark] CLARK UNIVERSITY, Statistical & Thermal Physics Curriculum Development Project, http://stp.clarku.edu/; Density of States of the 2D Ising Model 65
[C0,65] COOLEY, J. W. AND J. W. TUKEY, (1965), Math. Comput., 19, 297. 354, 357
[Cour 28] COURANT, R., K. FRIEDRICHS, AND H. LEWY (1928), Mathematische Annalen 100, 32. 231
[Cre 81] CREUTZ, M. AND B. FREEDMAN, A statistical approach to quantum mechanics, (1981), Ann. Phys. (N. Y.), 132, 427-462.
[CYG] Cygwin, a Linux-like environment for Windows, http://x.cygwin.com/
[Da,42] DANIELSON, G. C. AND C. LANCZOS, (1942), J. Franklin Inst., 233, 365. 66
[Daub 95] DAUBECHIES, I. (1995), Wavelets and other phase domain localization methods, Proc. Int. Cong. Mathematicians, 1, 2, Basel, 56 (1995). Birkhäuser. 231
[DeJ 92] DE JONG, M. L. (1992), Chaos and the Simple Pendulum, The Physics Teacher 30, 115. 254
[Dong 05] DONGARRA, J., T. STERLING, H. SIMON, AND E. STROHMAIER (2005), High Performance Compuding, IEEE/AIP Comp. in Science & Engr. 7, 51. 280
[Dong 11] DONGARRA, J., On the Fuure of High Performance Computing: How
to Think for Peta and Erascale Computing, Conference on Computational Physics 2011, Gatlinburg. 2011; Emerging Technologies for High Perfor mance Computing, GPU Club presentation, 2011, University of Manchester,
http://www.netlib.org/utk/people/JackDongarra/SLIDES/gpu-0711.pdf. 322, 325
[Donn 05] DONNELLY, D. AND B. RUST (2005), The Fast Fourier Transform for Experimentalists, IEEE/AIP Comp. in Science & Engr. 7, 71. 331, 342, 343
[D&J 94] DONOHO, D.L. AND I. M. JOHNSTONE, (1994a), Ideal denoising in an orthonormal basis chosen from a library of bases, Compt. Rend. Acad. Sci. Paris Ser. A, 319, 1317. 231
[Eclipse] ECLIPSE, an open development platform, http://www.eclipse.org/. 491
[Erco] ERCOLESSI, F., A Molecular Dynamics Primer,
www.ud.infn.it/"ercolessi/md/. V
[E&P 88] EUGENE, S. H., AND M. PAUL (1988). Nature 335, 405. 374,379
[F&S] FALKOVICH, G., AND K. R. SREENIVASAN (2006), Lesson from Hydrodynamic Turbulence, Physics Today 43. 290
[Fam 85] FAMILY, F., AND T VICSEK (1985), J. Phys. A 18, L75. 445, 462
[Feig 79] FEIGENBAUM, M. J. (1979), J. Stat. Physics 21, 669. 296 262, 265
[F&W 80J FETTER, A. L., AND J. D. WALECKA (1980), Theoretical Mechanics of Particles and Continua, McGraw-Hill, New York. 443, 453
[F&H 65] FEYNMAN, R. P., AND A. R. HIBBS (1965), Quantum Mechanics and Path Integrals, McGraw-Hill, New York. 345, 361
[Fitz 04] FITZGERALD, R. (2004), New Experiments Set the Scale for the onset of Turbulence in Pipe Flow, Phys. Today, 57, 21. 462
[Fos 96] FOSDICK L. D, E. R. JESSUP, C. J. C. SCHAUBLE, AND G. DOMIK (1996), An Introduction to High Performance Scientific Computing, MIT Press, Cambridge. 374
[Fox 94] Fox, G., Parallel Computing Works!, (1994) Morgan Kaufmann, San Diego. 312
[Gara 05] GARA, A., M. A. BLUMRICH, D. CHEN, G. L.-T. CHIU, P. COTEUS, M. E. GIAMPA PA, R. A. HARING, P. HEIDELBERGER, D. HOENICKE, G. V. KOPCSAY, T. A. LIEBSCH, M. OHMACHT, B. D. STEINMACHER-BUROW, T. TAKKEN, AND P. VRANAS, Overview of the Blue Gene/L system architecure, (2005) IBM J. Res & Dev 49, 195. 327, 328, 330
[Gar 00] GARCIA, A. L. (2000), Numerical Methods for Physics, 2nd ed., Prentice Hall, Upper Saddle River. 393
[Gibbs 75] GIBBS, R. L. (1975), The quantum bouncer, Am. J. Phys., 43, 25-28. 370
[Good 92] GOODINGS, D. A. AND T. SZEREDI (1992). The quantum bouncer by the path integral method, Am. J. Phys., 59, 924-930. 370
[Gimp] GIMP, the GNU image manipulation program, www.gimp.org/. 489
[GNU] Gnuplot, a portable command-line driven interactive data and function plotting utility,
www.gnuplot.info/.
[Gold 67] GOLDBERG, A., H. M. SCHEY, AND J. L. SCHWARTZ (1967), Am. J. Phys. 3, 177.
[Gos 99] GOSWANI, J. C., A. K. Chan, (1999) Fundamentals of Wavelets, John Wiley & Sons,Inc., New York.
[Gott 66] GOTTFRIED, K. (1966). Quantum Mechanics, Benjamin, New York. 140, 471, 477
[G,T&C 06] GOULD, H., J. TOBOCHNIK AND W. CHRISTIAN (2006), An Introduction to Computer Simulation Methods, 3rd ed., Addison-Wesley, Reading, MA. 126, 267, 270, 280, 353, 374
[Grace] GRACE, a WYSIWYG 2D plotting tool for the X Window System (descendant of ACE/gr, Xmgr), plasma-gate.weizmann.ac.il/Grace/. 65, 66 [Graps 95] GRAPS, A. (1995), An Introduction to Wavelets, IEEE/AIP Comp. in Science & Engr. 2, 50.
[Gurney] GURNEY, W. S. C. AND R. M. NISBET, (1998), Ecological Dynamics, Oxford Uni. Press, Oxford, New York.
[H&T 70] HAFTEL, M. I., AND E. TABAKIN (1970), Nucl. Phys. 158, 1. 475 [Har 96] HARDWICH, J., Rules for Optimization, http;//www.cs.cmu.edu/jch/java. 331
[Hart 98] HARTMANN, W. M. (1998), Signals, Sound, and Sensation, AIP Press, Springer Verlag, New York. 227, 228
[Hi,76] HIGGINS, R. J., (1976), Am. J. Phys., 44, 766. 234
[Hock 88] HOCKNEY, R.W. AND J.W. EASTWOOD (1988), Computer Simulation Using Particles, Adam Hilger, Bristol, UK. 374
[Huang 87] HUNAG, K. (1987), Statistical Mechanics, Wiley, New York. 348 [irfanview] IRFANVIEW, www.irfanview.com/. 489 [Jack 88] JACKSON, J. D. (1988), Classical Electrodynamics, 3rd ed., Wiley, New York.
387, 388
[J&S 98] JOSÉ, J. V, AND E. J. SALATAN, (1988) Classical Dynamics, Cambridge Univ. Press, Cambridge, UK. 181, 277
[jEdit] JEDIT, a mature programmer's text editor, www.jedit.org/. V
[K&R 88] KERNIGHAN, B. AND D. RITCHIE (1988) The C Programming Language, 2nd ed., Prentice Hall, Englewood Cliffs, NJ.
[Koon 86] KOONIN, S. E. (1986), Computational Physics, Benjamin, Menlo Park, CA. 129, 195, 431, 462
[KdeV 95] KORTEWEG, D. J., AND G. DEVRIES (1895), Phil. Mag. 39, 4. 449 111
[Krey 98] KREYSZIG, E. (1998), Advanced Engineering Mathematics, 8th ed., Wiley, New York. 390
[Kutz] KUTZ N., Scientific Computing, http://www.amath.washington.edu/courses/581-autumn-2003/.
[Lamb 93] LAMB, H., (1993), Hydrodynamics, 6th ed., Cambridge University Press, Cam bridge, UK. 460
[L&L,F 87] LANDAU, L. D., AND E. M. LIFSHITZ (1987), Fluid Mechanics, 2nd Ed., Butterworth-Heinemann, Oxford, UK. 443
[L&L,M 76] LANDAU, L. D., AND E. M. LIFSHITZ (1976). Quantum Mechanics, Pergamon, Oxford, UK. 212, 270, 271, 280, 433, 444
[L&L,M 77] LANDAU, L. D., AND E. M. LIFSHITZ (1976), Mechanics, 3rd ed.,
Butterworth-Heinemann, Oxford, UK.
[L 05] LANDAU, R. H. (2005). A First Course in Scientific Computing, Princeton Univ. Press, Princeton. 45, 398
[L 96] LANDAU, R. H. (1996), Quantum Mechanics II, A Second Course in Quantum Theory, 2nd ed., Wiley, New York. 196, 371, 468, 469
[Lang] LANG, W. C., K. FORINASH (1998), Time-frequency analysis with the continuous wavelet transform, Amer. J. of Phys, 66, 794. 246
[Lang 08] LANGTANGEN, H. P. (2008), Python Scripting for Computational Science, Springer-Verlag, Heidelberg. 2
[Lang 09] LANGTANGEN, H. P. (2009), A Primer on Scientific Programming with Python, Springer-Verlag, Heidelberg. 2
[LAP 00] ANDERSON, E., Z. BAI, C. BISCHOF, J. DEMMEL, J. DONGARRA, J. Du
CROZ, A. GREENBAUM, S. HAMMARLING, A. McKENNEY, S. OSTROUCHOV, AND D. SORENSEN (2000), LAPACK Users' Guide, 3rd ed., SIAM, Philadelphia;
http://www.netlib.org. 2, 47, 49
[Li] LI, Z., Numerical Methods for Partial Differential Equations - Finite Element Method, http://www.ncsu.edu/~zhilin/. 399, 400, 404 [Libb 03] LIBOFF, R. L., (2003), Introductory Quantum Mechanics, Addison Wesley, Reading, MA.
[Lot 25] LOTKA, A. J., (1925) Elements of Physical Biology, Williams & Wilkins, Baltimore. 284
[LP&B 08] LANDAU, R. H., PÁEZ, M. J. AND BORDEIANU, C. C. (2008), A Survey of Computational Physics, Princeton University Press, Princeton. 46
[MacK 85] MACKEOWN, P. K. (1985), Am. J. Phys. 53, 880. 345
[M&N 87] MACKEOWN, P. K., AND D. J. NEWMAN (1987) Computational Techniques in Physics, Adam Hilger, Bristol, UK. 345
[MLP 00] MAESTRI, J. J. V., R. H. LANDAU, AND M. J P/ Aez (2000) Two-Particle Schrödinger Equation animations of wave packet-wave packet scattering. . Am. J. Phys. 68, 1113-1119. 430, 433
[Mallat 89] MALLAT, P.G. (1982), A Theory for Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Transaction on Pattern Analysis and Machine Intelligence Vol. 11, No. 7, 674-693.
[Mand 67] MANDELBROT, B. (1967), How long is the coast of Britain?, Science, 156, 638. 298
[Mand 82] MANDELBROT, B. (1982), The Fractal Geometry of Nature, 29, Freeman, San Francisco. 290
[Mann 90] MANNEVILLE, P., (1990), Dissipative Structures and weak Turbulence, Academic Press, San Diego. 266
[Mann 83] MANNHEIM, P. D. (1983), Am. J. Phys. 51, 328. 345
[M&T 03] MARION, J. B. AND S. T. THORNTON (2003), Classical Dynamics of Particles and Systems, 5th ed., Harcourt Brace Jovanovich, Orlando, FL. 204, 207, 271
[Math 02] MATHEWS, J., (2002), Numerical Methods for Mathematics, Science and Engineering, Prentice Hall, Upper Saddle River. 186
[Math 92] MATHEWS, J. (1992), Numerical Methods for Mathematics, Science and Engineering, Prentice Hall, Englewood Cliff, NJ. 188
[M&W 65] MATHEWS, J. AND R. L. WALKER (1965), Mathematical Methods of Physics, Benjamin, Reading, MA. 170
[Metp 53] METROPOLIS, M., A. W. ROSENBLUTH, M. N. ROSENBLUTH, A. H. TELLER, AND E. TELLER (1953), J. Chem. Phys. 21, 1087. 349
[Mold] REFSON, K. Moldy, A General-Purpose Molecular Dynamics Simulation Program, http://www.ccp5.ac.uk/moldy/moldy.html. 374
[M&L 85] MOON, F. C. AND G.-X. LI (1985), Phys. Rev Lett. 55, 1439. 284
[M&F 531 MORSE, P. M., AND H. FESHBACH (1953), Methods of Theoretical Physics, McGraw-Hill, New York. 387
[NAMD] NELSON, M., W. HUMPHREY, A. GURSOY, A. DALKE, L. KALE, R.
D. SKEEL, AND K. SCHULTEN, (1996). NAMD - Scalable Molecular Dy namics, J. of Supercomputing Applications and High Performance Computing,
http://www.ks.uiuc.edu/Research/namd/. 374
[Nes 02) NESVIZHEVSKY, V.V., H. G. BORNER, A. K. PETUKHOV, H. ABELE, S.
BAESSLER, F. J. RUESS, T. STOFERLE, A. WESTPHAL, A. M. GAGARSKI, G. A. PETROV, AND A. V. STRELKOV, Quantum states of neutrons in the Earth's gravita tional field, (2002), Nature 415, 297. 370
[Netpbm] NETPBM, a package of graphics programs and programming library,
http://netpbm.sourceforge.net/doc/. 489 [Ott 02] OTT, E., (2002), Chaos in Dynamical Systems, Cambridge University Press, Cambridge. 267
[Otto] OTTO A., Numerical Simulations of Fluids and Plasmas
http://how.gi.alaska.edu/ao/sim/chapters/chap6.pdf. 399
[Pan 96] PANCAKE, C. M., (1996), Is Parallelism for You?, IEEE Computational Sci. & Engr, 3, 18. 312, 325
[P&D 81] PEDERSEN, N. F., AND A. DAVIDSON (1981), Appl. Phys. Lett. 39, 830. [Peit 94] PEITGEN, H.-O., H. JÜRGENS, AND D. SAUPE (1992), Chaos and Fractals, New York. 305
[Penn 94] PENNA, T. J. P. (1994), Comput. in Phys. 9, 341.
[Perlin] PERLIN, K., NYU Media Research Laboratory, http://mrl.nyu.edu/~perlin. 307, 309
[P&R 95] PHATAK, S.C., AND S. S. RAO (1995), Logistic map: A possible random-number generator, Phys. Rev. E 51, 3670. 265
[PhT 88] PHYSICS TODAY, Special issue on chaos, December 1988. 290
[P&B 94] PLISCHKE, M., AND B. BERGERSEN (1994), Equilibrium Statistical Physics, 2nd Ed., World Scientific Pub. Co., Singapore. 348
[Polikar] POLIKAR, R., The Wavelet Tutorial, http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html.
[Poll 06] KENNEDY, R., The Case of Pollocks Fractals Focuses on Physics, New York Times, 2 December 2006; 5 December 2006. 304
[Potv 93] POTVIN, J. (1993), Comput. in Phys. 7, 149. 345
[Pov-Ray] Persistence of Vision Raytracer, http://www.povray.org. 309
[Pres 94] PRESS, W. H., B. P. FLANNERY, S. A. TEUKOLSKY, AND W. T. VETTERLING (1994), Numerical Recipes, Cambridge University Press, Cambridge, UK. 129, 134, 146, 166, 167, 170, 172, 181, 186, 228, 393, 410, 415, 422, 446
[Pres 00] PRESS, W. H., B. P. FLANNERY, S. A. TEUKOLSKY, AND W. T. VETTERLING (2000), Numerical Recipes in C++, 2nd Ed., Cambridge University Press, Cambridge, UK. 129, 148, 181, 188, 371
[Quinn 04] QUINN, M. J. (2004), Parallel Programming in C with MPI and OpenMP, McGraw Hill Higher Education, New York, NY. 312, 319, 323
[Ram 00] RAMASUBRAMANIAN, K. AND M. S. SRIRAM, (2000), A comparative study of computation of Lyapunov spectra with different algorithms, Physica D, 139 72. 266
[Rap 95] RAPAPORT, D.C (1995), The Art of Molecular Dynamics Simulation, Cambridge University Press, Cambridge, UK. 374 [Rash 90] RASBAND, S. N. (1990), Chaotic Dynamics of Nonlinear Systems, Wiley, New York. 260, 261, 270
[Raw 96] RAWITSCHER, G., I. KOLTRACHT, H. DAT, AND C. RIBETTI (1996), Comput. in Phys., 10, 335. 418
[R&M93] REITZ, J.R., F. J. MILFORD, AND CHRISTY, R. W. (1993), Foundations of Electromagnetic Theory, Fourth Ed., Addison-Wesley, Reading, PA.
[Rey 83] REYNOLDS, O. (1883), Proc. R. Soc. London, 35, 84. 462
[Rhei 74] RHEINBOLD, W. C. (1974), Methods for Solving Systems of Nonlinear Equations, SIAM, Philadelphia.
[Rich 61] RICHARDSON. L. F., (1961), Problem of contiguity: an appendix of statistics of deadly quarrels, General Systems Yearbook, 6, 139. 298
[Riz] RIZNICHENKO G. Y., Mathematical Models in Biophysics.
http://www.biophysics.org/Portals/1/PDFS/Education/galina.pdf.
[Rowe 95] ROWE, A. C. H. AND P. C. ABBOTT (1995). Daubechies Wavelets and Mathemarica, Comput. in Phys. 9, 635-548.
[Russ 44] RUSSELL, J. S. (1844). Report of the 14th Meeting of the British Association for the Advancement of Science, John Murray, London. 443
[Sand 94] SANDER, E., L. M. SANDER, AND R. M. ZIFF (1994), Comput. in Phys. 8, 420. 290
[Schd 007 SCHMID, E. W., G. SPITZ, AND W. Lösch (2000), Theoretical Physics on the Personal Computer, 2nd Ed., Springer-Verlag, Berlin.
[Schw 02] SCHWARZCHILD, B., (2002). Phys. Today, 55, 20. 195
[Schk 94] SCHECK, E. (1994), Mechanics, from Newton's Laws to Deterministic Chaos, 2nd ed., Springer-Verlag. New York.
[Shannon 48] SHANNON, C. E., . (1948), The Bell System Technical Journal, 27, 379. 181, 271
[Shar] SHAROV, A., Quantitative Population Ecology.
http://home.comcast.net/ sharov/PopEcol/popecol.html. 267
[Shaw 92] SHAW C. T. (1992), Using Computational Fluid Dynamics, Prentice Hall, Engle wood Cliff, NJ.
[S&T 93] SINGH, P. P., AND W. J. THOMPSON (1993). Comput. in Phys. 7, 388. 399, 443
[Sipp 96] SIPPER., M. (1997), Evolution of Parallel Cellular Machines Springer-Verlag, Heidelberg: cell-auto.com/. 474
[Smi 91] SMITH, D. N. (1991), Concepts of Object-Oriented Programming, McGraw-Hill, New York. 305
[Smi 99] SMITH, S. W. (1999). The Scientist and Engineer's Guide to Digital Signal Processing, California Technical Publishing, San Diego, California. 88, 230
[Stez 73] STETZ, A., J. CARROLL, N. CHIRAPATPIMOL, M. DIXIT, G. IGO, M. NASSER, D. ORTENDAHL, AND V. PEREZ-MENDEZ (1973). Determination of the Arial Vector Form Factor in the Radiative Decay of the Pion, LBL 1707. 229
[Sull 00] SULLIVAN, D. (2000), Electromagnetic Simulations Using the FDTD Methods, IEEE Press, New York. 167, 169
[SunJ] SUN JAVA DEVELOPER'S SITE, java.sun.com/. 435, 437, 438 [Tab 89] TABOR, M. (1989), Chaos and Integrability in Nonlinear Dynamics, Wiley, New York. v
[Taf 89] TAFLOVE, A AND S. HAGNESS. (2000), Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd Ed., Artech House, Boston. 181, 284, 446
[Tait 90] TAIT, R. N., T. SMY, AND M. J. BRETT (1990), Thin Solid Films 187, 375. 437, 438
[Thij 99] THIJSSEN J. M. (1999), Computational Physics, Cambridge University Press, Cambridge, UK. 301
[Thom 92] THOMPSON, W. J. (1992), Computing for Scientists and Engineers, Wiley, New York. 374,378
[Tick 04] TICKNER, J. (2004). Simulating nuclear particle transport in stochastic media using Perlin noise functions, Nucl. Instru. & Mtds, B, 203, 124. 166, 170, 172
[Vall 00] VALLÉE, O., (2000) Comment on a quantum bouncing ball by Julio Gea Banacloche, Am J. Phys., 68, 672-673. 307
[VdeV 94] VAN DE VELDE, E. F. (1994), Concurrent Scientific Computing, Springer-Verlag, New York. 370
[VdB 99] VAN DEN BERG, J. C. (ED.) (1999), Wavelets in Physics, Cambridge University Press, Cambridge. 312
[Vida 99] VIDAKOVIC, B. (1999), Statistical Modeling by Wavelets, Wiley. 244
[Viss 91] VISSCHER, P. B. (1991), Comput. in Phys. 5,596.
[Vold 59] VOLD, M. J. (1959), J. Collod. Sci. 14, 168. 430, 431
[Volt 26] VOLTERRA, V. (1926) Variazioni e fluttuazioni del numero d'individui in specie animali convivenri, Mem. R Accad. Naz. dei Lincei. Ser. VI, 2. 296 [VUE] VUE The Visual Understanding Environment, a tool for managing and integrating digital resources in support of teaching, learning and research, http://vue.tufts.edu. 284
[Ward 04] WARD, D. W AND K. A. NELSON (2004), Finite Difference Time Domain (FDTD) Simulations of Electromagnetic Wave Propagation using a Spreadsheet, ArXiv Physics 0402091 1-8. 8
[WL 04] LANDAU, D. P, S.-H. TSAI AND M. EXLER, (2004), A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling, Am. J. Phys. 72, 1294:
[WL 01] LANDAU, D. P, AND F. WANG, (2001), Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram, Phys. Rev. E 64,056101. 435
[WW 04] WARBURTON, R. D. H. AND J. WANG, (2004), Analysis of asymptotic projectile motion with air resistance using the Lambert W. function, Am. J. Phys. 72, 1404. 354
[Whine 92] WHINERAY, J., (1992), An energy representation approach to the quantum bouncer, Am. J. Phys. 60. 948-950.
[Wiki] WIKIPEDIA, the free encyclopedia, http://en.wikipedia.org/. 370
[Will 97] WILLIAMS, G. P., (1997), Chaos Theory Tamed, Joseph Henry Press, Washington, D.C. 230
[W&S 83] WITTEN, T. A., AND L. M. SANDER (1981), Phys. Rev. Lett. 47, 1400; (1983), Phys. Rev. B 27,5686. 266
[Wolf 85] WOLF, A., J. B. SWIFT, H. L. SWINNEY, AND J. A. VASTANO, (1985), Determining Lyapunov Exponents from a Time Series Physica D, 16, 285. 302
[Wolf 83] WOLFRAM S. (1983), Staristical Mechanics of Cellular Automata, Rev. Mod. Phys. 55, 601. 266
[Yang 52] YANG, C. N. (1952), The Spontaneous Magnetization of a Two-Dimensional Ising Model Phys. Rev. 85, 809. 307
[Yee 66] YEE, K. (1966), IEEE Transactions on Antennas and Propagation AP-14, 302. 347, 348
[Z&K 65] ZABUSKY, N. J., AND M. D. KRUSKAL (1965). Phys. Rev. Lett. 15, 240. 436
[Zucker] ZUCKER, M. The Perlin Noise FAQ: see too JÖNSSON, A., Generating Per lin Noise, http://webstaff.itn.liu.se/stegu/TNM022-2005/perlinnoiselinks/perlin-noise-math-faq.html. 449

docker

上記ソースコードをdocker上で利用できるようにした.

macOS
$ docker run -v /Users/administrator/Downloads/work:/home/work  -p 8080:8080 -it  kaizenjapan/computational-physics /bin/bash 

dockerが起動したら。

# cd home
# ls
cp  mkall.sh  url0.txt  url1.txt  url2.txt  url3.txt  url4.txt  url5.txt  url6.txt  url7.txt  wgeturl.sh  work
# cd cp
# ls
Animations  HPCodes  PythonCodes  pythoncodes

ごめんなさい。小文字のフォルダは練習用が残ったままです。

python環境だけ で、まだfortranとCは導入(install)していない。
近日中に導入予定。
 でなく、fortranとCも利用できるようにした。
python は import visualでエラー中。
javaは導入のエラーでここでは使えない。

別記事の方は使える。

計算物理学 Rubin H. Landau docker登録その2
https://qiita.com/kaizen_nagoya/items/a72a79de29a2b43b172b

java error

今日のdocker error: java E: Sub-process /usr/bin/dpkg returned an error code (1)
https://qiita.com/kaizen_nagoya/items/d0d890c6bdf455c66087

python error

今日のpython error: import visual
https://qiita.com/kaizen_nagoya/items/ae8209ba4cff4218f1e7

今日のpython error: psychopy
https://qiita.com/kaizen_nagoya/items/e47f5ee6cc522485f109

fortran error

今日のfortran error
https://qiita.com/kaizen_nagoya/items/97a95ea3bb6786c76b1f

c warning

今日のCの警告 warning: type specifier missing, defaults to 'int'
https://qiita.com/kaizen_nagoya/items/94e4080235e75194213e

bibliographyの入力作業

Google Drive OCR機能を試してみた
https://qiita.com/kaizen_nagoya/items/5ad1ada6577396601eaa

dockerへの登録作業

計算物理学 Rubin H. Landau docker内 script
https://qiita.com/kaizen_nagoya/items/799b72523826f5fc7043

登録作業でのエラーは下記。
今日のshell error : File exists
https://qiita.com/kaizen_nagoya/items/2b6223b34fb81a7b871a

Qiitaへの記事分類は下記。

Qiitaに掲載する記事の分類
https://qiita.com/kaizen_nagoya/items/7b966ae426859d7ef0d7

参考資料(reference)

docker(19) 言語処理100本ノックをdockerで。python覚えるのに最適。
https://qiita.com/kaizen_nagoya/items/7e7eb7c543e0c18438c4

プログラムちょい替え(11) Fortran 多次元配列のアクセス順序による計算時間の違い
https://qiita.com/kaizen_nagoya/items/3d657649d74fdd753bad

Cコンパイラ3種をdockerで
https://qiita.com/kaizen_nagoya/items/77184cf005490d7579e6

文書履歴(document history)

ver. 0.01 初稿 20190806
ver. 0.02 docker追記 20190807 朝
ver. 0.03 fortran導入 20190807 午前
ver. 0.04 bibliograpy記入 20190807 昼
ver. 0.05 clang導入 20190807 午後

Why not register and get more from Qiita?
  1. We will deliver articles that match you
    By following users and tags, you can catch up information on technical fields that you are interested in as a whole
  2. you can read useful information later efficiently
    By "stocking" the articles you like, you can search right away
3
Help us understand the problem. What are the problem?