Change figure width from 800px to 100% for PDF compatibility

Author: ggorman

chapters/advec/advec.qmd

@@ -822,9 +822,9 @@ one with a discontinuity in the first derivative (Figure
 the left plots in the figures, we get small ripples behind the main
 wave, and this main wave has the amplitude reduced.
 
-![Advection of a Gaussian function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right).](fig/gaussian_LF_C08){#fig-advec-1D-LF-fig1-C08 width="800px"}
+![Advection of a Gaussian function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right).](fig/gaussian_LF_C08){#fig-advec-1D-LF-fig1-C08 width="100%"}
 
-![Advection of half a cosine function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right).](fig/cosinehat_LF_C08){#fig-advec-1D-LF-fig2-C08 width="800px"}
+![Advection of half a cosine function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right).](fig/cosinehat_LF_C08){#fig-advec-1D-LF-fig2-C08 width="100%"}
 
 ### Analysis
 
@@ -901,9 +901,9 @@ Experiments show, however, that
 reducing $\Delta t$ or $\Delta x$, while keeping $C$ reduces the
 error.
 
-![Advection of a Gaussian function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.01$ (left) and $\Delta t=0.001$ (right).](fig/gaussian_UP_C08){#fig-advec-1D-UP-fig1-C08 width="800px"}
+![Advection of a Gaussian function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.01$ (left) and $\Delta t=0.001$ (right).](fig/gaussian_UP_C08){#fig-advec-1D-UP-fig1-C08 width="100%"}
 
-![Advection of half a cosine function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right).](fig/cosinehat_UP_08){#fig-advec-1D-UP-fig2-C08 width="800px"}
+![Advection of half a cosine function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right).](fig/cosinehat_UP_08){#fig-advec-1D-UP-fig2-C08 width="100%"}
 
 The amplification factor can be computed using the
 formula (@eq-form-exp-fd1-bw),
@@ -1219,9 +1219,9 @@ $$
 A = \frac{1 - (1-\theta) i C\sin p}{1 + \theta i C\sin p}\tp
 $$
 
-![Crank-Nicolson in time, centered in space, Gaussian profile, $C=0.8$, $\Delta t = 0.01$ (left) and $\Delta t=0.005$ (right).](fig/gaussian_CN_C08){#fig-advec-1D-CN-fig-C08 width="800px"}
+![Crank-Nicolson in time, centered in space, Gaussian profile, $C=0.8$, $\Delta t = 0.01$ (left) and $\Delta t=0.005$ (right).](fig/gaussian_CN_C08){#fig-advec-1D-CN-fig-C08 width="100%"}
 
-![Backward-Euler in time, centered in space, half a cosine profile, $C=0.8$, $\Delta t = 0.01$ (left) and $\Delta t=0.005$ (right).](fig/cosinehat_BE_C08){#fig-advec-1D-BE-fig-C08 width="800px"}
+![Backward-Euler in time, centered in space, half a cosine profile, $C=0.8$, $\Delta t = 0.01$ (left) and $\Delta t=0.005$ (right).](fig/cosinehat_BE_C08){#fig-advec-1D-BE-fig-C08 width="100%"}
 
 Figure @fig-advec-1D-CN-fig-C08 depicts a numerical solution for $C=0.8$
 and the Crank-Nicolson
@@ -1357,17 +1357,17 @@ The curves are labeled according to the table below.
 | LW | Lax-Wendroff's method                                |
 | BE | Backward Euler in time, centered difference in space |
 
-![Dispersion relations for $C=1$.](fig/disprel_C1_LW_UP_LF){#fig-advec-1D-disprel-C1-1 width="800px"}
+![Dispersion relations for $C=1$.](fig/disprel_C1_LW_UP_LF){#fig-advec-1D-disprel-C1-1 width="100%"}
 
-![Dispersion relations for $C=1$.](fig/disprel_C1_CN_BE_FE){#fig-advec-1D-disprel-C1-2 width="800px"}
+![Dispersion relations for $C=1$.](fig/disprel_C1_CN_BE_FE){#fig-advec-1D-disprel-C1-2 width="100%"}
 
-![Dispersion relations for $C=0.8$.](fig/disprel_C0_8_LW_UP_LF){#fig-advec-1D-disprel-C08-1 width="800px"}
+![Dispersion relations for $C=0.8$.](fig/disprel_C0_8_LW_UP_LF){#fig-advec-1D-disprel-C08-1 width="100%"}
 
-![Dispersion relations for $C=0.8$.](fig/disprel_C0_8_CN_BE_FE){#fig-advec-1D-disprel-C08-2 width="800px"}
+![Dispersion relations for $C=0.8$.](fig/disprel_C0_8_CN_BE_FE){#fig-advec-1D-disprel-C08-2 width="100%"}
 
-![Dispersion relations for $C=0.5$.](fig/disprel_C0_5_LW_UP_LF){#fig-advec-1D-disprel-C05-1 width="800px"}
+![Dispersion relations for $C=0.5$.](fig/disprel_C0_5_LW_UP_LF){#fig-advec-1D-disprel-C05-1 width="100%"}
 
-![Dispersion relations for $C=0.5$.](fig/disprel_C0_5_CN_BE_FE){#fig-advec-1D-disprel-C05-2 width="800px"}
+![Dispersion relations for $C=0.5$.](fig/disprel_C0_5_CN_BE_FE){#fig-advec-1D-disprel-C05-2 width="100%"}
 
 The total damping after some time $T=n\Delta t$ is reflected by
 $A_r(C,p)^n$. Since normally $A_r<1$, the damping goes like
@@ -1516,9 +1516,9 @@ and millions of cells are required to resolve the boundary layer.
 Fortunately, this is not strictly necessary as we have methods in
 the next section to overcome the problem!
 
-![Comparison of exact and numerical solution for $\epsilon =0.1$ and $N_x=20,40$ with centered differences.](fig/twopt_BVP_cen_01){#fig-advec-1D-stationary-fdm-fig1 width="800px"}
+![Comparison of exact and numerical solution for $\epsilon =0.1$ and $N_x=20,40$ with centered differences.](fig/twopt_BVP_cen_01){#fig-advec-1D-stationary-fdm-fig1 width="100%"}
 
-![Comparison of exact and numerical solution for $\epsilon =0.01$ and $N_x=20,40$ with centered differences.](fig/twopt_BVP_cen_001){#fig-advec-1D-stationary-fdm-fig2 width="800px"}
+![Comparison of exact and numerical solution for $\epsilon =0.01$ and $N_x=20,40$ with centered differences.](fig/twopt_BVP_cen_001){#fig-advec-1D-stationary-fdm-fig2 width="100%"}
 
 :::{.callout-note title="Solver"}
 A suitable solver for doing the experiments is presented below.
@@ -1598,9 +1598,9 @@ in Section @sec-advec-1D-stationary-fdm. The results appear in Figures
 @fig-advec-1D-stationary-upwind-fig1 and
 @fig-advec-1D-stationary-upwind-fig2: no more oscillations!
 
-![Comparison of exact and numerical solution for $\epsilon =0.1$ and $N_x=20,40$ with upwind difference.](fig/twopt_BVP_upw_01){#fig-advec-1D-stationary-upwind-fig1 width="800px"}
+![Comparison of exact and numerical solution for $\epsilon =0.1$ and $N_x=20,40$ with upwind difference.](fig/twopt_BVP_upw_01){#fig-advec-1D-stationary-upwind-fig1 width="100%"}
 
-![Comparison of exact and numerical solution for $\epsilon =0.01$ and $N_x=20,40$ with upwind difference.](fig/twopt_BVP_upw_001){#fig-advec-1D-stationary-upwind-fig2 width="800px"}
+![Comparison of exact and numerical solution for $\epsilon =0.01$ and $N_x=20,40$ with upwind difference.](fig/twopt_BVP_upw_001){#fig-advec-1D-stationary-upwind-fig2 width="100%"}
 
 We see that the upwind scheme is always stable, but it gives a thicker
 boundary layer when the centered scheme is also stable.

chapters/diffu/diffu_analysis.qmd

@@ -130,7 +130,7 @@ oscillations do not have a visible amplitude, while we have to wait
 until $t\sim 0.5$ before the amplitude of the long wave $\sin (\pi x)$
 becomes very small.
 
-![Evolution of the solution of a diffusion problem: initial condition (upper left), 1/100 reduction of the small waves (upper right), 1/10 reduction of the long wave (lower left), and 1/100 reduction of the long wave (lower right).](fig/diffusion_damping){#fig-diffu-pde1-fig-damping width="800px"}
+![Evolution of the solution of a diffusion problem: initial condition (upper left), 1/100 reduction of the small waves (upper right), 1/10 reduction of the long wave (lower left), and 1/100 reduction of the long wave (lower right).](fig/diffusion_damping){#fig-diffu-pde1-fig-damping width="100%"}
 
 ## Analysis of discrete equations
 A counterpart to (@eq-diffu-pde1-sol1) is the complex representation
@@ -475,11 +475,11 @@ damped by the various schemes compared to the exact damping. As long
 as all schemes are stable, the amplification factor is positive,
 except for Crank-Nicolson when $F>0.5$.
 
-![Amplification factors for large time steps.](fig/diffusion_A_F20_F2){#fig-diffu-pde1-fig-A-err-C20 width="800px"}
+![Amplification factors for large time steps.](fig/diffusion_A_F20_F2){#fig-diffu-pde1-fig-A-err-C20 width="100%"}
 
-![Amplification factors for time steps around the Forward Euler stability limit.](fig/diffusion_A_F05_F025){#fig-diffu-pde1-fig-A-err-C05 width="800px"}
+![Amplification factors for time steps around the Forward Euler stability limit.](fig/diffusion_A_F05_F025){#fig-diffu-pde1-fig-A-err-C05 width="100%"}
 
-![Amplification factors for small time steps.](fig/diffusion_A_F01_F001){#fig-diffu-pde1-fig-A-err-C01 width="800px"}
+![Amplification factors for small time steps.](fig/diffusion_A_F01_F001){#fig-diffu-pde1-fig-A-err-C01 width="100%"}
 
 The effect of negative amplification factors is that $A^n$ changes
 sign from one time level to the next, thereby giving rise to

chapters/diffu/diffu_exer.qmd

@@ -697,9 +697,9 @@ time steps.
 
 Running the `investigate` function, we get the following plots:
 
-![FIGURE: [fig-diffu/welding_gamma0_2, width=800 frac=1]](fig/welding_gamma0_025){width="800px"}
+![FIGURE: [fig-diffu/welding_gamma0_2, width=800 frac=1]](fig/welding_gamma0_025){width="100%"}
 
-![FIGURE: [fig-diffu/welding_gamma5, width=800 frac=1]](fig/welding_gamma1){width="800px"}
+![FIGURE: [fig-diffu/welding_gamma5, width=800 frac=1]](fig/welding_gamma1){width="100%"}
 
 ![For $\gamma\ll 1$ as in $\gamma = 0.025$, the heat source moves very
 slowly on the diffusion time scale and has hardly entered the medium,
@@ -709,7 +709,7 @@ each of the scalings work, but with the diffusion time scale, the heat
 source has not moved much into the domain. For $\gamma=1$, the
 mathematical problems are identical and hence the plots too. For
 $\gamma=5$, the time scale based on the source is clearly the best
-choice, and for $\gamma=40$, only this scale is appropriate.](fig/welding_gamma40){width="800px"}
+choice, and for $\gamma=40$, only this scale is appropriate.](fig/welding_gamma40){width="100%"}
 
 A conclusion is that the scaling in b) works well for a range of $\gamma$
 values, also in the case $\gamma\ll 1$.

chapters/diffu/diffu_fd1.qmd

@@ -1124,18 +1124,18 @@ Increasing $F$ slightly beyond the limit 0.5, to $F=0.51$,
 gives growing, non-physical instabilities,
 as seen in Figure @fig-diffu-pde1-FE-fig-F-051.
 
-![Forward Euler scheme for $F=0.5$.](fig/plug_FE_F05){#fig-diffu-pde1-FE-fig-F-05 width="800px"}
+![Forward Euler scheme for $F=0.5$.](fig/plug_FE_F05){#fig-diffu-pde1-FE-fig-F-05 width="100%"}
 
-![Forward Euler scheme for $F=0.25$.](fig/plug_FE_F025){#fig-diffu-pde1-FE-fig-F-025 width="800px"}
+![Forward Euler scheme for $F=0.25$.](fig/plug_FE_F025){#fig-diffu-pde1-FE-fig-F-025 width="100%"}
 
-![Forward Euler scheme for $F=0.51$.](fig/plug_FE_F051){#fig-diffu-pde1-FE-fig-F-051 width="800px"}
+![Forward Euler scheme for $F=0.51$.](fig/plug_FE_F051){#fig-diffu-pde1-FE-fig-F-051 width="100%"}
 
 Instead of a discontinuous initial condition we now try the smooth
 Gaussian function for $I(x)$. A simulation for $F=0.5$
 is shown in Figure @fig-diffu-pde1-FE-fig-gauss-F-05. Now the numerical solution
 is smooth for all times, and this is true for any $F\leq 0.5$.
 
-![Forward Euler scheme for $F=0.5$.](fig/gaussian_FE_F05){#fig-diffu-pde1-FE-fig-gauss-F-05 width="800px"}
+![Forward Euler scheme for $F=0.5$.](fig/gaussian_FE_F05){#fig-diffu-pde1-FE-fig-gauss-F-05 width="100%"}
 
 Experiments with these two choices of $I(x)$ reveal some
 important observations:
@@ -1575,7 +1575,7 @@ with sawtooth-like noise when starting with a discontinuous initial
 condition. We can also verify that we can have $F>\half$,
 which allows larger time steps than in the Forward Euler method.
 
-![Backward Euler scheme for $F=0.5$.](fig/plug_BE_F05){#fig-diffu-pde1-BE-fig-F-05 width="800px"}
+![Backward Euler scheme for $F=0.5$.](fig/plug_BE_F05){#fig-diffu-pde1-BE-fig-F-05 width="100%"}
 
 The Backward Euler scheme always produces smooth solutions for any $F$.
 Figure @fig-diffu-pde1-BE-fig-F-05 shows one example.
@@ -1592,9 +1592,9 @@ increases. Figures @fig-diffu-pde1-CN-fig-F-3 and @fig-diffu-pde1-CN-fig-F-10
 demonstrate the effect for $F=3$ and $F=10$, respectively.
 Section @sec-diffu-pde1-analysis explains why such noise occur.
 
-![Crank-Nicolson scheme for $F=3$.](fig/plug_CN_F3){#fig-diffu-pde1-CN-fig-F-3 width="800px"}
+![Crank-Nicolson scheme for $F=3$.](fig/plug_CN_F3){#fig-diffu-pde1-CN-fig-F-3 width="100%"}
 
-![Crank-Nicolson scheme for $F=10$.](fig/plug_CN_F10){#fig-diffu-pde1-CN-fig-F-10 width="800px"}
+![Crank-Nicolson scheme for $F=10$.](fig/plug_CN_F10){#fig-diffu-pde1-CN-fig-F-10 width="100%"}
 
 ## The Laplace and Poisson equation
 

chapters/diffu/diffu_rw.qmd

@@ -49,7 +49,7 @@ We introduce the symbol $N$ for the number of steps in a random walk.
 Figure @fig-diffu-randomwalk-1D-fig-ensemble shows four different
 random walks with $N=200$.
 
-![Ensemble of 4 random walks, each with 200 steps.](fig/rw1D_ensemble4){#fig-diffu-randomwalk-1D-fig-ensemble width="800px"}
+![Ensemble of 4 random walks, each with 200 steps.](fig/rw1D_ensemble4){#fig-diffu-randomwalk-1D-fig-ensemble width="100%"}
 
 ## Statistical considerations {#sec-diffu-randomwalk-1D-EVar}
 
@@ -215,7 +215,7 @@ at the origin and moves with $p=\half$. Since the seed is the same,
 the plot to the left is just a magnification of the first 1,000 steps in
 the plot to the right.
 
-![1,000 (left) and 50,000 (right) steps of a random walk.](fig/rw1D_1sample){#fig-diffu-randomwalk-1D-code1-fig1 width="800px"}
+![1,000 (left) and 50,000 (right) steps of a random walk.](fig/rw1D_1sample){#fig-diffu-randomwalk-1D-code1-fig1 width="100%"}
 
 ### Verification
 
@@ -790,11 +790,11 @@ arising from solving the diffusion equation
 that one needs significantly more statistical samples to estimate a
 histogram accurately than the expectation or variance.
 
-![Estimated expected value for 1000 steps, using 100 walks (upper left), 10,000 (upper right), 100,000 (lower left), and 1,000,000 (lower right).](fig/rw1D_EX_100_10000_100000_1000000){#fig-diffu-randomwalk-1D-fig-demo1-EX width="800px"}
+![Estimated expected value for 1000 steps, using 100 walks (upper left), 10,000 (upper right), 100,000 (lower left), and 1,000,000 (lower right).](fig/rw1D_EX_100_10000_100000_1000000){#fig-diffu-randomwalk-1D-fig-demo1-EX width="100%"}
 
-![Estimated variance over 1000 steps, using 100 walks (upper left), 10,000 (upper right), 100,000 (lower left), and 1,000,000 (lower right).](fig/rw1D_VarX_100_10000_100000_1000000){#fig-diffu-randomwalk-1D-fig-demo1-VarX width="800px"}
+![Estimated variance over 1000 steps, using 100 walks (upper left), 10,000 (upper right), 100,000 (lower left), and 1,000,000 (lower right).](fig/rw1D_VarX_100_10000_100000_1000000){#fig-diffu-randomwalk-1D-fig-demo1-VarX width="100%"}
 
-![Estimated probability distribution at step 800, using 100 walks (upper left), 10,000 (upper right), 100,000 (lower left), and 1,000,000 (lower right).](fig/rw1D_HistX_100_10000_100000_1000000){#fig-diffu-randomwalk-1D-fig-demo1-HistX width="800px"}
+![Estimated probability distribution at step 800, using 100 walks (upper left), 10,000 (upper right), 100,000 (lower left), and 1,000,000 (lower right).](fig/rw1D_HistX_100_10000_100000_1000000){#fig-diffu-randomwalk-1D-fig-demo1-HistX width="100%"}
 
 ## Empty figure cache
 \clearpage
@@ -882,7 +882,7 @@ as a walk on a *rectangular mesh* as we move from any spatial
 mesh point $(i,j)$ to one of its four neighbors in the rectangular directions:
 $(i+1,j)$, $(i-1,j)$, $(i,j+1)$, or $(i,j-1)$.
 
-![Random walks in 2D with 200 steps: rectangular mesh (left) and diagonal mesh (right).](fig/rw2D_sample200){#fig-diffu-randomwalk-2D-fig-rect-vs-diag width="800px"}
+![Random walks in 2D with 200 steps: rectangular mesh (left) and diagonal mesh (right).](fig/rw2D_sample200){#fig-diffu-randomwalk-2D-fig-rect-vs-diag width="100%"}
 
 ## Random walk in any number of space dimensions
 From a programming point of view, especially when implementing a random
@@ -1926,7 +1926,7 @@ def random_walkdD_vec(x0, N, p):
     return position
 ```
 
-![Four random walks with 5000 steps in 2D.](fig/rw2D_samples_5000){#fig-diffu-randomwalk-2D-fig-samples width="800px"}
+![Four random walks with 5000 steps in 2D.](fig/rw2D_samples_5000){#fig-diffu-randomwalk-2D-fig-samples width="100%"}
 
 ## Multiple random walks in any number of space dimensions
 As we did in 1D, we extend one single walk to a number of walks (`num_walks`

chapters/nonlin/nonlin_ode.qmd

@@ -715,9 +715,9 @@ value for $\omega$ in this case is 0.5, which results in an average of only
 $\Delta t = 1$: Picard iteration does not convergence in 1000 iterations,
 but $\omega=0.5$ again brings the average number of iterations down to 2.
 
-![Impact of solution strategy and time step length on the solution.](fig/logistic_u){#fig-nonlin-timediscrete-logistic-impl-fig-u width="800px"}
+![Impact of solution strategy and time step length on the solution.](fig/logistic_u){#fig-nonlin-timediscrete-logistic-impl-fig-u width="100%"}
 
-![Comparison of the number of iterations at various time levels for Picard and Newton iteration.](fig/logistic_iter){#fig-nonlin-timediscrete-logistic-impl-fig-iter width="800px"}
+![Comparison of the number of iterations at various time levels for Picard and Newton iteration.](fig/logistic_iter){#fig-nonlin-timediscrete-logistic-impl-fig-iter width="100%"}
 
 __Remark.__
 The simple Crank-Nicolson method with a geometric mean for the quadratic

chapters/nonlin/nonlin_split.qmd

@@ -228,7 +228,7 @@ But in very simple problems, like the logistic ODE, splitting is just an
 inferior technique. Still, the logistic ODE is ideal for introducing all
 the mathematical details and for investigating the behavior.
 
-![Effect of ordinary and Strange splitting for the logistic equation.](fig/split_logistic){#fig-nonlin-splitting-ODE-logistic-fig width="800px"}
+![Effect of ordinary and Strange splitting for the logistic equation.](fig/split_logistic){#fig-nonlin-splitting-ODE-logistic-fig width="100%"}
 
 ## Reaction-diffusion equation {#sec-nonlin-splitting-RD}