Update index.md

Author: mtian8

docs/index.md

@@ -78,118 +78,116 @@ SciCode sources challenging and realistic research-level coding problems across
 Nobel prized related problems:
 
 ### Numerical Linear Algebra
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+1_CG
+3_Gauss_Seidel
+4_IncomChol
+5_Lanczos
+9_Weighted_Jacobi
+29_Gram_Schmidt_orthogonalization
+31_independent_component_analysis
+74_Householder_QR
 ### Computational Mechanics
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+18_NURBS
+24_Burgers_equation
+40_Spliting_Operator
+54_SUPG
+78_Chaotic_Dynamics_Pendulum
 
 ### Computational Finance
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+63_Estimating_Stock_Option_Price
 
 ### Condensed Matter Physics
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+17_linear_tetrahedron_method
+20_phonon_angular_momentum
+33_phase_diagram_chern_haldane_model
+38_Reciprocal_lattice_vector
+48_MEELS_conversion
+50_Replica_symmetry_breaking
+62_dmrg
+67_LEG_Dyson_equation_bulk
+69_LEG_Dyson_equation_semi_infinite
+72_ising_model
+73_Xray_conversion_II
+75_graphene_tight_binding
 
 ### Optics
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+2_Gaussian_Beam_Focus
+6_Spatial_filters_I
+7_Spatial_filters_II
+8_Spatial_filters_III
+14_Brownian_motion_in_the_optical_tweezer
+22_Beam_translation_reexpansion
+28_Gaussian_Beam_Intensity
+32_Multiparticle_dynamics_in_the_optical_tweezer_array
+37_ray_optics_spherical_aberration
+43_two_end_fiber_laser_generator
 
 ### Quantum Information/Computing
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+11_GADC_entanglement
+19_n_tangle
+23_Blahut_Arimoto
+59_VQE
+65_GHZ_protocol_fidelity
+71_GADC_rev_coherent_info
 
 ### Computational Physics
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+13_Maxwell_Equation_Solver
+15_Crank_Nicolson_for_time_dependent_Schrodinger
+45_finite_difference_heat_equation
+52_Shooting_algo_H_atom
+57_1D_harmonic_oscillator_numerov_shooting
 
 ### Astrophysics
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+49_nbody
+58_Tolman_Oppenheimer_Volkoff_star
 
 ### Particle Physics
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+70_neutrino_oscillation
 
 ### Quantum Chemistry
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+12_Schrodinger_DFT_with_SCF
+30_helium_slater_jastrow_wavefunction
+46_helium_atom_vmc
+66_kolmogorov_crespi_potential
+68_helium_atom_dmc
 
 ### Computational Chemistry
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+10_ewald_summation
+16_Davidson_method
+60_Widom_particle_insertion
 
 ### Ecology
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+25_CRM_in_chemostat
+26_CRM_in_serial_dilution
+41_Structural_stability_in_serial_dilution
+53_Stochastic_Lotka_Volterra
+55_Swift_Hohenberg
+56_temporal_niches
 
 ### Biochemistry
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+44_two_mer_entropy
 
 ### Genetics
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+76_protein_dna_binding
 
 ### Semiconductor Materials
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+21_Absorption_coefficient_for_alloy_GaAlAs
+27_Design_trade_offs_for_high_speed_photodetectors
+34_PN_diode_band_diagram
+35_Quantum_Dot_Absorption_Spectrum
+36_Quasi_Fermi_levels_of_photo_resistor_out_of_equilibrium
+39_Reflection_spectra_for_a_Distributed_Bragg_Reflector
+42_The_threshold_current_for_multi_quantum_well_lasers
 
 ### Molecular Modeling
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-## Example Problem: Calculate Chern numbers for the Haldane Model
+47_Internal_Energy
+51_Simple_Molecular_Dynamics
+64_GCMC
+77_Berendsen_thermostat
+79_Nose_Hoover_chain_thermostat
+80_Anderson_thermostat
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+## Example: Calculate Chern numbers for the Haldane Model
 ### Main Problem and Dependencies
 **1. Generate an array of Chern numbers for the Haldane model on a hexagonal lattice by sweeping the following parameters: the on-site energy to next-nearest-neighbor coupling constant ratio ($m/t_2$ from -6 to 6 with $N$ samples) and the phase ($\phi$ from -$\pi$ to $\pi$ with $N$ samples) values. Given the lattice spacing $a$, the nearest-neighbor coupling constant $t_1$, the next-nearest-neighbor coupling constant $t_2$, the grid size $\delta$ for discretizing the Brillouin zone in the $k_x$ and $k_y$ directions (assuming the grid sizes are the same in both directions), and the number of sweeping grid points $N$ for $m/t_2$ and $\phi$.**