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  2. Geometric design of roads - Wikipedia

    en.wikipedia.org/wiki/Geometric_design_of_roads

    Sag vertical curves are those that have a tangent slope at the end of the curve that is higher than that of the beginning of the curve. When driving on a road, a sag curve would appear as a valley, with the vehicle first going downhill before reaching the bottom of the curve and continuing uphill or level. Crest vertical curves are those that ...

  3. Bohr–Sommerfeld model - Wikipedia

    en.wikipedia.org/wiki/Bohr–Sommerfeld_model

    The whole theory did not extend to non-integrable motions, which meant that many systems could not be treated even in principle. In the end, the model was replaced by the modern quantum-mechanical treatment of the hydrogen atom, which was first given by Wolfgang Pauli in 1925, using Heisenberg's matrix mechanics.

  4. Nearly free electron model - Wikipedia

    en.wikipedia.org/wiki/Nearly_free_electron_model

    Dispersion relation for the 2D nearly free electron model as a function of the underlying crystalline structure. The nearly free electron model is a modification of the free-electron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid.

  5. Molecular mechanics - Wikipedia

    en.wikipedia.org/wiki/Molecular_mechanics

    A force field is used to minimize the bond stretching energy of this ethane molecule.. Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields.

  6. Bohr model - Wikipedia

    en.wikipedia.org/wiki/Bohr_model

    The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell model. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory .

  7. Streeter–Phelps equation - Wikipedia

    en.wikipedia.org/wiki/Streeter–Phelps_equation

    Streeter–Phelps DO sag curve and BOD development. where D {\displaystyle D} is the saturation deficit, which can be derived from the dissolved oxygen concentration at saturation minus the actual dissolved oxygen concentration ( D = D O s a t − D O {\displaystyle D=DO_{sat}-DO} ).

  8. Rutherford scattering experiments - Wikipedia

    en.wikipedia.org/wiki/Rutherford_scattering...

    The prevailing model of atomic structure before Rutherford's experiments was devised by J. J. Thomson. [1]: 123 Thomson had discovered the electron through his work on cathode rays [2] and proposed that they existed within atoms, and an electric current is electrons hopping from one atom to an adjacent one in a series.

  9. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons , quarks , gauge bosons and the Higgs boson .