BirefringenceBirefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress.
Monochromatic radiationIn physics, monochromatic radiation is electromagnetic radiation with a single constant frequency. When that frequency is part of the visible spectrum (or near it) the term monochromatic light is often used. Monochromatic light is perceived by the human eye as a spectral color. When monochromatic radiation propagates through vacuum or a homogeneous transparent medium, it has a single constant wavelength. No radiation can be totally monochromatic, since that would require a wave of infinite duration as a consequence of the Fourier transform's localization property (cf.
Polarization (physics)Polarization (also polarisation) is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string.
Sinusoidal plane waveIn physics, a sinusoidal plane wave is a special case of plane wave: a field whose value varies as a sinusoidal function of time and of the distance from some fixed plane. It is also called a monochromatic plane wave, with constant frequency (as in monochromatic radiation). For any position in space and any time , the value of such a field can be written as where is a unit-length vector, the direction of propagation of the wave, and "" denotes the dot product of two vectors.
QR decompositionIn linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning ) and R is an upper triangular matrix (also called right triangular matrix).
Plane waveIn physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position in space and any time , the value of such a field can be written as where is a unit-length vector, and is a function that gives the field's value as dependent on only two real parameters: the time , and the scalar-valued displacement of the point along the direction . The displacement is constant over each plane perpendicular to .
LU decompositionIn numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.
Stress–strain analysisStress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. In simple terms we can define stress as the force of resistance per unit area, offered by a body against deformation.
Sine waveA sine wave, sinusoidal wave, or sinusoid is a mathematical curve defined in terms of the sine trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in mathematics, as well as in physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is: where: A, amplitude, the peak deviation of the function from zero. f, ordinary frequency, the number of oscillations (cycles) that occur each second of time.
Stress (mechanics)In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).
Cholesky decompositionIn linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ʃəˈlɛski ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.
Wave interferenceIn physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.
Coherence (physics)In physics, coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere. Physical sources are not strictly monochromatic: they may be partly coherent. Beams from different sources are mutually incoherent. When interfering, two waves add together to create a wave of greater amplitude than either one (constructive interference) or subtract from each other to create a wave of minima which may be zero (destructive interference), depending on their relative phase.
Electromagnetic radiationIn physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. Types of EMR include radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays, all of which are part of the electromagnetic spectrum. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields.
AbsorbanceAbsorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls)". Alternatively, for samples which scatter light, absorbance may be defined as "the negative logarithm of one minus absorptance, as measured on a uniform sample". The term is used in many technical areas to quantify the results of an experimental measurement. While the term has its origin in quantifying the absorption of light, it is often entangled with quantification of light which is “lost” to a detector system through other mechanisms.
Cauchy stress tensorIn continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e: or, The SI units of both stress tensor and traction vector are N/m2, corresponding to the stress scalar.
ElectromagnetismIn physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, two distinct but closely intertwined phenomena.
TransmittanceTransmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field. Internal transmittance refers to energy loss by absorption, whereas (total) transmittance is that due to absorption, scattering, reflection, etc.
Ultraviolet–visible spectroscopyUV spectroscopy or UV–visible spectrophotometry (UV–Vis or UV/Vis) refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible regions of the electromagnetic spectrum. Being relatively inexpensive and easily implemented, this methodology is widely used in diverse applied and fundamental applications. The only requirement is that the sample absorb in the UV-Vis region, i.e. be a chromophore. Absorption spectroscopy is complementary to fluorescence spectroscopy.
PhotoelasticityPhotoelasticity describes changes in the optical properties of a material under mechanical deformation. It is a property of all dielectric media and is often used to experimentally determine the stress distribution in a material, where it gives a picture of stress distributions around discontinuities in materials. Photoelastic experiments (also informally referred to as photoelasticity) are an important tool for determining critical stress points in a material, and are used for determining stress concentration in irregular geometries.
