|
Magic Angle
The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, , and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle. This property makes the magic angle of particular importance in magic angle spinning solid-state NMR spectroscopy. In magnetic resonance imaging, structures with ordered collagen, such as tendons and ligaments, oriented at the magic angle may appear hyperintense in some sequences; this is called the magic angle artifact or effect. Mathematical definition The magic angle ''θ''m is : \theta_\mathrm = \arccos \frac = \arctan \sqrt \approx 0.955\,32\ \text \approx 54.7^\circ \! , where arccos and arctan are the inverse cosine and tangent functions respectively. ''θ''m is the angle between the space diagonal of a cube and any of its three connecting edges, see image. Another representation of the magic angle is half of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legendre Polynomial
In physical science and mathematics, Legendre polynomials (named after Adrien-Marie Legendre, who discovered them in 1782) are a system of complete and orthogonal polynomials, with a vast number of mathematical properties, and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and associated Legendre functions. Definition by construction as an orthogonal system In this approach, the polynomials are defined as an orthogonal system with respect to the weight function w(x) = 1 over the interval 1,1/math>. That is, P_n(x) is a polynomial of degree n, such that \int_^1 P_m(x) P_n(x) \,dx = 0 \quad \text n \ne m. With the additional standardization con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dipolar Coupling
In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: *An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system is a pair of charges of equal magnitude but opposite sign separated by some typically small distance. (A permanent electric dipole is called an electret.) *A magnetic dipole is the closed circulation of an electric current system. A simple example is a single loop of wire with constant current through it. A bar magnet is an example of a magnet with a permanent magnetic dipole moment. Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges. (To be precise: for the definition of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuclear Magnetic Resonance Spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio waves into nuclear magnetic resonance, which is detected with sensitive radio receivers. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. As the fields are unique or highly characteristic to individual compounds, in modern organic chemistry practice, NMR spectroscopy is the definitive method to identify monomolecular organic compounds. The principle of NMR usually involves three sequential steps: # The alignment (polarization) of the magnetic nuclear spins in an applied, constant magnetic field B0. # The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hose
A hose is a flexible hollow tube designed to carry fluids from one location to another. Hoses are also sometimes called ''pipes'' (the word ''pipe'' usually refers to a rigid tube, whereas a hose is usually a flexible one), or more generally '' tubing''. The shape of a hose is usually cylindrical (having a circular cross section). Hose design is based on a combination of application and performance. Common factors are size, pressure rating, weight, length, straight hose or coilhose, and chemical compatibility. Applications mostly use nylon, polyurethane, polyethylene, PVC, or synthetic or natural rubbers, based on the environment and pressure rating needed. In recent years, hoses can also be manufactured from special grades of polyethylene (LDPE and especially LLDPE). Other hose materials includPTFE(Teflon), stainless steel, and other metals. Dredge rubber hoses have a long story, which features high strength and flexibility. A flexible dredging hose widely used in dredgers t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supraspinatus Tendinitis
Shoulder impingement syndrome is a syndrome involving tendonitis (inflammation of tendons) of the rotator cuff muscles as they pass through the subacromial space, the passage beneath the acromion. It is particularly associated with tendonitis of the supraspinatus muscle. This can result in pain, weakness, and loss of movement at the shoulder. Signs and symptoms The most common symptoms in impingement syndrome are pain, weakness and a loss of movement at the affected shoulder. The pain is often worsened by shoulder overhead movement and may occur at night, especially when lying on the affected shoulder. The onset of the pain may be acute if due to an injury or insidious if due to a gradual process such as an osteoarthritic spur. The pain has been described as dull rather than sharp, and lingers for long periods of time, making it hard to fall asleep. Other symptoms can include a grinding or popping sensation during movement of the shoulder. The range of motion at the shoulder may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotator Cuff
The rotator cuff is a group of muscles and their tendons that act to stabilize the human shoulder and allow for its extensive range of motion. Of the seven scapulohumeral muscles, four make up the rotator cuff. The four muscles are the supraspinatus muscle, the infraspinatus muscle, teres minor muscle, and the subscapularis muscle. Structure Muscles composing rotator cuff The supraspinatus muscle spreads out in a horizontal band to insert on the superior facet of the greater tubercle of the humerus. The greater tubercle projects as the most lateral structure of the humeral head. Medial to this, in turn, is the lesser tubercle of the humeral head. The subscapularis muscle origin is divided from the remainder of the rotator cuff origins as it is deep to the scapula. The four tendons of these muscles converge to form the rotator cuff tendon. These tendinous insertions along with the articular capsule, the coracohumeral ligament, and the glenohumeral ligament complex, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MRI Sequence
An MRI sequence in magnetic resonance imaging (MRI) is a particular setting of pulse sequences and pulsed field gradients, resulting in a particular image appearance. A multiparametric MRI is a combination of two or more sequences, and/or including other specialized MRI configurations such as spectroscopy. Spin echo T1 and T2 Each tissue returns to its equilibrium state after excitation by the independent relaxation processes of T1 ( spin-lattice; that is, magnetization in the same direction as the static magnetic field) and T2 ( spin-spin; transverse to the static magnetic field). To create a T1-weighted image, magnetization is allowed to recover before measuring the MR signal by changing the repetition time (TR). This image weighting is useful for assessing the cerebral cortex, identifying fatty tissue, characterizing focal liver lesions, and in general, obtaining morphological information, as well as for post-contrast imaging. To create a T2-weighted image, magnetizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Angle Spinning
In solid-state NMR spectroscopy, magic-angle spinning (MAS) is a technique routinely used to produce better resolution NMR spectra. MAS NMR consists in spinning the sample (usually at a frequency of 1 to 130 kHz) at the magic angle θm (ca. 54.74°, where cos2θm=1/3) with respect to the direction of the magnetic field. Three main interactions responsible in solid state NMR (dipolar, chemical shift anisotropy, quadrupolar) often lead to very broad and featureless NMR lines. However, these three interactions in solids are orientation-dependent and can be averaged to some extent by MAS: * The nuclear dipolar interaction has a 3\cos^2\theta - 1 dependence, where \theta is the angle between the internuclear axis and the main magnetic field. As a result, the dipolar interaction vanish at the magic angle θm and the interaction contributing to the line broadening is removed. Even though all internuclear vectors cannot be all set to the magic angle, rotating the sample around this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid-state Nuclear Magnetic Resonance
Solid-state NMR (ssNMR) spectroscopy is a technique for characterizing atomic level structure in solid materials e.g. powders, single crystals and amorphous samples and tissues using nuclear magnetic resonance (NMR) spectroscopy. The anisotropic part of many spin interactions are present in solid-state NMR, unlike in solution-state NMR where rapid tumbling motion averages out many of the spin interactions. As a result, solid-state NMR spectra are characterised by larger linewidths than in solution state NMR, which can be utilized to give quantitative information on the molecular structure, conformation and dynamics of the material. Solid-state NMR is often combined with magic angle spinning to remove anisotropic interactions and improve the resolution as well as the sensitivity of the technique. Nuclear spin interactions The resonance frequency of a nuclear spin depends on the strength of the magnetic field at the nucleus, which can be modified by isotropic (e.g. chemical shift, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Shift Anisotropy
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a molecule. Chemical shifts are also used to describe signals in other forms of spectroscopy such as photoemission spectroscopy. Some atomic nuclei possess a magnetic moment (nuclear spin), which gives rise to different energy levels and resonance frequencies in a magnetic field. The total magnetic field experienced by a nucleus includes local magnetic fields induced by currents of electrons in the molecular orbitals (note that electrons have a magnetic moment themselves). The electron distribution of the same type of nucleus (e.g. ) usually varies according to the local geometry (binding partners, bond lengths, angles between bonds, and so on), and with it the local magnetic field at each nucleus. This is reflected in the spin energy leve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
