Relaxation

relaxation

1. Physics the return of a system to equilibrium after a displacement from this state 2. Maths a method by which errors resulting from an approximation are reduced by using new approximations

Relaxation

the process of the achievement of thermodynamic and, consequently, statistical equilibrium in a physical system consisting of a large number of particles. Relaxation is a multistage process, since the physical parameters of the system—such as the distribution of the particles with respect to coordinates and momenta and the temperature, pressure, and concentration in small volumes and throughout the entire system—do not all approach equilibrium at the same rate. Usually, a state of partial equilibrium is first reached, that is, equilibrium with respect to some parameter. The term “relaxation” is also applied to this case. All relaxation processes are nonequi-librium processes in which energy is dissipated in the system—that is, entropy is produced (in a closed system the entropy increases). The characteristics of relaxation are different in different systems and depend on the nature of the interaction between the system’s particles; relaxation processes are therefore extremely varied. The characteristic time required for a system to approach partial or complete equilibrium is called the relaxation time.

The process of the achievement of equilibrium in a gas is determined by the mean free path l of the particles and by the mean free time τ, which are the average distance and average time, respectively, between two successive collisions of molecules. The ratio l/τ is of the order of the speed of the particles. The quantities l and τ are very small compared with macroscopic scales of length and time. On the other hand, for gases the mean free time is much greater than the collision time τ₀: τ ≫ τ₀. Relaxation is determined solely by binary collisions of molecules only when this condition is satisfied.

Monatomic gases. In monatomic gases, which lack internal degrees of freedom and have only translational degrees of freedom, relaxation occurs in two stages. In the first stage, the initial state, which may be even a markedly nonequilibrium state, is randomized in a short period of time of the order of the collision time τ₀ of the molecules. The randomization occurs in such a way that the details of the initial state become insignificant, and an abbreviated description of the nonequilibrium state of the system is possible. This means that knowledge of the probability of the distribution of all particles in the system with respect to coordinates and momenta is not required. It is sufficient to know the single-particle distribution function, that is the distribution of one particle with respect to coordinates and momenta as a function of time. (Higher-order distribution functions, which describe distributions with respect to the states of two, three, or more particles, depend on time only through the single-particle function.) The one-particle function satisfies the Boltzmann equation, which describes the process of relaxation. This stage is called the kinetic stage and is a very rapid relaxation process.

In the second stage, local equilibrium is achieved in macro-scopically small volumes of the system in a time of the order of the mean free time τ of the molecules as a result of only a few collisions. To this local equilibrium there corresponds a local-equilibrium, or quasi-equilibrium, distribution, which is characterized by the same parameters as in the case of complete equilibrium of the system but is dependent on the spatial coordinates and time. These small volumes still contain numerous molecules, and since they interact with the surroundings only at the surface, they may be considered approximately isolated. The parameters of a local-equilibrium distribution in a relaxation process slowly tend toward the equilibrium parameters, and the state of the system usually differs little from the equilibrium state. The relaxation time for local equilibrium is t_e ≈ τ. After local equilibrium is reached, the equations of hydrodynamics, such as the Navier-Stokes equations and the heat-flow and diffusion equations, are used to describe the relaxation of the nonequilibrium state of the system. Here it is assumed that the thermodynamic parameters of the system, such as density and temperature, and the mass velocity (the average rate of transfer of mass) vary little during a time τ and over a distance l. This stage of relaxation is called the hydrodynamic stage.

The further relaxation of the system to a state of complete statistical equilibrium, in which the average speeds of the particles, the average, temperature, the average concentration, and other parameters are equalized, proceeds slowly because of the large number of collisions. Such slow processes include viscosity, heat conduction, diffusion, and electrical conduction. The corresponding relaxation time t_e depends on the dimensions L of the system and is great compared with τ: t_e ~ τ (L/l)² ≫ τ. This relation holds when l ≪ L —that is, for gases that are not extremely rarefied.

Polyatomic gases. In polyatomic gases, which have internal degrees of freedom, the exchange of energy between transla-tional and internal degrees of freedom may be slow, and a relaxation process associated with this phenomenon arises. Equilibrium with respect to translational degrees of freedom is achieved rather quickly—in a time of the order of the time between collisions; such an equilibrium state can be characterized by the corresponding temperature. Equilibrium between translational and rotational degrees of freedom is achieved much more slowly. The excitation of vibrational degrees of freedom can occur only at high temperatures. Multistage processes of relaxation of vibrational and rotational degrees of freedom are therefore possible in polyatomic gases.

Gaseous mixtures. In mixtures of gases whose molecules are of markedly differing mass, the energy exchange between the components is slow. Consequently, a state wherein the components have different temperatures may occur, and temperature relaxation processes are possible. For example, in a plasma the masses of the ions and electrons are very different. The electronic component reaches equilibrium before the ionic component. A much longer time is required to achieve equilibrium between electrons and ions. For this reason, in a plasma there can exist for a long time states in which the ion and electron temperatures are different and in which, consequently, the processes of relaxation of the temperatures of the components occur.

Liquids. In liquids, the concept of the mean free time and path of particles and, consequently, the kinetics equations for the single-particle distribution function are not applicable. For liquids, a role analogous to that of the mean free time and mean free path is played by the quantities τ₁ and l₁, the correlation time and correlation length, respectively, of the dynamic variables describing the fluxes of energy or momentum. The quantities τ₁ and l₁, characterize the attenuation in time and space of the mutual influence of the molecules—that is, they characterize the attenuation of a correlation. Here the concepts of the hydrodynamic stage of relaxation and of the local-equilibrium state remain fully valid. In macroscopically small volumes of a liquid that are still quite large compared with the correlation length l_l a local-equilibrium distribution is achieved in a time of the order of the correlation time τ₁ (t_e ≈ τ₁) as a result of intensive interaction between the molecules. Although the local-equilibrium distribution is not a result of binary collisions, as in a gas, these volumes may still be assumed to be approximately isolated. In the hydrodynamic stage of relaxation in a liquid, the thermodynamic parameters and mass velocity satisfy the same equations of hydrodynamics as for gases, if the change in the thermodynamic parameters and mass velocity during a time τ₁ and over a distance l₁, is small. As in a gas or solid, the relaxation time to complete thermodynamic equilibrium is t_e ≈ τ₁(L/l₁)² and can be estimated by using the kinetic coefficients (seeKINETICS, PHYSICAL). For example, the concentration relaxation time in a binary mixture in the volume L³ is of the order of t_e ≈ L²/D, where D is the diffusion coefficient. Another example is the temperature relaxation time, which is t_e ≈ L²/x, where x is the thermal diffusivity. For a liquid where the molecules have internal degrees of freedom, the hydrodynamic description of translational degrees of freedom can be combined with additional equations-to describe the relaxation of the internal degrees of freedom.

Solids. In solids, as in quantum fluids, relaxation can be described as relaxation in a gas of quasiparticles. In this case, we can speak of the mean free time and path of the corresponding quasiparticles, provided that the excitation of the system is small. For example, elastic vibrations in a crystal lattice at low temperatures can be interpreted as a phonon gas. The interaction between the phonons results in quantum transitions, that is, in collisions between the phonons. In the system of spin magnetic moments of a ferromagnetic substance, magnons are the quasiparticles; relaxation of, for example, magnetization can be described by the kinetic equation for magnons. The relaxation of the magnetic moment in a ferromagnetic material occurs in two stages. In the first stage, the absolute value of the magnetic moment reaches its equilibrium value through a relatively strong exchange interaction. In the second stage, the magnetic moment is slowly oriented along the direction of easy magnetization as a result of a weak spin-orbit interaction. This stage is analogous to the hydrodynamic stage of relaxation in gases.

REFERENCE

Uhlenbeck, G., and J. Ford. Lektsiipo statisticheskoi mekhanike. Moscow, 1965. (Translated from English.)

D. N. ZUBAREV

Relaxation

in physiology and medicine, the decrease in the tonus of the skeletal musculature, caused, in particular, by various chemical substances and manifested in a decrease of motor activity or complete immobilization, or paralysis.

The extensiveness, degree, and duration of relaxation depend on the site of disruption of conduction of the nerve impulse and on the chemical substance used. Narcotic substances act on the central sections of the nervous system and produce a widespread but incomplete relaxation. Substances used for local anesthesia act on peripheral nerves, causing local incomplete relaxation. The most extensive and complete relaxation is observed upon injection of special preparations called muscle relaxants.

relaxation

[‚rē‚lak′sā·shən] (geology) In experimental structural geology, the diminution of applied stress with time, as the result of any of various creep processes. (mathematics) relaxation method (mechanics) Relief of stress in a strained material due to creep. The lessening of elastic resistance in an elastic medium under an applied stress resulting in permanent deformation. (physics) A process in which a physical system approaches a steady state after conditions affecting it have been suddenly changed, and in which the presence of dissipative agents prevents the system from overshooting and then oscillating about this state.

relaxation

[re″lak-sa´shun] a lessening of tension.relaxation/breathing techniques in the omaha system, activities that relieve muscle tension, induce a quiet body response, and rebuild energy resources; this may include deep breathing exercises, imagery, meditation, and other techniques.force relaxation the decrease in the amount of force required to maintain a tissue at a set amount of displacement or deformation over time.progressive relaxation a method of deep muscle relaxation based on the premise that muscle tension is the body's physiological response to anxiety-provoking thoughts and that muscle relaxation blocks anxiety.progressive muscle relaxation 1. progressive relaxation.2. in the nursing interventions classification, a intervention" >nursing intervention defined as facilitating the tensing and releasing of successive muscle groups while attending to the resulting differences in sensation.relaxation techniques methods used to promote lessening of tension, reduction of anxiety, and management of pain. Physiologic effects include a decrease in pulse rate, respiratory rate and oxygen consumption, carbon dioxide production and elimination, blood pressure, metabolic rate, and muscle tension. Additionally, relaxation can cause peripheral vasodilation and increased peripheral temperature.

Relaxation techniques include full-body relaxation, color exchange, in which a discomfort is given a color and eliminated, and listening to restful music or meditative sounds. Such techniques are helpful in many situations in which persons are tense, in pain, highly stressed, or anxious. They can be useful in the treatment of asthma, hyperventilation, high blood pressure, Raynaud's disease, headache, and peptic ulcers.
Though varied, techniques have several features in common: rhythmic breathing, reduced muscle tension, and an altered state of consciousness. In the latter, the relaxed person sinks into an alpha level of consciousness, which falls between full consciousness and unconsciousness. In this state thought processes become less logical and more associative and creative; hence, one is more receptive to positive suggestions, and better able to concentrate on a single mental image or idea. Upon returning from the alpha state of consciousness to full consciousness one feels rested and more alert.

re·lax·a·tion

(rē'lak-sā'shŭn), 1. Loosening, lengthening, or lessening of tension in a muscle. 2. Loss of adequate muscle tone (for example, pelvic relaxation episiotomy). 3. In nuclear magnetic resonance, relaxation is the decay in magnetization of protons after the direction of the surrounding magnetic field is changed; the different rates of relaxation for individual nuclei and tissues are used to provide contrast in imaging. [L. relaxatio (see relax)]

relaxation

(rē′lăk-sā′shən)n.1. The act of relaxing or the state of being relaxed.2. Refreshment of body or mind; recreation: played golf for relaxation.3. A loosening or slackening.4. A reduction in strictness or severity.5. Physiology The lengthening of inactive muscle or muscle fibers.6. Physics The return or adjustment of a system to equilibrium following displacement or abrupt change.7. Mathematics A method of solving equations in which the errors resulting from an initial approximation are reduced by succeeding approximations until all errors are within specified limits.

relaxation

(1) The act of relaxing by limiting activity or movement.
(2) A generic term for intentional nonactivity, in which a person performs active or passive exercises intended to reduce mental and physical stress.

relaxation

1. The proactive act of not actively acting.2. Intentional inactivity, where a person performs active or passive exercises to ↓ mental and physical stress. See Longitudinal relaxation, Progressive relaxation, Relaxation training.

re·lax·a·tion

(rē'lak-sā'shŭn) 1. Loosening, lengthening, or lessening of tension in a muscle. 2. magnetic resonance imaging The decay in magnetization of tissue after the direction of the surrounding magnetic field is changed; the different rates of relaxation for individual nuclei and tissues are used to provide contrast in imaging.

re·lax·a·tion

(rē'lak-sā'shŭn) Loosening, lengthening, or lessening of tension in a muscle.

Patient discussion about relaxation

Q. I become quite normal when relaxed but I am not able to do so. I don’t know how to make myself happy? I am a normal person but some of my action due to continuous stress is making me to think as If I am a lunatic. I cannot tolerate the stress and it makes me to drink a lot of alcohol. This takes a lot of energy out of me and I eat heavily. My love for snacks and grilled chicken has increased now and I feel satisfied when I eat them and I feel relaxed too. Sometimes I tend to tear everything near to me and run away. I become quite normal when relaxed but I am not able to do so. I don’t know what to do and how to make myself happy.A. The stress must be controlled or else it will ruin your physical, mental and emotional wellbeing. You are eating a lot of junks and alcohol and this will pile up the problem. You must meet a doctor but try my tips before that. Try to go for meditation classes. Go for some sports or exercise. Have a very good sleep as it’s a big buster. Limit on any drugs if you are taking. Think what makes you stressed up. Find a way to solve it. Talk to someone if you cannot find a solution. If no one can suggest you better then meet a doctor for the help.
http://www.youtube.com/watch?v=1b7MPdfzoQI&eurl=http://www.imedix.com/health_community/v1b7MPdfzoQI_10_tips_better_sleep?q=meditation%20alcohol&feature=player_embedded

Q. I need to know how to get rid of stress, can someone help? because either i am stressing about a project or something about school or im just stressed about life in general. Please help me and no negative comments.A. 1.Take a deep breath. This is your first, most immediate defense against stress. If you can get in the habit of pausing and taking a nice, deep breath every time you feel stress beginning to take hold, you'll have won half the battle just by preventing it from taking over.
2.Communicate. Whether you talk to a friend or talk to your cat, getting it off your chest will help a lot. If you don't feel like talking about it, write it down. Keep a journal and write down whatever it is that's bothering you. Writing is a therapy of its own.
3.Laugh. Rediscover your sense of humor by making fun of your situation. View it from your future self's perspective, telling this story to a bunch of your friends over pizza and soda. Crack some jokes. Do your goofiest impression. Tickle a child that you love. Laughter, whether it's yours or someone else's, is the best medicine--and it's contagious!
For complete article :http://www.wikihow.com/Relieve-Stress
Hope this helps.

Q. Is “domestic violence” can be considered a medical issue? Is it curable? My partner is showing scary signs of violence…can it be treated with some sort of medication?A. you can also tyr to get him into an anger management class,that might also help both of you.

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REFERENCE

Relaxation

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Patient discussion about relaxation

relaxation

Synonyms for relaxation

noun leisure

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noun lessening

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noun freedom from labor, responsibility, or strain

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noun (physiology) the gradual lengthening of inactive muscle or muscle fibers

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noun (physics) the exponential return of a system to equilibrium after a disturbance

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noun a feeling of refreshing tranquility and an absence of tension or worry

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noun an occurrence of control or strength weakening

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noun freedom from activity (work or strain or responsibility)

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noun a method of solving simultaneous equations by guessing a solution and then reducing the errors that result by successive approximations until all the errors are less than some specified amount

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noun the act of making less strict

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