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Showing posts with label Physics:general. Show all posts
Showing posts with label Physics:general. Show all posts
April 9, 2014
February 10, 2014
Accuracy and precision
In industrial instrumentation: Accuracy is the measurement tolerance, or transmission of the instrument and defines the limits of the errors made when the instrument is used in normal operating conditions, according to the book of industrial instrumentation Antonio Creus.
Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the known value. The accuracy and precision of a measurement process is usually established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units (abbreviated SI from French: Système international d'unités) and maintained by national standards organizations such as the National Institute of Standards and Technology in the United States.
This also applies when measurements are repeated and averaged. In that case, the term standard error is properly applied: the precision of the average is equal to the known standard deviation of the process divided by the square root of the number of measurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements.
With regard to accuracy we can distinguish:
A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Here, when not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m (the last significant place is the tenths place), while a recording of 8,436 m would imply a margin of error of 0.5 m (the last significant digits are the units).
A reading of 8,000 m, with trailing zeroes and no decimal point, is ambiguous; the trailing zeroes may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: 8.0 × 103 m indicates that the first zero is significant (hence a margin of 50 m) while 8.000 × 103 m indicates that all three zeroes are significant, giving a margin of 0.5 m. Similarly, it is possible to use a multiple of the basic measurement unit: 8.0 km is equivalent to 8.0 × 103 m. In fact, it indicates a margin of 0.05 km (50 m). However, reliance on this convention can lead to false precision errors when accepting data from sources that do not obey it.
Precision is sometimes stratified into:
Repeatability — the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; and
Reproducibility — the variation arising using the same measurement process among different instruments and operators, and over longer time periods.
Terminology of ISO 5725
A shift in the meaning of these terms appeared with the publication of the ISO 5725 series of standards, which is also reflected in the 2008 issue of the "BIPM International Vocabulary of Metrology" (VIM), items 2.13 and 2.14. [1]
According to ISO 5725-1,[3] the terms trueness and precision are used to describe the accuracy of a measurement. Trueness refers to the closeness of the mean of the measurement results to the actual (true) value and precision refers to the closeness of agreement within individual results. Therefore, according to the ISO standard, the term "accuracy" refers to both trueness and precision.
ISO 5725-1 also avoids the use of the term bias, because it has different connotations outside the fields of science and engineering, as in medicine and law.
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Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the known value. The accuracy and precision of a measurement process is usually established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units (abbreviated SI from French: Système international d'unités) and maintained by national standards organizations such as the National Institute of Standards and Technology in the United States.
This also applies when measurements are repeated and averaged. In that case, the term standard error is properly applied: the precision of the average is equal to the known standard deviation of the process divided by the square root of the number of measurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements.
With regard to accuracy we can distinguish:
- the difference between the mean of the measurements and the reference value, the bias. Establishing and correcting for bias is necessary for calibration.
- the combined effect of that and precision.
A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Here, when not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m (the last significant place is the tenths place), while a recording of 8,436 m would imply a margin of error of 0.5 m (the last significant digits are the units).
A reading of 8,000 m, with trailing zeroes and no decimal point, is ambiguous; the trailing zeroes may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: 8.0 × 103 m indicates that the first zero is significant (hence a margin of 50 m) while 8.000 × 103 m indicates that all three zeroes are significant, giving a margin of 0.5 m. Similarly, it is possible to use a multiple of the basic measurement unit: 8.0 km is equivalent to 8.0 × 103 m. In fact, it indicates a margin of 0.05 km (50 m). However, reliance on this convention can lead to false precision errors when accepting data from sources that do not obey it.
Precision is sometimes stratified into:
Repeatability — the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; and
Reproducibility — the variation arising using the same measurement process among different instruments and operators, and over longer time periods.
Terminology of ISO 5725
A shift in the meaning of these terms appeared with the publication of the ISO 5725 series of standards, which is also reflected in the 2008 issue of the "BIPM International Vocabulary of Metrology" (VIM), items 2.13 and 2.14. [1]
According to ISO 5725-1,[3] the terms trueness and precision are used to describe the accuracy of a measurement. Trueness refers to the closeness of the mean of the measurement results to the actual (true) value and precision refers to the closeness of agreement within individual results. Therefore, according to the ISO standard, the term "accuracy" refers to both trueness and precision.
ISO 5725-1 also avoids the use of the term bias, because it has different connotations outside the fields of science and engineering, as in medicine and law.
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August 24, 2011
Induced radioactivity
Wikipedia, the free encyclopedia
Induced radioactivity occurs when a previously stable material has been made radioactive by exposure to specific radiation. Most radioactivity does not induce other material to become radioactive.
Neutron activation is the main form of induced radioactivity, which happens when free neutrons are captured by nuclei. This new heavier isotope can be stable or unstable (radioactive) depending on the chemical element involved. Because free neutrons disintegrate within minutes outside of an atomic nucleus, neutron radiation can be obtained only from nuclear disintegrations, nuclear reactions, and high-energy reactions (such as in cosmic radiation showers or particle accelerator collisions). Neutrons that have been slowed down through a neutron moderator (thermal neutrons) are more likely to be captured by nuclei than fast neutrons.
A less common form involves removing a neutron via photodisintegration. In this reaction, a high energy photon (gamma ray) strikes a nucleus with an energy greater than the binding energy of the atom, releasing a neutron. This reaction has a minimum cutoff of 2 MeV (for hydrogen)
and around 10 MeV for most heavy nuclei. Many radionuclides do not
produce gamma rays with energy high enough to induce this reaction. The isotopes used in food irradiation (cobalt-60, caesium-137) both have energy peaks below this cutoff and thus cannot induce radioactivity in the food.[1]
Some induced radioactivity is produced by background radiation, which is mostly natural. However, since natural radiation is not very intense in most places on Earth, the amount of induced radioactivity in a single location is usually very small.
The conditions inside certain types of nuclear reactors with high neutron flux
can cause induced radioactivity. The components in those reactors may
become highly radioactive from the radiation to which they are exposed.
Induced radioactivity increases the amount of nuclear waste that must eventually be disposed, but it is not referred to as radioactive contamination unless it is uncontrolled.
See also
Notes- ^ Caesium-137 emits gammas at 662 keV while cobalt-60 emits gammas at 1.2 and 1.3 MeV.
Energies in electron volts
Room temperature thermal energy of a molecule..................................0.04 eV
Visible light photons...........................................................................1.5-3.5 eV
Energy for the dissociation of an NaCl molecule into Na+ and Cl- ions:.............................................................................................4.2 eV
Ionization energy of atomic hydrogen ...................................................13.6 eV
Approximate energy of an electron striking a color television screen (CRT display) ...............................................................................20,000 eV
High energy diagnostic medical x-ray photons..................200,000 eV (=0.2 MeV)
Typical energies from nuclear decay:
(1) gamma..................................................................................0-3 MeV
(2) beta.......................................................................................0-3 MeV
(3) alpha......................................................................................2-10 MeV
Cosmic ray energies ...........................................................1 MeV - 1000 TeV
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Visible light photons...........................................................................1.5-3.5 eV
Energy for the dissociation of an NaCl molecule into Na+ and Cl- ions:.............................................................................................4.2 eV
Ionization energy of atomic hydrogen ...................................................13.6 eV
Approximate energy of an electron striking a color television screen (CRT display) ...............................................................................20,000 eV
High energy diagnostic medical x-ray photons..................200,000 eV (=0.2 MeV)
Typical energies from nuclear decay:
(1) gamma..................................................................................0-3 MeV
(2) beta.......................................................................................0-3 MeV
(3) alpha......................................................................................2-10 MeV
Cosmic ray energies ...........................................................1 MeV - 1000 TeV
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July 7, 2011
June 18, 2011
Cherenkov radiation
Here is a snapshot from Google Earth. A boat moves with velocity higher than the phase velocity of the waves in water.
June 3, 2011
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:
where
F is the force (in newtons)
E is the electric field (in volts per metre)
B is the magnetic field (in teslas)
q is the electric charge of the particle (in coulombs)
v is the instantaneous velocity of the particle (in metres per second)
× is the vector cross product
All the quantities written in boldface are vectors (in particular, F, E, v, B).
Trajectory of a particle with a positive or negative charge q under the influence of a magnetic field B, which is directed perpendicularly out of the screen.
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F is the force (in newtons)
E is the electric field (in volts per metre)
B is the magnetic field (in teslas)
q is the electric charge of the particle (in coulombs)
v is the instantaneous velocity of the particle (in metres per second)
× is the vector cross product
All the quantities written in boldface are vectors (in particular, F, E, v, B).
Trajectory of a particle with a positive or negative charge q under the influence of a magnetic field B, which is directed perpendicularly out of the screen.
June 2, 2011
Lenz's Law and Eddy currents
This is a short animation which depicts Lenz's Law and how changing magnetic flux creates an induced current.
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In 1834, Heinrich Lenz stated Lenz's law, which says that the direction of induced current flow in an object will be such that its magnetic field will oppose the magnetic field that caused the current flow. Eddy currents develop secondary flux that cancels a part of the external flux.
Eddy currents (also called Foucault currents) are currents induced in conductors, when a conductor is exposed to a changing magnetic field due to relative motion of the field source and conductor; or due to variations of the field with time. This can cause a circulating flow of electrons, or a current, within the body of the conductor. These circulating eddies of current have inductance and thus induce magnetic fields.
The stronger the applied magnetic field, or the greater the electrical conductivity of the conductor, or the faster the field changes, then the greater the currents that are developed and the greater the fields produced.
Eddy currents, like all electric currents, generate heat as well as electromagnetic forces.
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©
In 1834, Heinrich Lenz stated Lenz's law, which says that the direction of induced current flow in an object will be such that its magnetic field will oppose the magnetic field that caused the current flow. Eddy currents develop secondary flux that cancels a part of the external flux.
Eddy currents (also called Foucault currents) are currents induced in conductors, when a conductor is exposed to a changing magnetic field due to relative motion of the field source and conductor; or due to variations of the field with time. This can cause a circulating flow of electrons, or a current, within the body of the conductor. These circulating eddies of current have inductance and thus induce magnetic fields.
The stronger the applied magnetic field, or the greater the electrical conductivity of the conductor, or the faster the field changes, then the greater the currents that are developed and the greater the fields produced.
Eddy currents, like all electric currents, generate heat as well as electromagnetic forces.
©
May 24, 2011
Standing Wave in a String
Interference between two waves traveling in opposite directions in a string whose ends are both fixed produces a standing wave. These videos show the first 6 modes of vibration of a standing wave in a string (there is a node at each end). For each mode of vibration, a first movie shows the two moving waves (green and cyan) and the resulting standing wave (yellow); a second animation show the standing wave only.
©
April 6, 2011
definition of eigen-
from Oxford Dictionaries Online
eigen-
Pronunciation:/ˈʌɪg(ə)n/
Mathematics & Physics
proper; characteristic:eigenfunction
Origin:
from German eigen 'own'
©
eigen-
Pronunciation:/ˈʌɪg(ə)n/
Mathematics & Physics
proper; characteristic:eigenfunction
Origin:
from German eigen 'own'
©
October 20, 2010
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