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Zero-point

Additional assistance is provided by secondary modification options that allow among others for a depiction of the original signal, the reconstruction of the depiction of the impedance plane of the eddy-current signals or for modifications of phase, amplification or zero point virtually in real time. That way, once C-scan images have been recorded, they can now be evaluated as needed without having to repeat the test. [Pg.309]

Calibration procedure bases on rope specimens and corresponds to the Standard Pratice ASTM 1574. It takes a piece of the rope under test having a nominal metallic cross-section area (LMA=0) to set zero point of the instrument. Rope section with the LMA value known is used to set the second point of LMA calibration charactiristics. It is possible to use the air point calibration when there is no rope in a magnetic head (LMA=100%). [Pg.337]

Shoe Delay. Defines the shoe, or wedge, delay, in tenths of microseconds, of the prohe being used. This control is used to adjust the zero point of time interval measurement to correspond to the instant that the ultrasound pulse enters the test piece. [Pg.770]

Here the zero point energy is temporarily suppressed. Now the exponential is a product of independent factors. Thus one gets... [Pg.409]

This is the Planck distribution function. The themial average energy in theyth mode is (including the zero point energy)... [Pg.409]

Flere the zero point energy is ignored, which is appropriate at reasonably large temperatures when the average occupation number is large. In such a case one can also replace the sum over by an integral. Each of the triplet n can take the values 0, 1, 2,. . ., co. Thus the sum over can be replaced by an... [Pg.410]

The constant of integration is zero at zero temperature all the modes go to the unique non-degenerate ground state corresponding to the zero point energy. For this state S log(g) = log(l) = 0, a confmnation of the Third Law of Thennodynamics for the photon gas. [Pg.411]

The activation energy, is defined as tlie minimum additional energy above the zero-point energy that is needed for a system to pass from the initial to the final state in a chemical reaction. In tenns of equation (A2.4.132). the energy of the initial reactants at v = v is given by... [Pg.605]

Figure A3.13.il. Illustration of the time evolution of redueed two-dimensional probability densities I I and I I for the exeitation of CHD between 50 and 70 fs (see [154] for further details). The full eurve is a eut of tire potential energy surfaee at the momentary absorbed energy eorresponding to 3000 em during the entire time interval shown here (as6000 em, if zero point energy is ineluded). The dashed eurves show the energy uneertainty of the time-dependent wave paeket, approximately 500 em Left-hand side exeitation along the v-axis (see figure A3.13.5). The vertieal axis in the two-dimensional eontour line representations is... Figure A3.13.il. Illustration of the time evolution of redueed two-dimensional probability densities I I and I I for the exeitation of CHD between 50 and 70 fs (see [154] for further details). The full eurve is a eut of tire potential energy surfaee at the momentary absorbed energy eorresponding to 3000 em during the entire time interval shown here (as6000 em, if zero point energy is ineluded). The dashed eurves show the energy uneertainty of the time-dependent wave paeket, approximately 500 em Left-hand side exeitation along the v-axis (see figure A3.13.5). The vertieal axis in the two-dimensional eontour line representations is...
The unique feature in spontaneous Raman spectroscopy (SR) is that field 2 is not an incident field but (at room temperature and at optical frequencies) it is resonantly drawn into action from the zero-point field of the ubiquitous blackbody (bb) radiation. Its active frequency is spontaneously selected (from the infinite colours available in the blackbody) by the resonance with the Raman transition at co - 0I2 r material. The effective bb field mtensity may be obtained from its energy density per unit circular frequency, the... [Pg.1197]

Unlike the typical laser source, the zero-point blackbody field is spectrally white , providing all colours, CO2, that seek out all co - CO2 = coj resonances available in a given sample. Thus all possible Raman lines can be seen with a single incident source at tOp Such multiplex capability is now found in the Class II spectroscopies where broadband excitation is obtained either by using modeless lasers, or a femtosecond pulse, which on first principles must be spectrally broad [32]. Another distinction between a coherent laser source and the blackbody radiation is that the zero-point field is spatially isotropic. By perfonuing the simple wavevector algebra for SR, we find that the scattered radiation is isotropic as well. This concept of spatial incoherence will be used to explain a certain stimulated Raman scattering event in a subsequent section. [Pg.1197]

Historically, the first and most important capacitance method is the vibrating capacitor approach implemented by Lord Kelvin in 1897. In this technique (now called the Kelvin probe), the reference plate moves relative to the sample surface at some constant frequency and tlie capacitance changes as tlie interelectrode separation changes. An AC current thus flows in the external circuit. Upon reduction of the electric field to zero, the AC current is also reduced to zero. Originally, Kelvin detected the zero point manually using his quadrant electrometer. Nowadays, there are many elegant and sensitive versions of this technique. A piezoceramic foil can be used to vibrate the reference plate. To minimize noise and maximize sensitivity, a phase-locked... [Pg.1894]

Figure B3.4.1. The potential surfaee for the eollinear D + H2 DH + H reaetion (this potential is the same as for H + H2 — H2 + H, but to make the produets and reaetants identifieation elearer the isotopieally substituted reaetion is used). The D + H2 reaetant arrangement and the DH + H produet arrangement are denoted. The eoordinates are r, the H2 distanee, and R, the distanee between the D and the H2 eentre of mass. Distanees are measured in angstroms the potential eontours shown are 4.7 eV-4.55 eV,.. ., -3.8 eV. (The potential energy is zero when the partieles are far from eaeh other. Only the first few eontours are shown.) For referenee, the zero-point energy for H2 is -4.47 eV, i.e. 0.27 eV above the H2 potential minimum (-4.74 eV) the room-temperature thennal kinetie energy is approximately 0.03 eV. The graph uses the aeeiirate Liu-Seigbalm-Triihlar-Horowitz (LSTH) potential surfaee [195]. Figure B3.4.1. The potential surfaee for the eollinear D + H2 DH + H reaetion (this potential is the same as for H + H2 — H2 + H, but to make the produets and reaetants identifieation elearer the isotopieally substituted reaetion is used). The D + H2 reaetant arrangement and the DH + H produet arrangement are denoted. The eoordinates are r, the H2 distanee, and R, the distanee between the D and the H2 eentre of mass. Distanees are measured in angstroms the potential eontours shown are 4.7 eV-4.55 eV,.. ., -3.8 eV. (The potential energy is zero when the partieles are far from eaeh other. Only the first few eontours are shown.) For referenee, the zero-point energy for H2 is -4.47 eV, i.e. 0.27 eV above the H2 potential minimum (-4.74 eV) the room-temperature thennal kinetie energy is approximately 0.03 eV. The graph uses the aeeiirate Liu-Seigbalm-Triihlar-Horowitz (LSTH) potential surfaee [195].
Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... [Pg.2400]

After transforming to Cartesian coordinates, the position and velocities must be corrected for anharmonicities in the potential surface so that the desired energy is obtained. This procedure can be used, for example, to include the effects of zero-point energy into a classical calculation. [Pg.271]

Even at 0 K, molecules do not stand still. Quantum mechanically, this unexpected behavior can be explained by the existence of a so-called zero-point energy. Therefore, simplifying a molecule by thinking of it as a collection of balls and springs which mediate the forces acting between the atoms is not totally unrealistic, because one can easily imagine how such a mechanical model wobbles aroimd, once activated by an initial force. Consequently, the movement of each atom influences the motion of every other atom within the molecule, resulting in a com-... [Pg.359]


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Benzene zero-point energy results

Between Zero Points and Other Physical Quantities

Crystal zero-point energy

Debye zero-point energy

Eigenstate zero-point

Energy zero-point vibration

Energy, activation zero-point

Energy, configuration zero point

Equilibrium distance Zero-point energy

Flow rate zero-point

Force, zero creep point

Ground state zero-point energy

Hamiltonian equation zero-point energy

Harmonic oscillator zero-point energy

Harmonic zero-point energy

Heisenberg uncertainty principle and zero-point energy

Helium zero-point entropy

Hyperpolarizability zero-point vibrational average

Infrared spectroscopy zero-point energies

Methods zero point correction

Molecular vibrations zero point energy

Molecules zero-point energy

Point adjust, zero

Point of Zero Charge Adhesion Dominates

Point of zero charge

Point of zero charge , shift

Point of zero net charge

Point of zero net proton

Point of zero net proton charge

Point of zero proton charge

Point of zero salt effect

Point zero proton charge

Polarizability zero-point vibrational average

Pristine point of zero charge

Pristine point of zero charge PPZC)

Quantum numbers zero-point energy

RRKM rate constant zero-point energy

Radiation zero-point

Reaction path zero-point energy

Redox scale, zero point

Relaxation times zero-point energy results

Second-order Doppler shift and zero-point motion

Stationary Points and Normal-Mode Vibrations - Zero Point Energy

Subject zero-point energy

Temperature zero point

The Zero-Point Vibrational Energy

Transition state theory zero-point energy

Trimers zero point energy

True Zero Eigenvalues Catastrophe Points

Tunneling zero point energy

Tunneling zero-point

Vibrational energy, zero-point

What is zero-point energy

Zero charge, point

Zero order reaction point energy

Zero point anharmonicity

Zero point change upon association

Zero point charge measurement

Zero point charge measurement procedure

Zero point correction

Zero point determination

Zero point drift

Zero point energy definition

Zero point energy factor

Zero point energy problem

Zero point oscillation amplitudes

Zero point vibrational energy methods

Zero point vibrational energy transition state theory

Zero point, absolute

Zero point, temperature scale

Zero retardation point

Zero-Point Method

Zero-Point and Finite Temperature Vibrational Averaging

Zero-Point and Heat Content Energies

Zero-entropy-production melting points

Zero-phase difference point

Zero-point Energies and Thermodynamic Corrections

Zero-point analysis

Zero-point corrections, electronic structure

Zero-point data loss

Zero-point effects

Zero-point energies 0-0) bands

Zero-point energies of vibrations

Zero-point energy

Zero-point energy , nonadiabatic quantum

Zero-point energy , nonadiabatic quantum dynamics

Zero-point energy anharmonic oscillator

Zero-point energy approximation

Zero-point energy calculations

Zero-point energy corrections

Zero-point energy crystal structure

Zero-point energy determination

Zero-point energy effects

Zero-point energy enzymes

Zero-point energy factors reactions

Zero-point energy illustration

Zero-point energy linear chain

Zero-point energy restrictions

Zero-point energy separation

Zero-point energy variational transition state theory

Zero-point energy vibrational configuration interaction

Zero-point energy, ZPE

Zero-point entropy

Zero-point fluctuations

Zero-point motion

Zero-point oscillations

Zero-point titration

Zero-point vibrational

Zero-point vibrational average

Zero-point vibrational correction

Zero-point vibrations

Zero-point vibrations tunneling

Zero-point vibrations tunneling models

Zero-resolution points

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