Time Decay

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Time Decay

Options are wasting assets. They lose value over time and this phenomenon is called time decay. The rate at which the time value of an option is eroded is known as theta.

The effect of time decay is more pronounced for at-the-money and out-of-the-money options than in-the-money options since in-the-money options possess intrinsic value in addition to time value.

Time decay also accelerates as the options are approaching the last 30 to 60 days of their lifespan.

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Decay time: перевод, произношение, примеры, синонимы, антонимы, транскрипция

Перевод по словам

noun: распад, разрушение, разложение, упадок, гниение, загнивание, тление, расстройство, сгнившая часть

verb: распадаться, разлагаться, разрушаться, гнить, загнивать, портиться, приходить в упадок, загнить, ветшать, хиреть

  • branch of decay – ветвь ядерного распада
  • seed decay of cucurbits – загнивание семян тыквенных
  • alpha decay chain – цепочка альфа-распадов
  • phosphorescent decay – послесвечение люминофора
  • preserve from decay – уберегать от порчи
  • state of decay – состояние упадка
  • bacterial decay – гниение
  • decay retardant – замедлитель гниения
  • inverse decay – обратный распад
  • process of decay – процесс гниения

noun: время, раз, срок, период, времена, рабочее время, эпоха, жизнь, век, такт

verb: приурочить, приурочивать, показывать время, удачно выбирать время, рассчитывать по времени, назначать время, отбивать такт, танцевать в такт, согласовывать

  • have time – иметь время
  • zonal time – поясное время
  • kill time – убивать время
  • time keeper judge – судья-секундометрист
  • residence time – время пребывания
  • reverberation time – время реверберации
  • universal time – единое время
  • relaxation time – время релаксации
  • the time being – время
  • time of publication – время опубликования

Предложения с «decay time»

For this, a phosphor coating is applied to a surface of interest and, usually, the decay time is the emission parameter that indicates temperature. Для этого на интересующую поверхность наносится люминофорное покрытие и, как правило, время затухания является параметром излучения, который указывает на температуру.
One is, for instance, technetium is a radioactive element with a decay time of 4.2 million years. Возьмем, к примеру, технеций – радиоактивный элемент с периодом распада около 4,2 млн лет.
Другие результаты
For a considerable time they would descend, as the orbit decayed. Ведь этот спуск будет продолжаться долго, пока корабль будет терять запасенную энергию.
Compomers can also contain fluoride which is slowly released over time to help prevent additional decay of the tooth. Также компомеры содержат фтор, который медленно выделяется по прошествии времени, тем самым предотвращая дополнительное гниение зуба.
They are tooth-colored and can release fluoride over time to help prevent further tooth decay. Они имеют цвет зубов и могут с течением времени выделять фтор, позволяющий предотвращать дальнейшее гниение зуба.
We supposedly live in a time of decaying values, or perhaps of changing values. Такое впечатление, будто бы мы живем в эпоху разрушения ценностей, или, возможно, изменения ценностей.
And if that’s the case, there’s no reason why, given enough time, it couldn’t further decay to a much lower energy state! Если так, есть основания говорить о том, что при наличии времени она может еще больше ослабнуть, перейдя в новое, гораздо более низкое энергетическое состояние.
These trades, which are contrary to debit spreads, essentially profit from the decay of time value, and they don’t require any movement of the underlying to produce a profit. Эти сделки, в отличие от дебитных спрэдов, существенно выигрывают от временного распада и они не требуют никакого движения от базового актива, чтобы зарабатывать.
The longer it takes to reach this level, of course, the more time-value decay has helped us, perhaps even producing a gain if it occurs near the end of the expiration cycle. Чем дольше уйдет на достижение этого уровня, конечно, тем больше временной распад нам поможет, может быть даже получится прибыль, если это случится под экспирацию.
We fill corpses with embalming fluids, noxious carcinogenic chemicals that pollute the groundwater in the time it takes a body to decay. Мы наполняем трупы бальзамирующими составами, ядовитыми канцерогенными химикатами, которые загрязняют грунтовые воды всё то время, пока тело разлагается.
Time Lord engineering – you rip the star from its orbit, suspend it in a permanent state of decay. Технология Повелителей Времени. Срываешь звезду с орбиты и поддерживаешь её в состоянии распада.
Labour in the fields led to joints inflamed by arthritis, and the diet of sticky porridge brought tooth decay for the first time. Тяжкий труд в полях приводил к воспалению в суставах из-за артроза, а употребление каш с клейковиной вызывало гниение зубов.
It asserts, “One positive trait of radioactivity “that facilitates waste management is that with time comes decay”. В нем говорится: “Одной из позитивных сторон радиоактивного топлива, что облегчает обращение с отходами, это то, что со временем они распадаются.”
At one time, while engaged in cutting the grass, Gerhardt found, to his horror, not a handful, but literally boxes of half-burned match-sticks lying unconsumed and decaying under the fallen blades. Однажды, подстригая газон, Герхардт, к своему ужасу, нашел целую кучу полусгнивших спичек.
But time’s arrow – I got my head around that a bit. You don’t need maths, everything’s going forward and as it does, it decays. Насчёт стрелы времени – я в этом немного разбиралась, здесь не нужна математика, всё движется вперёд и постепенно разрушается.
From this time a new spirit of life animated the decaying frame of the stranger. С тех пор в изнуренное тело незнакомца влились новые силы.
This exit allows a large net circulation and is optimal for short uniform residence time as well as quickly decaying catalysts. Этот выход обеспечивает большую чистую циркуляцию и является оптимальным для короткого равномерного времени пребывания, а также быстро разлагающихся катализаторов.
The protoplanetary disk also had a greater proportion of radioactive elements than the Earth today because, over time, those elements decayed. Протопланетный диск также содержал большую долю радиоактивных элементов, чем современная Земля, потому что со временем эти элементы распадались.
This erosion of time value is called time decay. Эта эрозия ценности времени называется временным распадом.
There are certain risks involved in trading warrants—including time decay. Есть определенные риски, связанные с торговлей варрантами, включая временной спад.
It is either argued that the amount of time taken to perform this task or the amount of interference this task involves cause decay. Либо утверждается, что количество времени, затраченного на выполнение этой задачи, либо количество помех, которые эта задача включает, вызывают распад.
A model proposed to support decay with neurological evidence places importance on the firing patterns of neurons over time. Модель, предложенная для поддержки распада с помощью неврологических данных, придает большое значение паттернам возбуждения нейронов с течением времени.
Typical shutdown time for modern reactors such as the European Pressurized Reactor or Advanced CANDU reactor is 2 seconds for 90% reduction, limited by decay heat. Типичное время остановки для современных реакторов, таких как европейский реактор под давлением или усовершенствованный реактор CANDU, составляет 2 секунды для сокращения на 90%, ограниченного теплотой распада.
For a Higgs mass of 125 GeV/c2 the SM predicts that the most common decay is into a bottom–antibottom quark pair, which happens 57.7% of the time. Для массы Хиггса 125 ГэВ/с2 SM предсказывает, что наиболее распространенный распад происходит в паре кварков дно–антиботтом, что происходит в 57,7% случаев.
The second most common fermion decay at that mass is a tau–antitau pair, which happens only about 6.3% of the time. Вторым наиболее распространенным фермионным распадом при этой массе является пара тау–антитау, которая происходит только около 6,3% времени.
The critically damped response represents the circuit response that decays in the fastest possible time without going into oscillation. Критически затухающий отклик представляет собой отклик цепи, который распадается в кратчайшие сроки, не переходя в колебание.
Californium-252 undergoes alpha decay 96.9% of the time to form curium-248 while the remaining 3.1% of decays are spontaneous fission. Калифорния-252 подвергается Альфа-распаду 96,9% времени, чтобы сформировать кюрий-248, в то время как остальные 3,1% распадов являются спонтанным делением.
Thus, oscillations tend to decay with time unless there is some net source of energy into the system. Таким образом, колебания имеют тенденцию затухать со временем, если нет какого-то чистого источника энергии в системе.
Many chemicals undergo reactive decay or chemical change, especially over long periods of time in groundwater reservoirs. Многие химические вещества подвергаются реакционному распаду или химическому изменению, особенно в течение длительных периодов времени в подземных резервуарах.
Its proximity to the silver mines of Laurium probably contributed to its prosperity, which passed into a proverb; but even in the time of Cicero it had sunk into decay. Его близость к серебряным рудникам Лаурия, вероятно, способствовала его процветанию, что вошло в поговорку; но даже во времена Цицерона он пришел в упадок.
If a nucleus has too few or too many neutrons it may be unstable, and will decay after some period of time. Если ядро имеет слишком мало или слишком много нейтронов, оно может быть нестабильным и распадется через некоторое время.
In a radioactive decay process, this time constant is also the mean lifetime for decaying atoms. В процессе радиоактивного распада эта постоянная времени также является средним временем жизни распадающихся атомов.
Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide’s atoms to decay. Для образца конкретного радионуклида период полураспада – это время, необходимое для распада половины атомов радионуклида.
It would be easier to convert lead into gold via neutron capture and beta decay by leaving lead in a nuclear reactor for a long period of time. Было бы проще преобразовать свинец в золото путем захвата нейтронов и бета-распада, оставив свинец в ядерном реакторе на длительный период времени.
Organic mulches decay over time and are temporary. Органические мульчи разлагаются со временем и являются временными.
Without a functioning dynamo, the magnetic field of the Earth will decay in a geologically short time period of roughly 10,000 years. Без действующей динамо-машины магнитное поле Земли распадется за геологически короткий промежуток времени примерно в 10 000 лет.
They decay over time, and allow drainage, and even retain less water than growstones. Они разлагаются с течением времени, и позволяют дренажу, и даже сохраняют меньше воды, чем growstones.
The fission products are very radioactive, but the majority of the activity will decay away within a short time. Продукты деления очень радиоактивны, но большая часть активности распадается в течение короткого времени.
The oriented dipoles will be discharged spontaneously over time and the voltage at the electrodes of the capacitor will decay exponentially. Со временем ориентированные диполи будут самопроизвольно разряжаться, а напряжение на электродах конденсатора будет экспоненциально спадать.
They may have to be replaced in this time due to cracking, leaking, chipping, discoloration, decay, shrinkage of the gum line and damage from injury or tooth grinding. Они могут быть заменены в это время из-за трещин, протечек, сколов, обесцвечивания, распада, усадки линии десен и повреждения от травмы или зубного скрежета.
The danger of radiation from fallout also decreases rapidly with time due in large part to the exponential decay of the individual radionuclides. Опасность радиации от выпадения радиоактивных осадков также быстро уменьшается со временем из-за экспоненциального распада отдельных радионуклидов.
The decay of an unstable nucleus is entirely random in time so it is impossible to predict when a particular atom will decay. Распад нестабильного ядра полностью случаен во времени, поэтому невозможно предсказать, когда распадется конкретный атом.
However, it is equally likely to decay at any instant in time. Однако она с равной вероятностью может распасться в любой момент времени.
The negative sign indicates that N decreases as time increases, as the decay events follow one after another. Отрицательный знак указывает на то, что N уменьшается с увеличением времени, так как события распада следуют одно за другим.
So this triptych, these three panels portray the timeless truth that order tends to decay. Так что этот триптих, эти три панели, изображают вечную истину: порядку следует раздор.
I think we’d be wrong to reject them, to discard them, because we identify them as symptoms of the cultural decay of our times. И я думаю, будет неправильным, если мы отвергнем их или оставим без внимания, потому что считаем их предпосылками культурного упадка современного общества.
Over long enough times, comparable to the half-life of radionuclide A, the secular equilibrium is only approximate; NA decays away according to. В течение достаточно длительного времени, сравнимого с периодом полураспада радионуклида а, вековое равновесие является лишь приблизительным; NA распадается в соответствии с ним.
Radnor castle then gently fell into decay in the more peaceful times and by 1538 only one tower remained habitable and that was used as the county prison. В более спокойные времена замок Рэднор постепенно приходил в упадок, и к 1538 году только одна башня оставалась пригодной для жилья и использовалась как окружная тюрьма.
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Decay Time

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Migration Patterns of Pollutants in Construction & Demolition Waste

6.3.2 Migration of Pesticides in Simulated Washing Procedure

Decay time of volatile pesticides under the cool environment with low ventilation is long and potential environmental risk exists. For this kind of C&D waste, the possible migration and wash off with water should be investigated to get a further knowledge of its contamination and transformation pathways. The pyrethroid pesticides with low water solubility were used as target pollutants. Simulated seepage of water was carried out by adding water from the top. The flow was set as medium-intensity. The sampling outlet was set on the bottom. The water was continuously added for 24 h and added for another 24 h after a day’s interval. The leachate was collected and analyzed in frequency. According to the results, four pollutants with typical patterns were selected (A1 bifenthrin, A2 fenpropathrin, A3 beta-cyfluthrin, and A4 cypermethrin). The relationship between concentration in water (a) and in C&D waste (b) and the duration is demonstrated in Fig. 6.16 .

Figure 6.16 . Elution pattern of pyrethroids in construction and demolition waste by simulated seepage. (A) Elution rate curve and (B) pesticide residues–elution time curve.

The elution pattern figure showed that in early time period, large amounts of pesticides could be taken away with water. With the increase of injection time, the amount of pesticide taken away in certain time period rapidly reduced, and then gradually stabilized. The removal rate of pesticide with water tended to be constant.

When the flow stopped, the holding capacity of the surface water of C&D waste had some influence on the migration of pesticides, which is reflected in the curve projection in Fig. 6.16A . In the 24 h without injection of water, the pesticides on the surface of waste continuously dissolved in the residual water while the holding capacity of water of C&D waste prevented the water from dropping down. When the injection of water began, this portion of pesticide was washed off through water, which caused the immediate increase of pesticide amount in the wash-off water.

Different types of pyrethroid pesticide varied widely in release curve that may be due to the characteristic (e.g., solubility and viscosity) of pesticide itself. In the environment of the real industrial workshops, C&D waste is often mixed with soil, and make up a multisystem of water–C&D waste–soil. To further study the potential migration risk in a complex system, a new elution column based on this system was established. Fenvalerate was chosen as the contaminant and the device is shown in Fig. 6.17 . The device is devised as enclosed except for the inlet and outlet to minimize the volatilization of organic pollutants.

Figure 6.17 . Water– construction and demolition (C&D) waste system (left), water–soil–C&D waste system (right).

The wash-off water of 5–10 min, 15–20 min and 30–35 min was collected and analyzed using GC–MS. Results showed that the concentration of fenvalerate in system 2 was lower than that in system 1, which is listed in Table 6.6 . The procedures were repeatedly conducted and all the C&D waste were collected and extracted. The extraction liquid was merged with the elution (wash-off water) and pretreated for GC–MS analysis. Results showed that the total amount of fenvalerate in system 2 was about 7% less than that in system 1.

Table 6.6 . Concentration of Fenvalerate in Two Systems in Different Time Period

Time Period (min) Concentration (mg/L) Concentration (mg/L)
5–10 11.37 9.18
15–20 7.32 7.12
30–35 5.50 4.83



Charge decay time is a parameter characterizing charge accumulation and dissipation. It is the time required to dissipate an initial charge to its residual level under specific conditions of relative humidity and temperature. The following are the typical parameters of testing:

Initial charge 5,000 V
Residual charge 500 V (10% of initial)
Relative humidity 50% (alternatively 30%)
Temperature 23 ° C

Most test methods reported in open literature 41–44 use Federal Test Method Standard 101C, method 4046.1 and conditions listed above. Electro-tech Systems, Inc. developed equipment (Model 406D) which is composed of the control unit and the Faraday test cage. The test cage can be placed in an environmental chamber and tests can be performed under controlled conditions.

The control unit contains a stable, fully adjustable 0 to ±5.5 kV high voltage power supply, a precision electrostatic voltmeter, and a 0-99.99 second digital decay time readout. Cutoff levels of 50%, 10% (NFPA 99) and 1% (MIL-PRF-81705D), selected by push button switches, determine the cutoff point to which the decay time is measured.

The Faraday test cage, which shields the test sample from extraneous electrostatic fields, contains the sample holder electrodes and the electrostatic sensor. A safety interlock switch is incorporated that automatically opens the charge relay and grounds the test sample when the cage cover is opened.

Several types of sample holder electrodes are available which enable the user to test any reasonable size or shape of the material. Magnetic electrodes are used for film and fabric samples, clamp electrodes for sheet, foam, and samples up to one inch thick, IC tube electrodes for nondestructive testing of IC shipping tubes, loose fill electrodes for loose fill chips and ring electrodes for nondestructive testing of bottles, cups and canisters.

Model 406D meets the requirements of method 4046, MIL-PRF-81705D (formerly Mil-B-81705D), EIA-541, NFPA 99, INDA, ESD Association and other electrostatic decay test methods.

The testing method is very simple, including sample conditioning (usually under the same conditions as selected for testing; conditioning duration is usually 24 h), selection of clamp, mounting specimen, selection of parameters, automatic or manual measurements (5 seconds of dwell time is usually allowed between sequential measurements). Samples are measured for positive and negative charges and results from sequential measurements (repeats) are averaged.

The British standard 45 was also used for this testing, together with equipment developed by Grangemouth Research of BP Chemicals. 8

Older test methods included using a Static Honestometer produced in Japan. 46 The charge decay was evaluated as a half-life of generated charges. A sample was mounted on a disk rotating at 1200 rpm, the electric potential of up to 8,000 V was applied through a needle electrode. The initial charge and charge decay was measured by an electrode at 30% relative humidity and temperature of 30°C.

In still another older method, the electrostatic fieldmeter was used for measurements of samples which were frictionally charged. 47



Thermal decay time tools (TDTs) are used in cased holes in order to detect changes in the formation saturations occurring with time. Most commonly these changes arise from:

Depletion of the reservoir and zones becoming swept with either water from the aquifer or injection water

Formation of movement of the gas cap in the reservoir

The tool works by injecting neutrons, generated in a downhole minitron, into the formation. These neutrons get captured by atoms in the formation, most principally chlorine, which then yield gamma ray pulses that may be detected in the tool. Through the use of multiple detectors, the tool is able to differentiate between the signal arising from the borehole and that of the formation.

The components of the formation may be distinguished on the basis of their neutron capture cross-sections, measured in capture units (c.u.), denoted by Σ. The contractors provide charts to predict the values of Σ for different rock and fluid types. Typical values are:

Σm = 8c.u. (sandstone), 12 c.u. (limestone)

Σshale = 25–50c.u.; the value of Σ measured by the tool in a 100% shale-bearing interval

Σwater (200kppm NaCl at 250°F) = 100c.u.

The Σ measured by the tool is assumed to be a linear sum of the volume fractions of the components times their respective Σ values. Clearly the accuracy of the tool in differentiating oil and water is dependent mainly on the contrast in Σ between the oil and water. Hence the tool works well in saline environments and poorly in fresh environments. Even in a saline environment it might be found that small changes in the input parameters result in a large change in Sw. Hence the tool can give very unreliable results unless some of the water saturations are already well known in the formation.

The tool also has a limited depth of investigation, sufficient to penetrate one string of casing but not always two. It is essential to have a completion diagram of the well available when interpreting the tool, so that the relevant positions of tubing tail, casing shoes, and tops of liners are known.

Where the tool is used in time-lapse mode in a two-fluid system, clearly the variables relating to the nonmovable fluids drop out and changes in Sw can be calculated on the basis of only (Σw – Σhydrocarbon). Some of the equations that may be used for interpreting the tool will now be derived:

Two-component system without time-lapse mode:

where Vsh denotes the total volume fraction of shale. From which:

Two-component system in time-lapse mode:

For a situation in which gas replaces oil with constant water saturation in time-lapse mode:

where Sg is the new gas saturation appearing.

An example of an interpreted TDT is shown in Figure 5.7.1 .

Figure 5.7.1 . Example of Interpreted TDT Log

In this example, constants were chosen as follows:

Σw = capture cross section of water: 100cu

Σsh = capture cross section of shale: 50cu

Σsa = capture cross section of sand: 5 cu

Σg = capture cross section of gas: 7.8cu

Vsh = shale volume fraction, derived from GR using GRsa =15 and GRsh = 90API

ϕ = porosity from openhole logs

Thermal Decay Neutron Example

Consider a formation with the following properties:

Σ measured by the tool is 15.

Suppose that the value of Σsh can only be estimated to an accuracy of ±5. What is the uncertainty in Sw resulting from this?

Nitride LEDs based on quantum wells and quantum dots Increasing the overlap by using thin QWs and QD

The radiative decay time of carriers in an AlGaN/GaN QW and peak energy of emission as a function of well width is shown in Fig. 11.12 . 30 Increasing the width of the QWs leads to a red shift in emission due to QCSE, and a corresponding decrease in the radiative decay rate due to smaller electron-hole overlap. A similar trend is seen in GaN/AlN QDs. 31 By increasing the height of dots, photoluminescence decay time increases. This effect is due to the presence of polarization-induced electric fields in the active region.

Figure 11.12 . Comparison of the measured energy positions (circles) and decay times (squares) of the low-energy lines in GaN/AlGaN QWs calculated based on piezoelectric fields. 30

On the other hand, when the QW width or QD size is decreased, the electron-hole subband energies increase because of size quantization effects. Because the energy band-offset confining the carriers in the well is finite, very thin QWs or small QDs lead to poor confinement of carriers. This suggests that a careful design trade-off is necessary to determine the optimal QW and QD sizes for improving the overlap of carriers without compromising carrier confinement.

Antistatic and electrically conductive finishes for textiles

17.5.1 Charge decay time

The charge decay time depends on the size of the capacitor on which the charge is stored and the resistance through which it can flow to ground. In the case of conductors the capacitance and the resistance values are constants; however, for insulators the capacitance and the resistivity are more complicated. Mathematically the charge decay can be expressed as

where q = charge at time t, q0 = initial charge, and τ = time constant = RC = ερεoρ, where εo = relative permittivity of free space, ερ = relative permittivity of the medium, ρ = resistivity, R = resistance, and C = capacitance. τ is known as the characteristic decay time and is equal to the time to reach about 37% of the initial potential decay. An exponential decay on an insulator surface is shown in Figure 17.6 . Another parameter that can be used to measure the charge decay is the half-decay time, the time to reach 50% of the initial charge, which is also known as the half-life.

Figure 17.6 . Exponential decay of charge on a polymer surface with a time constant τ ( Cross, 1987 ).

It has been shown that charge decay from surfaces of textile materials is characterized by relatively fast initial decay, followed by slow final decay ( Sessler, 1987 ).

Devices and Applications Ultrafast Dynamics of the Nanocavity Lasers

Above lasing threshold, the decay time is reduced by another order of magnitude due to stimulated emission. Figures 18(a) and 18(b) show the time data for the single-defect cavity and coupled-cavity array lasers, respectively. The decays for both lasers are fitted by single exponentials with a decay constant of 2 ps.

Figure 18 . Time-resolved response of a photonic crystal laser above lasing threshold. (a, b) Time response (blue) of a single-defect cavity and coupled-cavity array laser at 7 K together with an exponential fit (red). (c) Delay-time measurement of a single-cavity laser (blue) with respect to pump laser (red). For this measurement, the cryostat temperature was raised from 7 K to 100 K to increase the relaxation rate of carriers from upper MQW levels to the lowest level by increasing phonon population. At 7 K, the delay time was 3–4 ps, while at 100 K, the delay time decreased to 1.5 ps. (d) Simulated photon number as a function of time for a single-defect cavity laser (red). The simulation result is convolved with a Gaussian of 4 ps width (blue) to take into account streak-camera response. Taken from Altug H, Englund D, and Vuckovic J (2006) Ultrafast photonic crystal nanocavity laser. Nature Physics 2: 484–488.

To understand the dynamics, we used the laser rate Equations (10) and (11) to simulate the photon and carrier densities as functions of time. Initially, the photon and carrier densities are taken as zero and above the transparency condition, respectively. The simulated photon density is also convolved with a Gaussian of 4-ps width to take into account streak camera response. The simulation results are shown in Figure 18(d) . The bare photon response (unconvolved data) shows that when the laser is pumped above threshold, the photon density decays with the cavity decay time (τp). For both the single and coupled-cavity array lasers, this is 0.5 ps (for Q of 1000), which is below the resolution limit of our streak camera. The photon response convolved with the streak camera response shows a decay time of 2 ps, which agrees very well with our experimental results.

As indicated above, one important parameter in this type of laser modulation scheme is the delay time, which decreases in high Purcell-factor cavities. We measured this delay time at 100 K (with 890 nm pump wavelength) to be 1.5 ps (shown in Figure 18(c) ), which is close to the streak camera resolution limit. The delay time is nearly two orders of magnitude lesser than in previous measurements on conventional semiconductor lasers.

Fluorescence Lifetime Spectroscopy and Imaging of Visible Fluorescent Proteins

Ankur Jain, . Vinod Subramaniam, in Advances in Biomedical Engineering , 2009

2.5.2 Frequency-domain lifetime measurement

The alternative method of measuring the decay time is the frequency domain or the phase modulation method [16] . In this case, the sample is excited using a continuous source of excitation that is modulated in intensity at a very high frequency. The resulting fluorescence emission is thus also modulated at the same frequency. However, owing to the finite lifetime of fluorescence, the emission is delayed in time relative to the excitation. This delay is measured as a phase shift (φ), which can be used to calculate the decay time, called the phase lifetime (τφ), given by the equation:

Further, the lifetime leads to a decreased modulation depth of the emission relative to that of the excitation light, as shown in Figure 5 . The extent to which this occurs depends upon the decay time of the fluorophore and the modulation frequency. The demodulation factor, m, is given by

Figure 5 . Principle of frequency domain lifetime measurement. The fluorescence lifetime is calculated from the phase shift and demodulation of the emitted light (gray curve) with respect to the sinusoidally modulated excitation light (black curve).

where b/a is the modulation of the excitation light and B/A, for the emitted light ( Figure 5 ). The lifetime calculated from the demodulation is called the modulation lifetime (τm) and is given by

For monoexponential decays, the phase and modulation lifetimes correspond. A difference in the phase and modulation lifetimes is indicative of multiexponential fluorescence decay or excited state interactions of the fluorophore. Frequency domain lifetime determination is particularly suited for wide-field illumination strategies and spatially-resolved fluorescence lifetime imaging [17] .

Principles of Frequency-Domain Fluorescence Spectroscopy and Applications to Protein Fluorescence


It has been known since 1970 that the decay time of NADH in water is near 0.4 nsec ( 55 ). The initial measurements were done by the phase method at 28 MHz. The decay appeared to be homogeneous, and, in fact, we used NADH as a short-lived standard for our own 10- and 30-MHz measurements ( 28 ). In 1981 the intensity decay of NADH was examined by Visser and Hoek ( 60 ), who reported a bioexponential decay, with decay times near 0.2 and 0.8 nsec. Hence, it was of interest to examine NADH using the GHz frequency range ( Fig. 13 ). These measurements were performed using the frequency doubled output of a pyridine 2 dye laser. This laser provides doubled output from 360 to 380 nm, which is a convenient range for many extrinsic fluorophores. Our attempt to fit the frequency response to a single exponential is shown by the solid line, resulting in an unreasonable value of χR 2 562. An acceptable fit was found for the double-exponential model, yielding χR 2 = 1.4. The decay times and amplitudes we recovered are in good agreement with those reported by Visser, which were 0.25 and 0.82 nsec, with fractional intensities of 0.58 and 0.42, respectively.

Fig. 13 . Intensity decay of NADH. The emission was observed through a Corning 3–73 filter. The source was a cavity-dumped pyridine 2 dye laser.

Polymer Characterization Translational diffusion

An estimate of the degree of broadening and correlation decay time , assuming a system of polystyrene with M̄w = 670000 in cyclohexane with DT = 1.66 × 10 −7 cm 2 s −1 and observed at 90°, leads to a linewidth of about 2 × 10 4 Hz and a characteristic decay time of the correlation function τc = 1/DTq 2 = 5 × 10 −5 s.

The diffusion coefficient D may be related to the molecular friction factor f through the Einstein relation

For a spherical molecule of radius a, f = 6πηa, where η is the dynamic viscosity of the solvent, then

where Rh is the hydrodynamic radius of the molecule.



Volume resistivity, surface resistivity, and charge decay time are major characteristics of electrostatic properties of materials. Volume resistivity, expressed in ohm-cm, is the resistivity of material measured on opposite ends of a material which is 1 cm thick. Surface resistivity, expressed in ohm, is a resistance between two electrodes placed along the same surface of the specimen. The charge decay time, expressed in s, is defined as the time needed to dissipate a certain percentage of charge induced on the surface of material. Other terms used include shielding effectiveness, decay half-time, peak voltage, and a percentage of charge retained. Shielding effectiveness, expressed in decibels, is a measure of attenuation of electromagnetic interference (EMI) by internal reflection, absorption, and partial reflection. Decay half-time, expressed in s, is the time to dissipate half the charge induced. Peak voltage, expressed in volts, is the maximum induced voltage in the charge decay test. The percentage of charge retained is a percentage of charge remaining in charge decay test after 500 s. The most frequently used methods of determining these quantities are characterized below. The respective standards are given in the next section.

Charge decay time.

A specimen is placed in Faraday cage with electrodes on each side of the specimen. One electrode induces the charge, the other electrode measures changes in electric field. In this measurement, charge decay time , decay half-time, peak voltage, and the percentage of voltage remaining after 500 s are determined.

Surface resistivity.

One side of the specimen is coated with a circle of silver paint surrounded by a ring of silver paint. The uncoated distance between the circle and the ring is an effective length on which surface resistivity is measured. The other surface of the specimen is fully coated with silver paint. Current and voltage are measured and surface resistivity calculated. If samples contain internal or external antistatics, the measurement is performed under a controlled atmosphere to eliminate the influence of temperature and relative humidity. Also, specimen conditioning is used to account for migration of the antistatic to the surface. The surface of specimen containing antistatics is not coated with silver paint, but electrodes are pressed to the surface. The resistivity of conductive pipes is determined in a special test arrangement. 66

Volume resistivity.

There are some differences between standard methods but the general principle is similar. A specimen of standard size is coated with a silver paint on the opposite surfaces to assure good surface conductivity. Two electrodes are attached to both surfaces in the manner minimizing contact resistance. The voltage applied depends on the expected resistance of the specimen and is in the range of 0.1 to 1000 v/mm thickness. Current and voltage are measured between the faces and volume resistance calculated. The edge effect can be minimized by means of guard electrodes. 65

Standard methods: electric resistance – ASTM D257, shielding effectiveness – ASTM F3057–14, D4935–10, BS 6667 (part 1 and 2), static decay – BS 2783 (part 2), surface resistivity – ASTM D4496, ASTM F1173 (pipe resistivity), volume resistivity – ASTM D257, ISO 3915

Major results: Figure 14.7 shows that the resistivity of aluminum-filled PMMA changes abruptly. Smaller volumes of filler contribute a little to resistivity but, after certain threshold value of filler concentration, further additions have little contribution. A similar relationship was obtained for nickel powder; the only difference is in the final value of resistivity, which was lower for nickel due to its higher conductivity. 63 The same conclusions can be obtained from conductivity determinations of epoxy resins filled with copper and nickel. 64 Figure 14.8 shows the effect of temperature on the electric conductivity of butyl rubber filled with different grades of carbon black. In both cases, conductivity decreases with temperature, but lamp black is substantially more sensitive to temperature changes. 67 Even more pronounced changes with temperature were detected for the dielectric loss factor and dissipation factor for mineral filled epoxy. 69

Figure 14.7 . Resistivity of aluminum powder filled PMMA.

[Adapted, by permission from Yang, L; Schruben, D L, Polym. Engng. Sci., 34, 14, 1109-14, 1994.] Copyright © 1994

Figure 14.8 . Conductivity of butyl rubber filled with carbon black vs. temperature.

[Data from Nasr, G M; Badawy, M M; Gwaily, S E; Shash, N M; Hassan, H H, Polym. Degradat. Stabil., 48, 2, 237-41, 1995.] Copyright © 1995

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