The Open Science Framework is infrastructure developed by the Center for Open Science for creating and linking inspectable research records. It supports registration of study plans, community-run preprint services and connections to related data, materials, code and publications. These records can connect several stages of an investigation rather than leaving only its final paper visible.^[ref]

For example, an investigator can register a planned analysis before collecting data, then link the resulting paper and analysis code to that plan. Comparing the records helps distinguish the prespecified analysis from subsequent exploratory analysis. Registration provides evidence of what was recorded at a particular time; it does not itself show that the study design is sound or that a result is correct. Research transparency and computational reproducibility answer different questions from the truth of a scientific claim.

In his account of the project's history, Brian Nosek describes a failed 2007 grant proposal, Jeff Spies's renewed development effort in 2011 and the opening of the service for public use in 2012. His August 2026 explanation of a change in direction also illustrates an infrastructure constraint: the long-term value of linked research records depends on which services an organization can sustainably maintain.^[ref]

Nuclear evaporation is statistical particle emission from an excited compound nucleus after energy has been redistributed among many nuclear degrees of freedom. It is the nuclear analogue of preferentially losing particles energetic enough to escape a bound system, rather than a direct knockout by the initial projectile.

For a particle separation energy $S$ and relative kinetic energy $ϵ$, the daughter excitation is $E_f^{\ast }=E_i^{\ast }-S-ϵ$. The emission probability depends on the available daughter nuclear level density and the inverse reaction probability. Neutron emission avoids a charged-particle Coulomb barrier, while proton or heavier-particle emission competes under different thresholds and barriers. The emitted spectrum is therefore not determined by temperature alone.

A nuclear resonance is an enhanced nuclear reaction or scattering response near the energy of an accessible quasi-bound nuclear state. For an isolated resonance, a common energy dependence is ${\sigma }_{ab}(E)\propto {\Gamma }_a{\Gamma }_b/[(E-E_r{)}^2+(\Gamma /2{)}^2]$, where $E_r$ is the resonance energy, $\Gamma$ the total width and ${\Gamma }_a,{\Gamma }_b$ partial widths for entrance and exit channels.

The lifetime scale is $\tau \sim \hslash /\Gamma$: narrower states persist longer. Spin factors, wavelength factors and interference with background amplitudes complete a cross-section model. Resonance spacings and widths provide input to statistical nuclear-reaction calculations.^[ref]

Neutron physics studies the production, interaction, transport and detection of neutrons. A neutron has no net electric charge, so it does not experience the long-range Coulomb repulsion that impedes charged particles approaching a positively charged atomic nucleus. Its nuclear interactions nevertheless depend strongly on energy and target isotope.

Elastic scattering can slow neutrons in a neutron moderator, capture can change a nucleus, and suitable reactions can initiate nuclear fission. Neutron magnetic moments also couple to magnetic structure, enabling magnetic neutron diffraction. A measured attenuation therefore combines different reaction channels and must not be interpreted as one universal absorption probability.

Beta equilibrium is a condition in which weak reactions interconverting neutrons and protons produce no net change of composition. For matter where neutrinos are thermally trapped, the reaction $n+{\nu }_e\rightleftharpoons p+e^{-}$ gives the chemical equilibrium conditionwhere each $\mu$ is the corresponding chemical potential. In cold neutrino-transparent neutron star matter, one usually takes ${\mu }_{{\nu }_e}=0$, giving ${\mu }_n={\mu }_p+{\mu }_e$. The escaping neutrinos do not form an equilibrated thermal bath in that approximation.^[ref]

Charge neutrality in matter containing only neutrons, protons and electrons additionally requires $n_p=n_e$. Given a total baryon density, these relations and an equation of state determine the composition. As an illustrative chemical-potential check, ${\mu }_n=1000$ MeV and ${\mu }_p=900$ MeV require ${\mu }_e=100$ MeV in the transparent approximation. At finite temperature, balancing emission and capture rates is the more general kinetic condition; nuclear statistical equilibrium under strong reactions alone does not impose beta equilibrium.

Nuclear induction is the detection of nuclear spin magnetization through the voltage it induces in a receiver coil. In nuclear magnetic resonance, magnetization precessing transverse to the applied field creates a time-varying magnetic flux and hence an alternating electrical signal.

After excitation, this signal can decay as a free induction decay, whose Fourier transform gives a frequency-domain spectrum. The detection is collective: the coil measures an ensemble magnetization rather than tracking one nucleus. The phrase also recalls early experiments establishing inductive observation of nuclear magnetic resonance.

Cross-polarization (nuclear magnetic resonance) transfers nuclear spin nuclear spin polarization between different nuclear populations, commonly from abundant hydrogen nuclei to dilute carbon-13 nuclei in a solid. Applied radio frequency fields bring the two spin populations into a condition that permits polarization exchange through magnetic dipolar coupling.^[ref]

For on-resonance spin locking, an ideal matching condition is $|{\gamma }_I|B_{1I}=|{\gamma }_S|B_{1S}$, where $\gamma$ is the gyromagnetic ratio and $B_1$ is the applied transverse field amplitude for each population. The fields match motion in the respective rotating frames, even though the nuclei have different laboratory resonance frequencies. This can enhance a weak carbon signal, but intensity also depends on transfer and relaxation, so peak areas need not directly count atoms without further controls.^[ref]

A stimulated echo is a delayed nuclear magnetic resonance signal produced by a sequence that stores part of a dephased magnetization pattern along the static magnetic field and later converts it back into detectable transverse magnetization. In a common ideal sequence, three $90^{\circ }$ pulses are applied at times $0$, $\tau$ and $\tau +T_{mathrmm}$. The selected stimulated echo appears a further $\tau$ after the third pulse, at $2\tau +T_{mathrmm}$.^[ref]

The first interval lets spins with different Larmor frequencies accumulate different phases. The second pulse converts part of that frequency-dependent pattern into longitudinal magnetization. During the storage interval $T_{mathrmm}$ this component does not precess as transverse magnetization does. The third pulse returns part of the pattern to the transverse plane, where the appropriate contribution rephases. Storage retains a frequency-dependent population pattern, not a continuously rotating transverse vector.^[ref]

For an original ideal calculation, hold $\tau$ fixed and neglect diffusion, pulse errors and exchange. If $T_1$ is the spin-lattice relaxation time, the selected echo contribution obeysA storage interval $T_{mathrmm}=T_1\ln 2$ therefore halves that contribution. The two transverse intervals still incur transverse relaxation; longitudinal storage does not undo every source of signal loss.

This distinction is useful for diffusion measurements when a longer observation interval is wanted without keeping the relevant pattern transverse throughout. A 1989 experiment used pulsed-gradient stimulated echo sequences to reduce particular background-gradient effects in heterogeneous samples. It tested specified pulse arrangements, rather than establishing that every stimulated echo removes every gradient error.^[ref]

Pulsed field gradient NMR, or PFG NMR, uses timed magnetic field gradients to encode position in the phase of a nuclear magnetic resonance signal. An appropriately refocused pair of encoding episodes cancels the position-dependent phase for stationary spins. Motion between the episodes can prevent cancellation, making the echo sensitive to displacement.

For an original narrow-pulse derivation in one spatial direction, let each effective encoding pulse have gradient magnitude $g$ and short duration $\delta$, and write $q=\gamma g\delta$, where $\gamma$ is the angular gyromagnetic ratio. Neglect displacement during each pulse. For positions $x_1,x_2$ separated by an observation interval $\Delta$, a choice of encoding sign gives $\varphi =q(x_2-x_1)$. The normalized signal is the ensemble average of $e^{i\varphi }$.

For free diffusion with diffusion coefficient $D$, displacement has a zero-mean normal distribution of variance $2D\Delta$. Its characteristic function givesFor invented values $q=10^5{\mathrm{m}}^{-1}$, $D=10^{-9}{\mathrm{m}}^2{\mathrm{s}}^{-1}$ and $\Delta =0.1\mathrm{s}$, the attenuation is $e^{-1}\approx 0.368$. Finite pulse duration, restricted motion and other sequence details require their corresponding model rather than automatic use of this narrow-pulse result.

The 1965 experiment of E. O. Stejskal and J. E. Tanner combined a derivation for time-dependent gradients with experimental tests. Reducing gradients during radio-frequency pulses and echo detection relaxed practical limitations of a continuously strong gradient; the authors measured slow diffusion in dry glycerol.^[ref]

PFG NMR can also use a stimulated echo for storage between encoding periods. Distinguishing motion-induced attenuation from other signal losses is part of the measurement, not a consequence of the method's name alone.

NMR dipolar coupling is the interaction between the magnetic moments of atomic nuclei through their magnetic fields. It depends on internuclear separation and orientation, allowing nuclear magnetic resonance measurements to constrain spatial structure. It differs from NMR scalar coupling, whose mechanism involves intervening electrons.

For two point magnetic dipoles separated by $\mathbf{r}=r\hat{\mathbf{r}}$, the interaction energy isHere ${\mu }_0$ is the vacuum permeability. Write ${\mathbf{\mu }}_I={\gamma }_I\hslash \mathbf{I}$ and ${\mathbf{\mu }}_S={\gamma }_S\hslash \mathbf{S}$, where $\mathbf{I},\mathbf{S}$ are dimensionless spin angular momentum operators and each $\gamma$ is an angular gyromagnetic ratio in radians per second per tesla. A signed angular-frequency coupling scale is thenThis convention puts the geometrical factor separately; some texts absorb an extra minus sign or convert to cycles per second. Comparing numerical coupling constants requires matching those conventions.

For an unlike-spin pair with well-separated resonance frequencies in a strong field, neglecting rapidly oscillating terms gives the ideal secular Quantum Hamiltonianwhere $\theta$ is the angle between the internuclear vector and the field. The angular factor vanishes at $\theta =\arccos (1/\sqrt{3})$. Magic angle spinning exploits related orientation averaging, while dipolar recoupling deliberately restores sensitivity to interactions suppressed by spinning.

An original scaling comparison is especially useful: doubling $r$ reduces $|d_{IS}|$ by a factor of eight. Thus a coupling strength can constrain distance, but orientation averaging, motion and additional spins must be modeled before turning a measured signal change into a unique distance. REDOR supplies an experimental route to that information. Its early carbon-13–nitrogen-15 alanine measurements compared a full rotational echo with a dephased echo under timed pulses.^[ref]

NMR phase cycling systematically changes radio frequency pulse phases and the receiver phase across repeated nuclear magnetic resonance acquisitions so that selected signals reinforce while unwanted contributions cancel. Pulse phase controls the rotation axis in the rotating frame; receiver phase controls how transverse magnetization is represented in the recorded complex signal. A phase change does not mean changing the resonant nucleus or physically rotating the sample.^[ref]

An original two-acquisition example makes the subtraction explicit. Suppose changing an excitation pulse by $\pi$ reverses the desired contribution $S$ while leaving an unwanted background $B$ unchanged. Before correcting the receiver phases, the two measurements areApplying the corresponding receiver sign and averaging gives $(s_1-s_2)/2=S$. With invented values $S=5$ and $B=2$, the recorded values7 and−3 yield5. Adding them without the intended sign would instead retain the background.

The assumptions matter. If the background changes between acquisitions, the residual is $(B_1-B_2)/2$. Nor does a two-step cycle separate contributions that transform in exactly the same way under its phase changes. More elaborate cycles select particular changes in NMR coherence, rather than indiscriminately removing every source of error.^[ref]

Phase patterns can also be built into a train of refocusing pulses. XY8 is an important example for controlling cumulative NMR pulse errors. Within-train pulse compensation and across-acquisition selection are related uses of phase control, but the eight pulses of an XY8 block do not by themselves specify a complete receiver cycle.

NMR coherence describes phase-bearing components of a nuclear-spin density matrix. Its description depends on a specified basis and rotation convention. Transverse magnetization is an observable example, while multispin coherences can require additional pulses before they contribute to the detected nuclear magnetic resonance signal.^[ref]

For an original spin one-half example, use dimensionless $I_z=\mathrm{diag}(1/2,-1/2)$ and $I_x={\sigma }_x/2$. A valid density matrix isIts populations in this basis are both one half, but its off-diagonal entries are $\epsilon /2$. The eigenvalues $(1+\epsilon )/2$ and $(1-\epsilon )/2$ are nonnegative, and the trace is one. Comparing $\epsilon =0$ with $\epsilon =1$ shows that identical populations do not require identical transverse coherence. This prepared-state example is not the thermal state of an actual bulk sample.

With rotation convention $U=\exp (-i\varphi I_z)$, the upper-right entry of $U\rho U^{†}$ becomes $(\epsilon /2)e^{-i\varphi }$, while the populations remain unchanged. More generally, a component $A_p$ of coherence order $p$ obeysSingle-quantum orders are $p=\pm 1$; a Hermitian transverse operator contains both signs. Longitudinal magnetization has order zero, but in a multispin system order zero also includes terms beyond populations.^[ref]

This phase response makes NMR phase cycling useful: contributions can be selected by how they transform under controlled phase changes. Selection alone does not establish that an experiment generated the desired component. The spin system and pulse sequence must also support it.^[ref]

An NMR distance restraint is a restriction on distances between selected atoms used in a structural calculation from nuclear magnetic resonance data. It often specifies an allowed interval or upper bound, with a penalty for a candidate structure violating it. Distances inferred from the nuclear Overhauser effect, including NOESY cross-peak information, are important examples. The restraint combines experimental interpretation with atom assignments and a model; it is not simply an exact ruler reading.^[ref]

For an original interval example, suppose a proton pair has allowed separation $l=2.0$ to $u=3.5$ angstroms. A flat-bottom quadratic penalty isA candidate distance of4.0angstroms contributes $0.25k{\mathring{\mathrm{A}}}^2$, whereas3.0angstroms contributes zero. Here $k$ has units of energy per squared length; the penalty is a fitting objective, not a measured pair interaction energy. Many restraints and stereochemical terms together constrain a protein structure.^[ref]

An ambiguous NMR distance restraint may describe several possible atom pairs contributing to one observation. In one inverse-sixth-power sum convention,For original candidate distances2 and4angstroms, this gives about1.995angstroms. Dividing the sum by2 before taking the inverse sixth root instead gives about2.239angstroms: an average and a sum are different models. An ambiguous assignment also does not assert that every candidate pair separately satisfies the nominal bound.^[ref]

Cross-peak overlap, nuclear spin diffusion and conformational averaging affect interpretation. A structural calculation therefore retains assignment and averaging information alongside its distance bounds; an absent or weak peak alone need not establish a large separation.

Radiation detection makes interactions of ionizing radiation with matter into observable signals. An ionization chamber collects charge created in a gas; a scintillation detector converts deposited energy into light; a semiconductor detector measures charge carriers created in a solid. The instrument detects interactions, so its response depends on radiation type, energy and geometry.

For an ideal counting model, expected detected events satisfy $N=\epsilon Rt$, where $R$ is the relevant incident event rate, $t$ is observation time and $\epsilon$ is detection efficiency. Background adds counts, while dead time can lose them. Estimating a source's radioactive activity therefore requires calibration and a model of emissions and transport, rather than equating the displayed count rate with decay rate.

A nuclear power plant converts energy from controlled nuclear fission into electrical energy. A nuclear reactor produces heat; a coolant carries it to the working cycle; a turbine drives an electrical generator. A pressurized water reactor transfers heat to a separate steam circuit, whereas a boiling water reactor generates steam in the reactor vessel.^[ref]

If thermal input is $P_{\mathrm{th}}$ and conversion efficiency is $\eta$, gross electrical output is approximately $\eta P_{\mathrm{th}}$; the remaining thermal power must be rejected. The plant also needs its own electrical supply, so gross output differs from net export. After the chain reaction stops, decay heat still requires removal.

Semiconductor device fabrication builds electronic or optoelectronic structures by controlling the geometry, composition and interfaces of semiconductor materials. Typical steps include deposition, photolithography, etching and controlled semiconductor doping. Repeating patterned steps creates devices and their interconnections.

For a simple patterned layer, deposit material, coat it with photoresist, expose through a photomask, develop the resist and transfer the pattern by etching. Later layers require alignment to earlier ones. A useful device depends on more than resolving a small feature: defects, contamination, interface quality and electrical contact resistance also affect performance. Fabrication therefore couples materials science with measurement and process control.^[ref]