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A two-terminal quantum spin-Hall heat engine and refrigerator with embedded Majorana bound states (MBSs) is analyzed for optimality in thermoelectric performance using the Landaeur–Buttiker approach. This investigation can be an effective tool to detect MBSs. Furthermore, the occurrence of MBSs can enhance the performance to rival, as well as outperform, some modern nanoscale quantum heat engines and quantum refrigerators. The optimal performance of this MBS quantum heat engine and quantum refrigerator can be further enhanced by an Aharonov–Bohm flux. [ABSTRACT FROM AUTHOR]

We theoretically analyze the electronic transport properties of a monolayer graphene/insulator/superconductor (G I S) tunnel junction subject to a temperature gradient. For intrinsic graphene, the system shows always dissipative charge transport even in the presence of an electronic temperature difference between the two leads. Differently, the G I S produces a thermoelectric response when the graphene electrochemical potential is lifted to energies comparable to the zero-temperature gap of the superconductor, i.e., the system is particle–hole asymmetric. Indeed, the thermally biased G I S system is able to produce both a short-circuit Peltier current and an open-circuit Seebeck voltage. This thermoelectric effect is made of a linear conventional component, due to the intrinsic particle–hole asymmetry of the system, and a non-linear contribution, due to a further spontaneous particle–hole symmetry breaking. In most of the thermal and charge configurations of the G I S system, the linear component prevails. Concluding, the G I S system could be employed in the design of thermometers, electromagnetic radiation sensors, and heat engines with profound influence in superconducting quantum technologies. [ABSTRACT FROM AUTHOR]

We present a fully quantum dynamical treatment of a quantum heat engine and its baths based on the Hierarchy of Pure States (HOPS), an exact and general method for open quantum system dynamics. We show how the change of the bath energy and the interaction energy can be determined within HOPS for arbitrary coupling strength and smooth time dependence of the modulation protocol. The dynamics of all energetic contributions during the operation can be carefully examined both in its initial transient phase and, also later, in its periodic steady state. A quantum Otto engine with a qubit as an inherently nonlinear work medium is studied in a regime where the energy associated with the interaction Hamiltonian plays an important role for the global energy balance and, thus, must not be neglected when calculating its power and efficiency. We confirm that the work required to drive the coupling with the baths sensitively depends on the speed of the modulation protocol. Remarkably, departing from the conventional scheme of well-separated phases by allowing for temporal overlap, we discover that one can even gain energy from the modulation of bath interactions. We visualize these various work contributions using the analog of state change diagrams of thermodynamic cycles. We offer a concise, full presentation of HOPS with its extension to bath observables, as it serves as a universal tool for the numerically exact description of general quantum dynamical (thermodynamic) scenarios far from the weak-coupling limit. [ABSTRACT FROM AUTHOR]

To investigate the impact of fractional parameters on the thermodynamic behaviors of quantum systems, we incorporate fractional quantum mechanics into the cycle of a quantum Stirling heat engine and examine the influence of fractional parameters on regeneration and efficiency. We propose a novel approach to control the thermodynamic cycle that leverages the fractional parameter structure and evaluates its effectiveness. Our findings reveal that by tuning the fractional parameter, the region of the cycle with the perfect regeneration and the Carnot efficiency can be expanded. [ABSTRACT FROM AUTHOR]

Typical textbook analyses of heat engines assume that the temperatures of thermal reservoirs do not change; that is, the reservoirs have infinite heat capacity. Several authors have investigated the performance of reversible heat engines for which reservoirs have finite heat capacities and thus the reservoir temperatures do change with time. We find that previous studies have been too restrictive in that they assumed that the reservoir temperature change per cycle is infinitesimal and that the engine ceases operation when the hot reservoir cools to match the temperature of the cold reservoir. We model a Carnot-like engine and show that (1) the problem can be solved exactly with no requirement for infinitesimal temperature changes and (2) there is nothing special about the instant when the temperatures converge, with the device transitioning smoothly from a heat engine to a refrigerator. We find explicit expressions for the limiting reservoir temperature and the total efficiency. Editor's Note: Most textbook thermodynamics problems assume thermal reservoirs of infinite heat capacity and consequently unchanging temperatures. Analyses involving engines operating between finite reservoirs are not unknown, but they typically assume that the temperature change per cycle is infinitesimal and that the engine stops operating when the hot reservoir has come to the temperature of the cold reservoir. This paper considers a Carnot-like engine operating between a finite hot reservoir and an infinite cold one, showing that the problem can be solved exactly with no requirement for infinitesimal changes and also that when the reservoir temperatures converge, the device simply transitions from being a heat engine to a refrigerator. Explicit expressions are developed for the limiting initially-hot reservoir temperature and the total efficiency. Appropriate for upper-level thermodynamics courses. [ABSTRACT FROM AUTHOR]

The possibility of utilizing quantum effects to enhance the performance of quantum heat engines has been an active topic of research, but how to enhance the performance by optimizing the engine parameters needs to be further studied. In this study, the temperature difference and dissipation modes affecting the performance of a three-level quantum heat engine were analyzed using an orthogonal test. The results indicated that the dissipation mode dominated the performance of the quantum heat engine. The quantum heat engine performs best when there is only resonance and no detuning; however, when detuning exists, a lower resonance can improve the efficiency by reducing energy losses. Regarding the temperature difference, the best performance was achieved at a medium temperature difference owing to the decreasing heat leakage. Finally, the "quantum friction" caused by the detuning could make the maximal efficiency lower than the Carnot efficiency. [ABSTRACT FROM AUTHOR]

Do quantum correlations lead to better performance with respect to several different systems working independently? For quantum thermal machines, the question is whether a working medium (WM) made of N constituents exhibits better performance than N independent engines working in parallel. Here, by inspecting a microscopic model with the WM composed by two non-interacting quantum harmonic oscillators, we show that the presence of a common environment can mediate non-trivial correlations in the WM leading to better quantum heat engine performance—maximum power and efficiency—with respect to an independent configuration. Furthermore, this advantage is striking for strong dissipation, a regime in which two independent engines cannot deliver any useful power. Our results show that dissipation can be exploited as a useful resource for quantum thermal engines and are then corroborated by optimization techniques here extended to non-Markovian quantum heat engines. [ABSTRACT FROM AUTHOR]

This Letter unveils a novel observation of condensation shock in a thermoacoustic prime mover with a wet stack, powered by a consistent 70 W heat input and maintained at atmospheric pressure. Intermittent pressure bursts, triggered by distinct acoustic cycles, reveal new characteristics of non-combustion-driven thermoacoustic instabilities, expanding the horizon beyond the energy conversion applications of traditional heat engines. Our findings, highlighted by pressure bursts reaching up to 35.8 kPa and detailed through time–frequency analysis, not only emphasize the critical role of phase-change dynamics but also pave the way for potential applications in heat transfer and material separation. [ABSTRACT FROM AUTHOR]

We present a theoretical study of quantum coherent dynamics of a three-level Λ-system driven by a thermal environment (such as blackbody radiation), which serves as an essential building block of photosynthetic light-harvesting models and quantum heat engines. By solving nonsecular Bloch–Redfield master equations, we obtain analytical results for the ground-state population and coherence dynamics and classify the dynamical regimes of the incoherently driven Λ-system as underdamped and overdamped depending on whether the ratio Δ/[rf(p)] is greater or less than one, where Δ is the ground-state energy splitting, r is the incoherent pumping rate, and f(p) is a function of the transition dipole alignment parameter p. In the underdamped regime, we observe long-lived coherent dynamics that lasts for τc ≃ 1/r, even though the initial state of the Λ-system contains no coherences in the energy basis. In the overdamped regime for p = 1, we observe the emergence of coherent quasi-steady states with the lifetime τc = 1.34(r/Δ2), which have a low von Neumann entropy compared to conventional thermal states. We propose an experimental scenario for observing noise-induced coherent dynamics in metastable He* atoms driven by x-polarized incoherent light. Our results suggest that thermal excitations can generate experimentally observable long-lived quantum coherent dynamics in the ground-state subspace of atomic and molecular Λ-systems in the absence of coherent driving. [ABSTRACT FROM AUTHOR]

By using the quasi-equilibrium Helmholtz energy, which is defined as the thermodynamic work in a quasi-static process, we investigate the thermal properties of both an isothermal process and a transition process between the adiabatic and isothermal states (adiabatic transition). Here, the work is defined by the change in energy from a steady state to another state under a time-dependent perturbation. In particular, the work for a quasi-static change is regarded as thermodynamic work. We employ a system–bath model that involves time-dependent perturbations in both the system and the system–bath interaction. We conduct numerical experiments for a three-stroke heat machine (a Kelvin–Planck cycle). For this purpose, we employ the hierarchical equations of motion (HEOM) approach. These experiments involve an adiabatic transition field that describes the operation of an adiabatic wall between the system and the bath. Thermodynamic–work diagrams for external fields and their conjugate variables, similar to the P–V diagram, are introduced to analyze the work done for the system in the cycle. We find that the thermodynamic efficiency of this machine is zero because the field for the isothermal processes acts as a refrigerator, whereas that for the adiabatic wall acts as a heat engine. This is a numerical manifestation of the Kelvin–Planck statement, which states that it is impossible to derive the mechanical effects from a single heat source. These HEOM simulations serve as a rigorous test of thermodynamic formulations because the second law of thermodynamics is only valid when the work involved in the operation of the adiabatic wall is treated accurately. [ABSTRACT FROM AUTHOR]

The current work presents a novel conceptual framework for the fluid and gasdynamics that govern the design and performance of an ideal scramjet flowpath. These include a theoretical comparison between ram and scram modes, the physics of thrust loss during inlet unstart, and the design of an optimal scramjet flowpath. We present a unique explicit, closed-form relation for the wall divergence of an ideal scramjet combustor. The accompanying derivations and discussions, which leverage this formulation, seek to address uncertainties and misconceptions regarding the dominant fluid processes present in these engines. It is shown that scram and ram modes exhibit theoretical similitude for maximum thrust potential at conditions beyond the one-dimensional Rayleigh choking limit but can diverge below the global choking threshold. Additionally, it is shown that even for an ideal scramjet heat engine cycle, thermodynamic efficiencies at various flight conditions deviate from those of the classical Brayton cycle. These insights and accompanying theoretical analyses are meant to establish a foundation for the thermodynamics and gasdynamics relevant to the performance of dual-mode scramjet engines. The resulting work offers an intuitive technical perspective on supersonic combustion and the fundamentals of dual-mode scramjet operation that can be applied across a wide range of scramjet-related experimental and computational studies and design efforts in the future. [ABSTRACT FROM AUTHOR]

One can use light to tune certain materials from a trivial to a topological phase. A prime example of such materials, classified as Floquet topological insulators (FTIs), is epitaxial graphene. In this paper, we probe the topological phase transition of a FTI via the efficiency and work output of quantum Otto and quantum Stirling heat engines. A maximum/minimum in the efficiency or work output invariably signals the phase transition point. Furthermore, both engines' work output and efficiency are markedly robust against the polarization direction of light. [ABSTRACT FROM AUTHOR]

Optimal non-local heat engines based on Coulomb-coupled systems demand a sharp step-like change in the energy-resolved system-to-reservoir coupling around the ground state of quantum dots. Such a sharp step-like transition in the system-to-reservoir coupling cannot be achieved in a realistic scenario. Here, I propose a realistic design for a non-local heat engine based on the Coulomb-coupled system, which circumvents the need for any change in the system-to-reservoir coupling, demanded by the optimal setups discussed in the literature. I demonstrate that an intentionally introduced asymmetry (or energy difference) in the ground state configuration between adjacent tunnel-coupled quantum dots, in conjugation with Coulomb coupling, is sufficient to convert the stochastic fluctuations from a non-local heat source into a directed flow of thermoelectric current. The performance, along with the regime of operation, of the proposed heat engine is then theoretically investigated using the quantum master-equation approach. It is demonstrated that the theoretical maximum power output for the proposed setup is limited to about 50 % of the optimal design. Despite a lower performance compared to the optimal setup, the novelty of the proposed design lies in the conjunction of fabrication simplicity along with a reasonable power output. At the end, the sequential transport processes leading to a performance deterioration of the proposed setup are analyzed and a method to alleviate such transport processes is discussed. The setup proposed in this paper can be used to design and fabricate high-performance non-local cryogenic heat engines. [ABSTRACT FROM AUTHOR]

Caloric materials respond to external field variations such as magnetic, stress, and electric. A simple caloric cycle uses entropy and temperature changes resulting from a single field variation to provide useful transfers of work and heat. An active regenerator cycle increases operating range and efficiency of a caloric material when property variations are appropriately matched to design conditions. However, the variability of material properties, wide range of design variables, and non-linear interactions complicate design of devices. Simplified analytic models are needed to increase understanding and quantify potential of calorics for commercial heat pumps and engines. An analytic model of a generic active caloric regenerator operating as a heat pump or engine is described. A thermal effectiveness is defined as an analytic function of operating, design, and material parameters. [ABSTRACT FROM AUTHOR]

A strong micro heat engine that can be used in the untethered state is essential for next-generation microrobotics. Here, we propose a rapid swimmer using explosive boiling due to electrical discharge in water. Specifically, we demonstrate that the water-repellent swimmer that has an aluminum discharge antenna in the rear part can swim with the maximum velocity of ∼14 cm/s on the water surface like a water strider between a pair of parallel electrodes in a shallow water pool by applying direct current high-voltage pulses repeatedly. Moreover, by the video observation with high speed (960 fps), we found that an asymmetrical wave was generated immediately after the discharge, and it propelled the swimmer. Our findings should contribute to next-generation microrobots in the future. [ABSTRACT FROM AUTHOR]

We present an Ito-Langevin model for freestanding graphene connected to an electrical circuit. The graphene is treated as a Brownian particle in a double-well potential and is adjacent to a fixed electrode to form a variable capacitor. The capacitor is connected in series with a battery and a load resistor. The capacitor and resistor are given separate thermal reservoirs. We have solved the coupled Ito-Langevin equations for a broad range of temperature differences between the two reservoirs. Using ensemble averages, we report the rate of change in energy, heat, and work using stochastic thermodynamics. When the resistor is held at higher temperatures, the efficiency of the heat engine rises linearly with temperature. However, when the graphene is held at higher temperatures, the efficiency instantly rises and then plateaus. Also, twice as much entropy is produced when the resistor is hotter compared to when the graphene is hotter. Unexpectedly, the temperature of the capacitor is found to alter the dissipated power of the resistor. [ABSTRACT FROM AUTHOR]

The generation of thermal currents in a miniaturized device modeled as a channel connected to reservoirs maintained at different temperatures and coupled to a periodic THz driving source is reported in this letter. Primarily, we show that while thermally activated electrons can be pumped from the hot reservoir into the cold side, the quantum of charge flow increases in the presence of the periodic source. We explain this phenomenon by taking recourse to the Floquet theory guided rearrangement of the energy levels under periodic driving, which, in turn, augments the electron injection into the channel. The calculations uncover a useful feature whereby the strength of such a thermally-pumped current is amenable through a joint control of the amplitude and frequency of the signal, offering an additional experimentally-adjustable set of tools to regulate their flow. In the final part, the Seebeck coefficient and the thermoelectric figure-of-merit for this setup are analytically determined. Results are shown for classes of materials defined by linear and quadratic dispersion. [ABSTRACT FROM AUTHOR]

The thermal wall function method offers an effective pathway for modeling heat transfer in engines. This paper reexamined the traditional construction method of the thermal wall function and improved it by correcting the integration scheme in the boundary layer; then, an enhanced heat transfer model was introduced. Since the heat release from the chemical reactions is of great significance to the near-wall flow, it is necessary to construct a law of the wall including the heat release effect. A new law of the wall including the impacts of the pressure work and the heat release from chemical reactions was obtained based on the analogy between the momentum transfer and the heat transfer predicted using the improved thermal wall function. In the analogy process, the formula of the eddy-viscosity ratio was reconstructed for the whole boundary layer, and then, the Prandtl number for turbulent flow was improved. The current research is beneficial for predicting the near-wall flow and heat transfer characteristics under conditions with strong interactions between the wall and the flame. [ABSTRACT FROM AUTHOR]

We analyze the role of coherent, non-perturbative system-bath interactions in a photosynthetic heat engine. Using the reaction-coordinate formalism to describe the vibrational phonon-environment in the engine, we analyze the efficiency around an optimal parameter regime predicted in earlier studies. We show that, in the limit of high-temperature photon irradiation, the phonon-assisted population transfer between bright and dark states is suppressed due to dephasing from the photon environment, even in the Markov limit where we expect the influence of each bath to have an independent and additive effect on the dynamics. Manipulating the phonon bath properties via its spectral density enables us to identify both optimal low- and high-frequency regimes where the suppression can be removed. This suppression of transfer and its removal suggests that it is important to consider carefully the non-perturbative and cooperative effects of system-bath environments in designing artificial photosynthetic systems and also that manipulating inter-environmental interactions could provide a new multidimensional “lever” by which photocells and other types of quantum devices can be optimized. [ABSTRACT FROM AUTHOR]

Solid-state pyroelectric heat engines that utilize the temperature and electric field dependence of electric displacement are promising for high-efficiency high-power thermal-to-electrical energy conversion. However, one of the key challenges for pyroelectric energy conversion is the inaccessibility of tunable transient heat sources for energy harvesting. This Perspective analyzes the potential of thermal waveform engineering for pyroelectric energy generation. We use the Landau-Devonshire phenomenological model to evaluate the energy conversion performance of a representative pyroelectric material coupled to (1) static heat source/sink via thermal switches, and (2) modulated heat source. Using this thermodynamic analysis, which accounts for thermal and electrical losses, we demonstrate a path toward maximizing pyroelectric energy conversion performance through purposeful thermal and electrical control. [ABSTRACT FROM AUTHOR]

We develop a general method for calculating the thermal efficiency of arbitrary thermodynamic cycles defined in the pressure-volume (p–V) diagram. To demonstrate how effective our approach is, we calculate the thermal efficiency of ideal gas engines for a few non-trivial cycles in the p–V diagram, including a circular shape, a heart shape, a cycloid of Ceva, and a star-shaped curve. We determine the segments along the cycle where heat is absorbed or released from the heat engine. Our method can be applied to any gas model, and, as an example, we present the results for the van der Waals gas. [ABSTRACT FROM AUTHOR]

We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)--which have a purely quantum mechanical origin--the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat currents and thework performed by the heat engine, and we find that their phases depend on the system-bath coupling strength. Through consideration of the bath heat current, we show that the efficiency of the heat engine decreases as the strength of the system-bath coupling increases, due to the CASBI contribution. In the case of a large system-bath coupling, the efficiency decreases further if the bath temperature is increased, even if the ratio of the bath temperatures is fixed, due to the discretized nature of energy eigenstates. This is also considered to be a unique feature of quantum heat engines. [ABSTRACT FROM AUTHOR]

Thermoelectric generators (TEGs) are solid-state heat engines consisting of p-type and n-type semiconductors that convert heat into electricity via the Seebeck effect. Conducting polymers are a viable alternative with intrinsic advantages over their inorganic counterparts, since they are abundant, flexible as thick-films, and have reduced manufacturing costs due to solution processing. Furthermore, polymers have an inherently low thermal conductivity, thus affording them the option of forgoing some heat exchanger costs. Current examples of polymer TE devices have been limited to traditional flat-plate geometries with power densities on the µW/cm² scale, where their potential is not fully realized. Herein, we report a novel radial device architecture and model the improved performance of polymer-based TEG based on this architecture. Our radial architecture accommodates a fluid as the heat source and can operate under natural convection alone due to heat spreading. Analytical heat transfer and electrical models are presented that optimize the device for maximum power density, and for the first time we obtain the geometry matching condition that maximizes the efficiency. We predict high power densities of ~1 mW/cm² using state-of-the-art polymer TEs subjected to a temperature difference of 100 K, which is nearly 1000x higher than polymer flat-plate architectures reported in literature. [ABSTRACT FROM AUTHOR]

Thermal transport and quantum thermodynamics at the nanoscale are nowadays garnering increasing attention, in particular, in the context of quantum technologies. Experiments relevant for quantum technology are expected to be performed in the nonlinear regime. In this work, we build on previous results derived in the linear response regime for the performance of an Aharonov-Bohm (AB) interferometer operated as a heat engine. In the nonlinear regime, we demonstrate the tunability, large efficiency, and thermopower that this mesoscopic quantum machine can achieve, confirming the exciting perspectives that this AB ring offers for developing efficient thermal machines in the fully quantum regime. [ABSTRACT FROM AUTHOR]

Recent evidence suggests that quantum effects may have functional importance in biological lightharvesting systems. Along with delocalized electronic excitations, it is now suspected that quantum coherent interactions with certain near-resonant vibrations may contribute to light-harvesting performance. However, the actual quantum advantage offered by such coherent vibrational interactions has not yet been established. We investigate a quantum design principle, whereby coherent exchange of single energy quanta between electronic and vibrational degrees of freedom can enhance a light-harvesting system's power above what is possible by thermal mechanisms alone. We present a prototype quantum heat engine which cleanly illustrates this quantum design principle and quantifies its quantum advantage using thermodynamic measures of performance. We also demonstrate the principle's relevance in parameter regimes connected to natural light-harvesting structures. [ABSTRACT FROM AUTHOR]

We have developed a thermally actuated liquid microlens. An embedded thermoelectric element is used to actuate the liquid based heat engine. A closed-loop system is harnessed to drive and stabilize the temperature of the heat engine. Direct contact between the thermoelectric device and the water results in greatly improved, sub-second thermal rise time (0.8 s). The water based heat engine reacts to the variation in the temperature via expansion and contraction. In turn, the shape of a pinned water-oil meniscus at a lens aperture is deformed in response to the net volume change in the water, creating a tunable microlens. A method to fabricate microfluidic devices with relatively high thickness (250-750 μm) and large length-to-depth aspect ratio (280:1) was developed and used in the process. After fabrication and thermal calibration, optical characteristic of the microlens was assessed. Back focal length of the microlens was shown to vary continuously from -19.6mm to -6.5mm as the temperature increased from 5 °C to 35°C. A thin film air was further introduced to insulate the heat engine from the substrate to protect the microlens area from the temperature fluctuation of the heat engine, thus preventing the change of the refractive indices and thermally induced aberrations. Wavefront aberration measurement was conducted. Surface profile of the microlens was mapped and found to have a conical shape. Both 3-dimensional and 1-dimensional thermal models for the device structure were developed and thermal simulation of the device was performed. [ABSTRACT FROM AUTHOR]

Theoretical thermoelectric nanophysics models of low-dimensional electronic heat engine and refrigerator devices, comprising two-dimensional hot and cold reservoirs and an interconnecting filtered electron transport mechanism have been established. The models were used to numerically simulate and evaluate the thermoelectric performance and energy conversion efficiencies of these low-dimensional devices, based on three different types of electron transport momentum-dependent filters, referred to herein as kx, ky, and kr filters. Assuming the Fermi-Dirac distribution of electrons, expressions for key thermoelectric performance parameters were derived for the resonant transport processes, in which the transmission of electrons has been approximated as a Lorentzian resonance function. Optimizations were carried out and the corresponding optimized design parameters have been determined, including but not limited to the universal theoretical upper bound of the efficiency at maximum power for heat engines, and the maximum coefficient of performance for refrigerators. From the results, it was determined that kr filter delivers the best thermoelectric performance, followed by the kx filter, and then the ky filter. For refrigerators with any one of three filters, an optimum range for the full width at half maximum of the transport resonance was found to be <2kBT. [ABSTRACT FROM AUTHOR]

Thermoelectric generators (TEGs) are solid state heat engines that generate electricity from a temperature gradient. Optimizing these devices for maximum power production can be difficult due to the many heat transport mechanisms occurring simultaneously within the TEG. In this paper, we develop a model for heat transport in thermoelectric materials in which an 'effective thermal conductivity' (κeff) encompasses both the one dimensional steady-state Fourier conduction and the heat generation/consumption due to secondary thermoelectric effects. This model is especially powerful in that the value of κeff does not depend upon the operating conditions of the TEG but rather on the transport properties of the TE materials themselves. We analyze a variety of thermoelectric materials and generator designs using this concept and demonstrate that κeff predicts the heat fluxes within these devices to 5% of the exact value. [ABSTRACT FROM AUTHOR]