Energy Flow Rate Research Articles

Testing method for thermal performance based rating of various solar dryer designs

► No load experimental study of various solar dryer designs has been performed. ► Non-dimensional parameter named no load performance index (NLPI) is identified. ► A thermal test method based on steady state heat balance concept is proposed for computation of NLPI. ► Invariable NLPI values are obtained for a wide range of parameters investigated. ► NLPI facilitates performance comparison of different dryer designs on equitable basis. A generalized methodology is developed for thermal testing of various solar dryer designs operated for natural and forced air flow conditions. The steady state mathematical model based on heat balance concept of solar dryer without load is applied to identify the dimensionless parameter called no-load performance index (NLPI). Laboratory models of direct (cabinet), indirect and mixed mode solar dryer are designed and constructed to perform steady state thermal tests for natural and forced air circulation. The dryers with no-load are operated with air passage between absorber plate and glass cover for the range of 300–800 W/m 2 and 0.009–0.026 kg/s of absorbed thermal energy and air mass flow rate respectively under indoor simulation conditions. The present study reveals that the forced convection operated dryer provides higher NLPI in contrast to that of natural convection . The comparative performance analysis of dryers indicates that the mixed mode dryer exhibits maximum value of NLPI followed by indirect and cabinet ones for both natural and forced air circulation. It is also found that for any dryer operating at given air flow condition, almost invariable NLPI values have been obtained for a wide range of absorbed energy and ambient air temperature data, thus facilitating performance comparison between different dryer designs on equitable basis. The results of statistical analysis showing low standard errors of mean further demonstrate good consistency in NLPI values for various dryer designs. The uncertainty in NLPI due to error in measurement of several parameters by instruments ranges from 0.79 to 1.96% for various dryer designs operated under different conditions.

Comparison of the performance of a spark-ignited gasoline engine blended with hydrogen and hydrogen–oxygen mixtures

This paper compared the effects of hydrogen and hydrogen–oxygen blends (hydroxygen) additions on the performance of a gasoline engine at 1400 rpm and a manifolds absolute pressure of 61.5 kPa. The tests were carried out on a 1.6 L gasoline engine equipped with a hydrogen and oxygen injection system. A hybrid electronic control unit was applied to adjust the hydrogen and hydroxygen volume fractions in the intake increasing from 0% to about 3% and keep the hydrogen-to-oxygen mole ratio at 2:1 in hydroxygen tests. For each testing condition, the gasoline flow rate was adjusted to maintain the mixture global excess air ratio at 1.00. The test results confirmed that engine fuel energy flow rate was decreased after hydrogen addition but increased with hydroxygen blending. When hydrogen or hydroxygen volume fraction in the intake was lower than 2%, the hydroxygen-blended gasoline engine produced a higher thermal efficiency than the hydrogen-blended gasoline engine. Both the additions of hydrogen and hydroxygen help reduce flame development and propagation periods of the gasoline engine. HC emissions were reduced whereas NOx emissions were raised with the increase of hydrogen and hydroxygen addition levels. CO was slightly increased after hydrogen blending, but reduced with hydroxygen addition.

EFCon: Energy flow control for sustainable wireless sensor networks

The rapid advances in processor, memory, and radio technology enable the development of small, inexpensive sensor nodes that are capable of sensing, computation, and communication. However, the severe energy constraints of the sensors present major challenges for long-term applications. In order to achieve sustainability, environmental energy harvesting has been demonstrated as a promising approach. In this work, the energy utilization scheme is investigated for wireless sensor networks with energy harvesting nodes. The energy utilization system is divided to three parts: energy harvesting, energy consuming and energy storage. Then the sustainability problem is formulated as an energy flow control problem. An energy flow control system, called EFCon, is proposed to keep the balance between energy supplies and demands. EFCon consists of two phases, energy flow direction control and flow rate control. In the phase of energy flow direction control, the system dynamically switches among four patterns: flood flow, direct flow, compensate flow, and backup flow, according to current environmental energy condition and the residual energy condition. Once the energy flow direction is determined, a corresponding energy flow rate control strategy will be adopted for efficient energy utilization. The EFCon is implemented and validated by a long-term deployment in real testbeds. The experimental results indicate that the EFCon outperforms existing designs.

Lattice Boltzmann Method and Modified Discrete Ordinate Method Applied to Radiative Transport in a Spherical Medium with and without Conduction

This article deals with the application of the modified discrete ordinate method (MDOM) to calculate volumetric radiative information with and without conduction in a concentric spherical enclosure containing a participating medium. With radiative information known from the MDOM, the energy equation of the combined mode transient conduction and radiation heat transfer is formulated and solved using the lattice Boltzmann method (LBM). Without conduction, for pure radiation case, two benchmark problems, representing nonradiative and radiative equilibrium situations are taken up. In the case of non-radiative equilibrium, an isothermal medium is bounded by cold walls and medium is the source of radiation, while in the case of radiative equilibrium, nonisothermal medium is confined between a hot and a cold wall, and the hot (inner sphere) wall is the radiation source. Depending upon the problem, heat flux, energy flow rate, emissive power, and temperature distributions in the medium are calculated for different values of parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the boundary emissivity, and the radius ratio. To validate the MDOM and the LBM-MDOM formulations, problems are also solved using the finite volume method (FVM) and the finite-difference method (FDM)–FVM approach, in which the FVM is used to calculate the volumetric radiation and the energy equation is also solved using the FDM. Results of the MDOM, LBM–MDOM, FVM and FDM–FVM are also benchmarked against those available in the literature. MDOM and LBM–MDOM have been found to provide accurate results.

Digraph and matrix method for the performance evaluation of carbide compacting die manufactured by wire EDM

This paper presents a methodology to evaluate the performance of carbide compacting die using graph theoretic approach (GTA). Factors affecting the die performance and their interactions are analysed by developing a mathematical model using digraph and matrix method. Permanent function or die performance index is obtained from the matrix model developed from the digraphs. This permanent function/index value compares and ranks the factors affecting the die performance. It helps in selection of optimum process parameters during die manufacturing. Hence, process output errors such as dimensional inaccuracy, large surface craters, deep recast layers, etc. will be minimised during die manufacturing which helps to achieve better die performance. In present illustration, factors affecting the performance of carbide compacting die are grouped into five main factors namely work material, machine tool, tool electrode, geometry of die and machining operation. GTA methodology reveals that the machine tool has highest index value. Therefore, it is the most influencing factor affecting the die performance. In case of die material low cobalt concentration and small grain size yields good surface finish, while in machine tool low discharge energy (i.e. low values of peak current, pulse-on time, servo voltage and high value of pulse-off time) and high dielectric flow rate yields good surface finish and, hence, favours the good die performance. In case of die geometry, large work piece thickness and small taper angles results in lesser geometrical deviations and hence helps to achieve better die performance.

Reducing the idle speed of a spark-ignited gasoline engine with hydrogen addition

Reducing idle speed is an effective way for decreasing engine idle fuel consumption. Unfortunately, due to the increased residual dilution and dropped combustion temperature, spark-ignited (SI) gasoline engines are prone to suffer high cyclic variation and even stall at low idle speeds. This paper investigated the effect of hydrogen addition on the performance of an SI gasoline engine at reduced idle speeds of 600, 700 and 800 rpm. The test results shows that cyclic variation was raised with the decrease of idle speed but reduced obviously with the increase of hydrogen energy fraction ( β H 2 ) . Decreasing idle speed and adding hydrogen were effective for reducing engine idle fuel consumption. The total fuel energy flow rate was effectively dropped from 30.8 MJ/h at 800 rpm and β H 2 = 0% to 17.6 MJ/h at 600 rpm and β H 2 = 19.9%. Because of the dropped fuel energy flow rate causing the reduced combustion temperature, both cooling and exhaust losses were markedly reduced after decreasing idle speed and adding hydrogen. HC and CO emissions were dropped with the increase of β H 2 , but increased after reducing idle speed. However, NOx emissions were decreased after reducing idle speed and adding hydrogen, due to the dropped peak cylinder temperature.

Effect of hydrogen addition on combustion and emissions performance of a spark-ignited ethanol engine at idle and stoichiometric conditions

Regarding the limited fossil fuel reserves, the renewable ethanol has been considered as one of the substitutional fuels for spark ignition (SI) engines. But due to its high latent heat, ethanol is usually hard to be well evaporated to form the homogeneous fuel–air mixture at low temperatures, e.g., at idle condition. Compared with ethanol, hydrogen possesses many unique combustion and physicochemical properties that help improve combustion process. In this paper, the performance of a hydrogen-enriched SI ethanol engine under idle and stoichiometric conditions was investigated. The experiment was performed on a modified 1.6 L SI engine equipped with a hydrogen port-injection system. The ethanol was injected into the intake ports using the original engine gasoline injection system. A self-developed hybrid electronic control unit (HECU) was adopted to govern the opening and closing of hydrogen and ethanol injectors. The spark timing and idle bypass valve opening were governed by the engine original electronic control unit (OECU), so that the engine could operate under its original target idle speed for each testing point. The engine was first fueled with the pure ethanol and then hydrogen volume fraction in the total intake gas was gradually increased through increasing hydrogen injection duration. For a specified hydrogen addition level, ethanol flow rate was reduced to keep the hydrogen–ethanol–air mixture at stoichiometric condition. The test results showed that hydrogen addition was effective on reducing cyclic variations and improving indicated thermal efficiency of an ethanol engine at idle. The fuel energy flow rate was reduced by 20% when hydrogen volume fraction in the intake rose from 0% to 6.38%. Both flame development and propagation periods were shortened with the increase of hydrogen blending ratio. The heat transfer to the coolant was decreased and the degree of constant volume combustion was enhanced after hydrogen addition. HC and CO emissions were first reduced and then increased with the increase of hydrogen blending fraction. The acetaldehyde emission from the hydrogen-enriched ethanol engine is lower than that from the pure ethanol engine. However, the addition of hydrogen tended to increase NO x emissions from the ethanol engine at idle and stoichiometric conditions.

Quantum localization, dephasing and vibrational energy flow in a trans-formanilide (TFA)–H 2O complex

Recent stimulated emission pumping-population transfer spectroscopic studies are providing measurements of energy barriers to hydrogen bond rearrangements involving biological molecules and water. To determine the kinetics of hydrogen bond rearrangements we need in addition information about energy flow in the biomolecule–water complex. We address the problem of quantum energy flow in one such complex system using a random matrix approach. We report here calculations of energy flow in the peptide trans-formanilide (TFA) that account for the hydrogen bonding of a water molecule to one of two sites on the peptide. Coupling to the water is found to enhance energy flow in the peptide. At energies near the hydrogen bond rearrangement barrier the rate of energy flow in TFA is nevertheless sufficiently sluggish to have a significant impact on the kinetics of water shuttling between hydrogen-bonding sites.

A short-cut method for assessing absorbents for post-combustion carbon dioxide capture

A short-cut method for the estimation of the minimum regeneration energy and optimum solvent flow rate in post-combustion carbon dioxide capture by absorption is presented. It is developed for comparing solvents of which only little thermo-physical data is known. The closed absorber–desorber cycle is described by an equilibrium stage model (modified Kremser equation with discretized equilibrium curves). The method can be implemented in any mathematical toolbox or as stand-alone solution. The only required input is the solubility data at absorber and desorber conditions, the heat of absorption and heat capacities. The caloric data may be estimated. The method was applied to monoethanolamine (MEA) and two solvents from the EU-project CASTOR. Comparisons with experimental results from pilot-plant studies with MEA show that the method, despite its simplicity, gives reasonable results. The method should also be useful in other applications where absorbents, of which only little data is available, need to be screened.

Importance of energy management in desiccated coconut industry

Energy flow rates across commonly used desiccators and associated heat transfer equipment are quantified. It is seen that approximately 726 percent excess heat energy over the actual requirement is presently used for drying in desiccators. Approximately 49 percent of heat energy is exhausted to the atmosphere through the chimney and approximately 23 percent along with the desiccator exhaust gases. Approximately 40 percent of energy could be saved by introducing recirculation techniques of heat recovery. This saving represents about 83.2 million kwh of energy for 1981 alone, which is an equivalent of 4.5 percent of the total electrical energy generated in Sri Lanka in 1981. COCOS, (1984) 2 18-28 doi: 10.4038/cocos.v2i0.812

Measurement of Input Energy of LNG-based Gaseous Fuels with Capillary-typed Thermal Mass Flowmeter for Fuel Cells

With capillary-typed thermal mass flowmeters (ctMFM) primarily calibrated with methane, it was investigated to measure input energy of LNG-based gaseous fuels to fuel cell systems. Energy flow rate can be expressed as <i>Q× CLNG× FR</i> where <i>Q</i> is heating value, <i>CLNG</i> is conversion factor from CH4 to the fuels, and <i>FR</i> is reading of ctMFM expressed as CH4 flow rate. Strong and negative correlation was observed between <i>Q</i> and <i>CLNG</i>, which will reduce deviation of the term "<i>Q× CLNG</i>" to 20% of deviation of <i>Q</i>. Calibration of ctMFM with an average composition of the fuels is necessary to obtain the correction factor <i>Q× CLNG</i>. It was found that input energy of LNG-based fuels can be measured with 40-100% range of ctMFM within {plus minus}1.5% uncertainty even if heating value of the fuels deviates by {plus minus}4.0%.

Solvent-Induced Photostability of Acetylene Molecules in Clusters Probed by Multiphoton Dissociation

We have studied the multiphoton photodissociation of (C(2)H(2))(n) and (C(2)H(2))(n) x Ar(m) clusters in molecular beams. The clusters were prepared in supersonic expansions under various conditions, and the corresponding mean cluster sizes were determined, for which the photodissociation at 193 nm was studied. The measured kinetic energy distributions (KEDs) of the H fragment from acetylene in clusters peak around 0.2 eV, in agreement with the KED from an isolated C(2)H(2) molecule. However, the KEDs from the clusters extend to kinetic energies of over 2 eV, significantly higher than the maximum fragment energies from an isolated molecule of about 1 eV. The photofragment acceleration upon solvation is a rather unusual phenomenon. The analysis based on ab initio calculations suggests the following scenario: (i) At 193 nm, photodissociation of acetylene occurs mostly in the singlet manifold. (ii) The solvent stabilizes the acetylene molecule, preventing it from undergoing hydrogen dissociation and funneling the population into a vibrationally hot ground state. (iii) The excited C(2)H(2) absorbs the next photon and eventually dissociates, yielding the H fragment with a higher kinetic energy corresponding to the first C(2)H(2) excitation. Thus, the H-fragment KED extending to higher energies is a fingerprint of the cage effect and the multiphoton nature of the observed processes. The photon-flux dependence of the KEDs reflects the rate of the vibrational energy flow from the hot ground state of acetylene to the neighboring solvent molecules.

Large Nonstatistical Branching Ratio in the Dissociation of Pentane-2,4-dione Radical Cation: An Ab Initio Direct Classical Trajectory Study

The dissociation of pentane-2,4-dione radical cation has been studied by ab initio direct classical trajectory calculations at the MP2/6-31G(d) level of theory. A bond additivity correction has been used to improve the MP2 potential energy surface (BAC-MP2). A microcanonical ensemble was constructed using quasiclassical normal-mode sampling by distributing 10 kcal/mol of excess energy above ZPE for the transition state for the tautomerization of the enol with a terminal double bond, 4-hydroxypent-4-en-2-one radical cation, to the diketo form. A total of 244 trajectories were run starting from this transition state, yielding pentane-2,4-dione radical cation and depositing energy in the terminal CC bond. As a result, the branching ratio for dissociation of the terminal CC bond versus the interior CC bonds is significantly larger than expected from RRKM theory. The branching ratio for the dissociation of the two interior CC bonds is ∼20:1, with the one closest to the activated methyl breaking more often. Since the two interior bonds are equivalent and should dissociate with equal probability, this branching ratio represents a very large deviation from statistical behavior. A simple kinetic scheme has been constructed to model the dissociation rates. The nonstatistical behavior is seen because the rate of energy flow within the molecule is comparable to or less than the rates of dissociation for the activated system. In addition to the expected dissociation products, some of the trajectories also lead to the formation of an ester-like product, prop-1-en-2-yl acetate radical cation.

On magneto-thermo-viscoelastic deformation and fracture

A thermodynamic formulation of magneto-thermo-viscoelastic constitutive and fracture theory is developed, accounting for non-linear, thermal and hysteresis effects. State equations and energy flux integral are obtained in consideration of the Helmholtz free energy including the contribution of the free magnetic field as a functional of the histories of deformation, temperature and magnetic induction in the reference configuration. The rate of energy flow towards the crack front per unit crack advance provides the crack driving force in the presence of magneto-thermo-mechanical coupling and hysteresis, which is evaluated through formation of energy-momentum tensor for steady-state crack propagation. A fracture criterion based on the generalized J ˜ -integral thus formulated overcomes the difficulty encountered by existing treatments and helps to understand the fracture behavior of both conservative and dissipative materials subject to combined magnetic, thermal and mechanical loadings. Reduction of this formulation to finite magneto-thermo-viscoelasticity is provided with polynomial expansion of the Helmholtz free energy functional.

In vivo imaging of blood flow in the mouse Achilles tendon using high-frequency ultrasound

Objective Achilles tendinitis is a common clinical problem with many treatment modalities, including physical therapy, exercise and therapeutic ultrasound. However, evaluating the effects of current therapeutic modalities and studying the therapeutic mechanism(s) in vivo remains problematic. In this study, we attempted to observe the morphology and microcirculation changes in mouse Achilles tendons between pre- and post-treatment using high-frequency (25 MHz) ultrasound imaging. A secondary aim was to assess the potential of high-frequency ultrasound in exploring therapeutic mechanisms in small-animal models in vivo. Methods A collagenase-induced mouse model of Achilles tendinitis was adopted, and 5 min treatment of continuous-mode low-frequency (45 kHz) ultrasound with 47 mW/cm 2 maximum intensity and 16.3 cm 2 effective beam radiating area was applied. The B-mode images showed no focal hypoechoic regions in normal Achilles tendons either pre- or post-treatment. The Doppler power energy and blood flow rate were measured within the peritendinous space of the Achilles tendon. Conclusion An increase in the microcirculation was observed soon after the low-frequency ultrasound treatment, which was due to immediate induction of vascular dilatation. The results suggest that applying high-frequency Doppler imaging to small-animal models will be an invaluable aid in explorations of the therapeutic mechanism(s). Our future work includes using imaging to assess microcirculation changes in tendinitis between before and after treatment over a long time period, which is expected to yield useful physiological data for future human studies.

Modeling C and N flows through a stream food web: an inverse approach*

Inverse analysis is a promising method for addressing a common problem in stream ecology: how to estimate material and energy flows through food webs when the total number of flows greatly exceeds the number of measured flows. Inverse analyses provide solutions to systems of linear difference equations, where each equation corresponds to a flow between 2 foodweb compartments. Physiological and isotopic constraints are used to reduce the number of possible solutions and to ensure that flow magnitudes are realistic. We used inverse methods to develop models of C and N flows through the food web in Kaiwiki Stream, a forested stream on the island of Hawaii. The empirical data used in the models included measurements of respiration and detritus ingestion and particulate organic matter dynamics. Constraints for the models included stable isotope ratios and assimilation and production efficiencies. Sensitivity analyses indicated that the models were robust to changes in the values of most empirical measurements. The models elucidated community- and ecosystem-level properties of Kaiwiki Stream that would have been obscured in simpler tracer or budget models. Among those properties are the flows of dissolved organic C and N through the food web, the roles of bacteria, fungi, and fruit in metazoan diets, and the differences in primary dietary sources of C and N, indicating differential assimilation of ingested food. The modeled C and N flow networks for Kaiwiki Stream had dissimilar structures, which might reflect a combination of differential C and N assimilation and dissimilar effects of physical processes on C and N flows between nonliving pools. Rates of ecosystem processes estimated by inverse analysis (e.g., gross primary productivity, community respiration) were comparable with rates measured in other tropical and temperate forested streams. Our study demonstrates the utility of inverse methods for reconstructing food webs, estimating material and energy flow rates, and generating hypotheses.

Luminosity Dependence of the Electron Temperature in the Bright Hard State of the Black Hole Candidate GX 339–4

Abstract We have analyzed 200 Rossi X-ray Timing Explorer observations of the black hole candidate GX339 $-$ 4, all from bright hard state periods between 1996 and 2005. The purpose of our study is to investigate the radiation mechanisms in the hard state of GX 339 $-$ 4. The broadband 3-200keV spectra were successfully modeled by a simple analytic model, power-law with an exponential cut-off modified with a smeared edge. The obtained energy cut-off ( $E_{\rm {cut}}$ ) was distributed over 50-200keV, and the photon index over 1.4-1.7. We found a clear anti-correlation ( $E_{\rm {cut}} \propto L^{-0.70\pm0.06}$ ) between the X-ray luminosity ( $L$ ) in 2-200keV and $E_{\rm {cut}}$ , when $L$ is larger than $7 \times 10^{37}$ ergs $^{-1}$ (assuming a distance of 8kpc), while $E_{\rm {cut}}$ is roughly constant at around 200keV when $L$ is smaller than $7 \times 10^{37}$ ergs $^{-1}$ . This anti-correlation remained unchanged by adopting a more physical thermal Comptonization model, which resulted in an anti-correlation that can be expressed as $kT_{\rm {e}} \propto L^{-0.24\pm0.06}$ . These anti-correlations can be quantitatively explained by a picture in which the energy-flow rate from protons to electrons balances with inverse Compton cooling.

Reheating the Universe in braneworld cosmological models with bulk–brane energytransfer

The emergence of the cosmological composition (the reheating era) after the inflationaryperiod is analyzed in the framework of the braneworld models, in which our Universe is a3-brane embedded in a five-dimensional bulk, by assuming the possibility of brane–bulkenergy exchange. The inflaton field is assumed to decay into normal matter only, while thedark matter is injected into the brane from the bulk. To describe the reheating process weadopt a phenomenological approach, by describing the decay of the inflaton fieldusing a friction term proportional to the energy density of the field. After theradiation dominated epoch the model reduces to the standard four-dimensionalcosmological model. The modified field equations are analyzed analytically andnumerically in both the extra-dimension dominated reheating phase (when thequadratic terms in energy density dominate the dynamics) and the general case. Theevolution profiles of the matter, of the scalar field and of the scale factor of theUniverse are obtained for different values of the parameters of the model and of theequations of state of the normal and dark matter. The equation describing thetime evolution of the ratio of the energy densities of the dark and the normalmatter is also obtained. The ratio depends on the rate of energy flow between thebulk and the brane. The observational constraint of an approximately constantratio of the dark and the baryonic matter requires that the dark matter must benon-relativistic (cold). The model predicts a reheating temperature of the order of3 × 106 GeV, a brane tensionof the order of 1025 GeV4, and the composition of the Universe obtained is consistent with the observationaldata.

V. Smil, Energy in Nature and Society: General Energetics of Complex Systems

Energy is a central concept in physics. Thus I was particularly drawn to this new book by an author who, in the last 30 years, has written 20 books, half of which have the word ‘‘energy’’ or ‘‘energetics’’ in their titles. Vaclav Smil, a Distinguished Professor at the University of Manitoba in Canada, has written on energy in the environmental context broadly, and specifically on agriculture, the biosphere and biomass, and in the developing world and China. Here, with erudite quotations Professor Smil provides an excellent, balanced overview of both the sources and the uses—by the human species—of different forms of energy on our planet. The fundamental aim of this book is ‘‘to produce a comprehensive, systematic, revealing (and hence interdisciplinary and quantitative) treatment of all major aspects of energy in nature and society’’. This most ambitious aim is definitely achieved by the analyses and syntheses presented. The first two chapters adopt a historical and physics approach to the concept of energetics, contrasting quantities such as power, or energy flow (in W or J/s), power density or rate of energy flow per unit area (in W/m), and specific energy or energy intensity (in J/kg). The conversions between different forms of energy—chemical, electrical, electromagnetic, gravitational, kinetic, nuclear and thermal—are explained. This discussion is highly relevant in the light of today’s discussions on biofuels. Energy fluxes are explored, ranging from that due to solar radiation (peaking at a wavelength of *500 nm) to terrestrial radiation (peaking at 10 lm), meridional heat transport in the ocean, tornadoes, geothermal processes, volcanoes and earthquakes. That ‘‘sets the stage for reviewing both the bioenergetic fundamentals and the specific and ecosystemic peculiarities of the plant and animal kingdoms’’. Chapter 3 is on photosynthesis, the bioenergetics of primary production in bacteria or green plants. Phototrophs are organisms which obtain energy from sunlight for the synthesis of organic compounds. They require oxygen in the atmosphere to remove carbon dioxide from the atmosphere, i.e. in order to assimilate (or ‘‘fix’’) carbon. The complicated enzymatic chemical reactions of ‘‘net primary productivity’’ are explained. Trees store *20 MJ/kg

Quantizing Ulam’s Control Conjecture

Like classically chaotic systems, can quantum systems be nudged from a given initial state to any other by arbitrarily weak control fields? We explore a scaling theory that sets fundamental limits on the time required for population transfer with weak control fields. Our results depend on the size of the quantum state space and on the rate and extent of energy flow within the system. When the unperturbed dynamics is quantum localized, the total distance in state space over which control can be achieved grows linearly with the number of photons that are expended.