State Equilibrium Research Articles

Can Education Policy Promote Environmental Quality: An Overlapping Generations Model

Education is a crucial aspect of the worldwide reaction to climate change. It aids younger generation realize and approach the effect of global warming, inspires changes in their points of view and comportment and aids them adjust to climate change-similar tendency. This paper develops a two-period overlapping-generations model featuring taxing revenues to finance education and environmental externalities, and studies how an uniform tax rate on both labour income and interests on savings, affects the capital accumulation and the quality of the environment. How does public spending on education affect the environment? We analyze this question by studying the comparative static analysis at the stable steady state equilibrium. Under this framework, results show that public spending on education leads from one hand to capital decreasing and from the other hand has an effect on the environmental quality and this effect depends on the share of human capital in production. In particular, there is a critical proportion of the share of human capital equal to 0,14 above which public spending on education influence negatively the environment, and below which the tax rate reacts inversely with a positive impact on the quality of the environment.

Unobservable Investments, Trade Efficiency and Search Frictions

Market participants can invest to increase their gains from trade before searching for partners. The entrants' type distribution and trade efficiency are jointly determined and correlated. This paper explores a random search model of ex ante investments and trade efficiency, assuming that the investment amount remains the investor's private information. We show that the ex ante payoffs are equivalent to the equilibrium payoffs when investments are observable. In the unique steady state equilibrium, non-degenerate investment distribution and price distribution emerge simultaneously with ex-ante identical agents. In the basic model, where investing agents have no bargaining power, the extra investments fail to improve social welfare even when the search friction vanishes and the investments become efficient due to the mismatches caused by unobservability. Allocating positive bargaining power to investors alleviates the mismatch problem and improves social welfare.

Liquidity in high resolution in limit order markets

This paper investigates, in high resolution, the role of liquidity in a limit order market. Liquidity in these markets has two parts - a liquidity store and liquidity flow (time dimension). We model the liquidity residing in a limit order book and the liquidity flow from the latent order book, using a fully probabilistic model. Using a sample of stocks from NASDAQ 100, we find that liquidity residing in the order book within five levels each on either side of the transaction price and the flow to this liquidity pool from the latent order book can explain the wealth traded through the trading system, when observed in business time. The explanatory power is satisfactory in high resolution and short periods of business time but weaker in aggregated longer time periods. We observe that the liquidity pool for a large part of the trading day goes into a steady state equilibrium.

Probing Metastable Space-Charge Potentials in a Wide Band Gap Semiconductor.

While the study of space-charge potentials has a long history, present models are largely based on the notion of steady state equilibrium, ill-suited to describe wide band gap semiconductors with moderate to low concentrations of defects. Here we build on color centers in diamond both to locally inject carriers into the crystal and probe their evolution as they propagate in the presence of external and internal potentials. We witness the formation of metastable charge patterns whose shape-and concomitant field-can be engineered through the timing of carrier injection and applied voltages. With the help of previously crafted charge patterns, we unveil a rich interplay between local and extended sources of space-charge field, which we then exploit to show space-charge-induced carrier guiding.

Breaking of the Similarity Principle in Markov Generators of Low Density Limit Type and the Role of Degeneracies in the Landscape of Invariant States

The similarity principle is an extension of the principle of thermal relaxation that naturally arises in the stochastic limit of quantum theory. We construct examples of Low Density Limit (LDL) generators, associated to an environment state in equilibrium at inverse temperature β, which admit non-(β, HS)-equilibrium states. We prove that in some cases, the attraction domain of the (β, HS)-equilibrium state is empty. This means that the similarity principle, in its original thermodynamical formulation, can be broken in the LDL limit. This result is obtained as a consequence of a more general phenomenon: the role of degeneracies in the spectrum of the Liouvillian of the system Hamiltonian associated to the generator. We start from the definition of LDL type generators given in [5] and we introduce a finer classification of these generators based on the above degeneracies. The simplest subclass, called 2-generic, is a nontrivial extension of the generators associated to the so-called Λ and V configurations, widely used in quantum optics and involving 2 levels of the system Hamiltonian. Since each 2-generic block involves 3 or 4 levels of the system Hamiltonian we expect that they can reveal some interesting new physical phenomenon, as it happened in the 2-level case. In the last section, we restrict our attention to a 3-level system with a Hamiltonian that is associated to a class of 2-generic LDL generators. Finally, we prove that, for some LDL generators in this class the statement formulated at the beginning holds true.

Analyzing the Grain Boundary Resistance in Oxygen Ion Conductors By Static and Dynamic Impedance Measurements

Electrochemical Impedance Spectroscopy (EIS) is a very powerful method for analyzing electrochemical systems with respect to the factors impacting conductivity, charge transfer and diffusion. A great advantage of EIS is that the system under test (SUT) can be measured in operando so that the SUT can be characterized under conditions as they prevail in a fully functional technical system – as compared to model cells where only certain properties are tested under well-defined conditions. The small-signal excitation ensures that the SUT remains in its predefined operating point. Those aspects are of great importance when trying to optimize devices for commercial application.However, some characteristics can only be assessed through dynamic measurements with macroscopic external triggers. For example, grain boundary potential barriers in oxygen ion conductors can be well characterized in steady-state by EIS. With an external bias voltage, the resistance of the grain boundaries can be decreased, and the magnitude of this decrease can also be determined very accurately by EIS. However, while the resistance shrinks, further information about how the bias impacts the grain boundaries remains elusive. Is it a direct voltage effect or does the charge carrier and dopant concentration change within and adjacent to the grain boundary? The dynamic evolution of relevant parameters during the transition when changing the bias voltage can help to provide the additional information required for a more incisive analysis.Classic EIS is not applicable for such measurements because the steady-state condition is one of the fundamental requirements for EIS. In the field of semiconductors, deep-level transient spectroscopy (DLTS) is an established technique to determine the energy levels of certain defects. Hereby, the capacity at high frequencies is monitored continuously during voltage or light pulses at different temperatures. The temperature at which the pulses impact the capacity is an indicator for the thermal energy required to activate those defects. With this information, their energy level within the band structure can be calculated.This is comparable to the concept of single-frequency EIS (SFEIS), where the impedance at one specific frequency is measured continuously. For example, high-frequency SFEIS measurements have been used to determine the temperature evolution in a fuel cell or battery by relating the Ohmic resistance to the electrolyte temperature.It might not be possible to measure full spectra during an externally triggered system transition, but it is possible to dynamically monitor the impedance at a specific frequency and analyze its dynamics in the time domain. Resistance or capacitance can both be used as indicative parameters for a specific process or behavior.In this study, we analyze the grain boundary resistance of a 3% Gd-doped CeO2 (GDC) thin film. GDC is one of the most prominent oxygen ion conductors but suffers, at lower doping levels, from a large grain boundary resistance that makes polycrystalline samples two to three orders of magnitude more resistive than single crystals. The additional resistance is caused, in large part, by the space-charge zone and associated potential barrier due to the positive charge of the grain boundary core. It is known that the grain boundary resistance of GDC decreases upon biasing with an external voltage. Recently, our group has demonstrated that illuminating the sample with light above the band-gap has a similar effect on the resistance. Basically, the light creates electrons and holes, that are able to compensate the space-charge and flatten the bands as generally assumed for photoelectrochemical systems.We measure the dynamic evolution of resistance and capacitance of a GDC thin film upon bias with voltage and light pulses. Then, we analyze the obtained time domain evolutions, to clarify the exact mechanisms that leads to the resistance decrease in each case.The method presented here nicely compliments a classic EIS analysis, where spectra recorded in two different static operating points represent the characteristics of the system in both states in equilibrium. The evolution of relevant parameters, such as capacitance and resistance at a certain frequency, can provide additional information about the causes and dynamics of the changes and thereby provide more information on the exact mechanism and the driving force.This work was supported by JSPS Core-to-Core Program, A. Advanced Research Networks: “Solid Oxide Interfaces for Faster Ion Transport”, Department of Energy, Basic Energy Sciences and the Swiss National Science Foundation. Figure 1

Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.

Ab initio investigation of the ground and lowest excited states of the YAl molecule

Ab initio CASSCF and MRCI (single and double excitations plus Davidson correction) calculations have been performed for the yttrium aluminide molecule YAl. The potential energy curves of 10 molecular electronic states in the representation 2S+1Λ(+/−) have been calculated along with the corresponding electronic energy with respect to the ground state Te, the harmonic frequency ωe, the internuclear distance Re, the rotational constant Be, and the permanent dipole moment have been investigated for the considered electronic states. To the best of our knowledge, this study represents the first theoretical investigation of the electronic structure of the low lying excited states of YAl. The ground state equilibrium bond length, the vibrational frequency (with and without the anharmonic correction) and the dissociation energy have also been investigated by different density functional methods DFT using different basis sets. The vibrational levels of different states have been studied using canonical approach. Comparison of the present results with the single experimental study for the ground state X3Σ− and the excited state (2)3Σ− shows very good agreement.

Effect of spraying of essential oils and passive modified atmosphere packaging on selected postharvest quality parameters and stem-end rot development in <em>Mangifera indica<em> (cultivar <em>Karthakolomban</em>)

Mangifera indica L. (cultivar Karthakolomban) is more prone to stem-end rot (SER) disease that causes substantial postharvest losses in quality as well as quantity. The objective of this study was to use aqueous emulsions of basil (1.6 μL/mL), clove (2.0 μL/mL), cinnamon leaf (2.0 μL/mL) and cinnamon bark (1.6 μL/mL) oils as sprays with passive modified atmosphere packaging (MAP) in low density polyethylene (LDPE) bags as a bio-safe strategy to control SER of ‘Karthakolomban’ mango stored at 12 – 14°C and 85 – 90% of relative humidity. Distilled water and 0.1% (w/v) carbendazim 50WP treatments were used as negative and positive controls respectively. In-package respiratory gases were measured during storage for 8 days. Pathological, physicochemical, sensory properties and peel color of mango were assessed after ripening fruits at the end of the storage period. All essential oil treatments combined with passive MAP significantly reduced SER severity of mango more than 93% when compared to the negative control without adversely affecting peel colour and some physicochemical properties like total soluble solids and firmness. Mango fruits treated with basil, clove and cinnamon leaf oils obtained a higher preference by the sensory panel than other treatments. In-package O2 concentration was at 3.8 – 5.8%, while CO2 was at 4.3 – 5.0% at the end of the 8-day storage period. Respiratory gas levels attained a steady state equilibrium which resulted in extending the shelf life. Further, T1, T2 and T3 treatments can be commercialized as eco-friendly treatment strategies to be used during transportation and storage of mango in local trade within one week and for exportation via air cargo that takes approximately 2 – 3 days.

Theoretical determination of a reaction intermediate: Fukui function analysis, dual reactivity descriptor and activation energy

In this work we present a study on the theoretical determination of reactivity and structures of complex phosphorus heterocycles. Applying the Fukui function and dual reactivity descriptors surprising rearrangement reactions and reactivities of a phosphorus bicycle are explained and, also the hitherto not completely understood structure of the main starting compound with a very short non-bonding CC-distance is described as a fast equilibrium in solid state rather than as non-classical ylid. Aspects on negative values of Fukui functions found in some structures are discussed.

An extended eight-chain model for hyperelastic and finite viscoelastic response of rubberlike materials: Theory, experiments and numerical aspects

Rubberlike materials exhibit strong rate-dependent mechanical response which manifests itself in creep and relaxation tests as well as in the hysteresis curves under cyclic loading. Unlike linear viscoelasticity, creep and relaxation response of rubber is nonlinear and amplitude-dependent. Within this context, the contribution of this work is three fold. (i) On the experimental side, the characterization of equilibrium and non-equilibrium responses are carried out by means of uniaxial and equibiaxial extension tests. Also performed are the creep and relaxation experiments at various stress and strain levels. (ii) On the theoretical side, we extend the well-known eight-chain model via incorporating a simple yet instrumental tube-constraint term composed of the second invariant into the non-affine network contribution reflecting the ground state equilibrium response. For the non-equilibrium response, we propose a new evolution equation for the creep/relaxation behavior of rubberlike materials based on a relaxation kinetics of a single polymer chain. The geometric non-linearity is incorporated via the finite deformation kinematics based on the multiplicative split of the deformation gradient into elastic and viscous parts, whereas the volumetric and isochoric split of the deformation gradient is entirely discarded. The rheology uses a nonlinear spring responsible for equilibrium elastic response in parallel to n number of Maxwell elements, leading to a generalized Maxwell-Wiechert viscoelastic solid. (iii) The algorithmic implementation of the model features the spectral decomposition of the respective terms and is demonstrated within the context of the finite element method. The developed model is validated by fitting both the elastic and viscoelastic model responses with respect to the experimental data in the sense of uniaxial, (equi)biaxial extensions, and pure shear tests. Relaxation and creep behavior of the model are thoroughly assessed. Also presented in the manuscript is the capability and the performance of the model in the face of a relevant non-homogeneous boundary value problem. The quality of the findings earns the model vast utilization areas from an engineering perspective.

Unitary preparation of many-body Chern insulators: Adiabatic bulk-boundary correspondence

We approach the long-standing problem of preparing an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. Herein, this is addressed by constructing a dynamical many-body Chern invariant exploiting the property of the bulk macroscopic electric polarisation (Resta polarisation) of the CI. This Chern invariant defined from observable correlations is also established to topologically classify many body Chern states in equilibrium. The non-equilibrium behavior of the invariant is probed by ramping the paradigmatic Haldane model of graphene from its trivial to the topological phase. We show that a non-linear ramp may work more efficiently in approaching the topological state, thereby establishing the existence of an optimal topological state preparation. Furthermore, to ensure the near adiabatic dynamics across the quantum critical point, we propose a novel counter-diabatic scheme. The topological nature of the prepared state is firmly established by observing an emerging $U(1)$ topological charge. We also compute the edge current in the time evolved state of the system under a semi-periodic boundary condition and clearly establish an adiabatic bulk-boundary correspondence which firmly ensconces the validity of the many-body invariant.

From heat to entropy

AbstractMilestones in the development of thermodynamics are the discovery of the absolute temperature scale and the recognition that differential “heat” is a form of energy given as the product of absolute temperature and differential entropy. Following a new path, the last statement results from a careful analysis of the heat transfer applying the first theorem without reference to the usual cycles in thermodynamics. This confirms also characteristic properties of entropy. In particular, the total entropy can never decrease in a process. In thermal equilibrium, the differential thermal energy is proportional to the differential entropy with the constant of proportionality being the temperature of the heat and entropy. Hence, thermal energy and entropy are transferred simultaneously into the same storage facilities, some of which are mentioned. However, the issue which one is the superior quantity is obsolete. The entropy is maximum for a given amount of exchanged thermal energy and, vice versa, for a given amount of exchanged entropy the concomitant energy is minimum. We calculate the thermal energy and entropy of phonons (as bosons) in oscillators and of electrons (as fermions) in their states of solids and melts as examples from statistical thermodynamics. The thermal energy or heat is the sum of the energies of all bosons and fermions in their elementary states or quantum states according to Bose Einstein and Fermi Dirac statistics in thermal equilibrium minus the total energy in the limit T→0 K. The entropy can be written as mixing entropy of all of these quantum states weighted with their occupancies, in agreement with an earlier publication. Thus, entropy is a logarithmic metrics of the number of all possible variants to distribute the respective total energy over all elementary states in thermal equilibrium.

Разряд ионов гидроксония на металлических катодах в присутствии пиридина

In this work, studies have been carried out on the electrochemical reduction of hydrogen (hydronium ion) from acidic aqueous solutions in the presence of an organic substance – pyridine. Electrolysis was carried out in an electrolyte with a sulfuric acid content (0.18; 0.36 M) with a pyridine additions of 8.4·10-3 M. Potentiostatic studies were carried out on a Potentiostat P-30Jcom Elins potentiostat using a three-electrode cell. Working electrodes (cathodes) were made of M1 copper with an area (S) of 0.09 cm2; aluminum (AD1) S – 0.125 cm2, zinc (Ts0A) S – 0.35 cm2, lead (Cl) S – 0.20 cm2, auxiliary (anode) – from a platinum plate with an area of 0.20 cm2, reference electrode – silver chloride (AgCl/Ag). In potentiometric measurements, the results are presented according to the average data obtained for 30 s of electrolysis in the potential range (-950 ÷ -1100 mV for AgCl/Ag), and in studies in the galvanostatic mode at current densities from 0 to 110 mV/cm2, the results are presented as average data, obtained in the initial 5 s of the process. The paper presents comparative data on the electrokinetic parameters studied under the same conditions of hydrogen discharge reactions at different cathodes in electrolytes with a sulfuric acid content of 0.36 M. It is shown that the highest discharge current density of the hydronium ion (Н3О+) is achieved at the copper electrode, and the lowest at the lead electrode. With the addition of 8.4∙10-3 M pyridine to the electrolyte, the reduction of hydrogen cations is somewhat reduced on the electrodes used, except for lead. The transfer coefficients of the hydrogen discharge at all electrodes are low, and with the addition of pyridine they decrease even more. The low transfer coefficients indicate that the process of the hydronium ion discharge proceeds in a non-activation mode. The lowest exchange current is recorded at the copper and lead electrode. At the zinc electrode, the exchange of current is one to two orders of magnitude higher than at the other electrodes, so it can be noted that at this electrode the system under consideration is closer to the equilibrium of state. The order of the reaction of the course of electrolysis by the hydronium cation on the copper, aluminum and zinc electrodes is close to unity. The addition of pyridine leads to a slight decrease in the order of the reaction. This is due to the fact that pyridine molecules in acidic solutions exist in the form of pyridinium ion, which is reduced at the cathode. In this case, a significant amount of hydrogen is absorbed, which should explain the decrease in the order of the reaction with respect to the hydronium ion in the presence of pyridine additives. The obtained low values of the transfer coefficients indicate that, during the discharge of hydronium ions, the process is limited to a greater extent by the concentration polarization. The diffusion nature of the reduction of hydronium ions in electrolytes with a sulfuric acid concentration of 0.18 and 0.36 M is also evidenced by data taken in a dynamic mode.

Anthryl-Appended Platinum(II) Schiff Base Complexes: Exceptionally Small Stokes Shift, Triplet Excited States Equilibrium, and Application in Triplet–Triplet-Annihilation Upconversion

Two anthryl platinum(II) N,N'-bis(3,5-di-tert-butylsalicylidene)-1,2-benzenediamine Schiff base complexes were synthesized, with the anthryl attached via its 9 position (Pt-9An) or 2 position (Pt-2An) to the platinum (Pt) Schiff base backbone. The complexes show unusually small Stokes shifts (0.23 eV), representing a very small energy loss for the photoexcitation/intersystem crossing process, which is beneficial for applications as triplet photosensitizers. Phosphorescence of the Pt(II) coordination framework (ΦP = 11.0%) is quenched in the anthryl-containing complexes (ΦP = 4.0%) and shows a biexponential decay (τP = 3.4 μs/87% and 18.2 μs/13%) compared to the single-exponential decay of the native Pt(II) Schiff base complex (τP = 3.7 μs). Femtosecond/nanosecond transient absorption spectroscopy suggests an equilibrium between triplet anthracene (3An) and triplet metal-to-ligand charge-transfer (3MLCT) states, with the dark 3An state slightly lower in energy (1.96 eV for Pt-9An and 1.90 eV for Pt-2An) than the emissive 3MLCT state (1.97 eV for Pt-9An and 1.91 eV for Pt-2An). Intramolecular triplet-triplet energy transfer (TTET) and reverse TTET take 4.8 ps/444 ps for Pt-9An and 55 ps/1.7 ns for Pt-2An, respectively. The triplet-state equilibrium extends the triplet-state lifetime of the complexes to 103 μs (Pt-2An) or 163 μs (Pt-9An), in comparison to the native Pt(II) complex, which shows a lifetime of 4.0 μs. The complexes were used for triplet-triplet-annihilation upconversion with perylene as the triplet acceptor. The upconversion quantum yield is up to 15%, and a large anti-Stokes shift (0.75 eV) is achieved by excitation into the singlet metal-to-ligand charge-transfer absorption band (589 nm) of the complexes (anti-Stokes shift is 0.92 eV with 9,10-diphenylanthracene as the acceptor).

A distal regulatory region of a class I human histone deacetylase

Histone deacetylases (HDACs) are key enzymes in epigenetics and important drug targets in cancer biology. Whilst it has been established that HDACs regulate many cellular processes, far less is known about the regulation of these enzymes themselves. Here, we show that HDAC8 is allosterically regulated by shifts in populations between exchanging states. An inactive state is identified, which is stabilised by a range of mutations and resembles a sparsely-populated state in equilibrium with active HDAC8. Computational models show that the inactive and active states differ by small changes in a regulatory region that extends up to 28 Å from the active site. The regulatory allosteric region identified here in HDAC8 corresponds to regions in other class I HDACs known to bind regulators, thus suggesting a general mechanism. The presented results pave the way for the development of allosteric HDAC inhibitors and regulators to improve the therapy for several disease states.

Speed of Navigation vis-a-vis Quality of Innovation as Sources of Progression towards Steady State Equilibrium: Insights and Inferences

This study formally and theoretically juxtaposes `speed of navigation' of the general equilibrium growth path (equivalently, a `low-high' innovation system), and `quality of innovations' (equivalently, a `top-down' innovation system) as alternate strategies for minimization of the time it takes for a country to arrive at its general equilibrium steady state growth phase. Formal theoretical predictions show that, whereas the speed of navigation strategy has feasibility of outperforming the quality of innovations strategy, superior performance at minimization of time to steady state is feasible only in presence of either of errors of implementation of the top-down innovation system, or incapacity of an economy at generation of high quality innovations. In absence of stated two factors, the quality of innovations strategy outperforms the speed of navigation strategy for minimization of the time it takes for a country to arrive at its general equilibrium steady state growth phase. Empirical findings provide corroboration for study findings, provide evidence that whereas the speed of navigation strategy generates a linear approach, the quality of innovations strategy generates a weakly convex approach to the general equilibrium steady state growth phase. Quality of elementary education is `poster boy' for the quality of innovations strategy. Simultaneously, size of stock markets and fixed capital formation are poster boys for the `speed of navigation' strategy.

Theoretical Study on Growth Mechanism of AlnNn (n = 2–9) Clusters

The growth of AlnNn (n = 2–9) clusters is evaluated by using density functional theory (DFT) to determine the growth pathway of AlnNn (n = 2–9) clusters. Fukui function was adopted to confirm the active spots of these structures, furthermore, the formation ways of AlnNn (n = 2–9) reactant clusters can be divided into three types. Based on the results of transition state search and equilibrium constant calculations, the growth pathway of AlnNn (n = 2–9) clusters can be identified as follows: AlN(plane) → Al2N2(plane) → Al3N3(plane) → Al4N4(plane) → Al5N5(bulk) → Al6N6(bulk) → Al7N7(bulk) → Al8N8(bulk) → Al9N9(bulk), the growth mechanism of AlN nano clusters can be explained in detail.

Reading the Stars

Following the global financial crisis, significant uncertainty has existed around the U.S. economy’s steady state equilibrium. This paper uses a factor model to provide a new approach to estimating “the stars” (i.e. the neutral interest rate, maximum employment, and the level and growth rate of potential output) that are most consistent with a medium-term equilibrium where inflation converges to the FOMC’s two percent target. It is applicable to any country with an inflation targeting central bank. It also explicitly incorporates estimates of the extensive margin of slack in the labor market, which has proven to be an important factor in describing the post-financial crisis landscape.

Ab initio spectroscopy of the aluminum methylene (AlCH2) free radical.

Extensive ab initio investigations of the ground and electronic excited states of the AlCH2 free radical have been carried out in order to predict the spectroscopic properties of this, as yet, undetected species. Difficulties with erratic predictions of the ground state vibrational frequencies, both in the literature and in the present work, have been traced to serious broken-symmetry instabilities in the unrestricted Hartree-Fock orbitals at the ground state equilibrium geometry. The use of restricted open-shell Hartree-Fock or complete active space self consistent field orbitals avoids these problems and leads to consistent and realistic sets of vibrational frequencies for the ground state. Using the internally contracted multireference configuration interaction method with aug-cc-pV(T+d)Z basis sets, we have calculated the geometries, energies, dipole moments, and vibrational frequencies of eight electronic states of AlCH2 and AlCD2. In addition, we have generated Franck-Condon simulations of the expected vibronic structure of the Ã-X̃, B̃-X̃, C̃-X̃, and C̃-Ã band systems, which will be useful in searches for the electronic spectra of the radical. We have also simulated the expected rotational structure of the 0-0 absorption bands of these transitions at modest resolution under supersonic expansion cooled conditions. Our conclusion is that if AlCH2 can be generated in sufficient concentrations in the gas phase, it is most likely detectable through the B̃2A2-X̃2B1 or C̃2A1-X̃2B1 electronic transitions at 515 nm and 372 nm, respectively. Both band systems have vibrational and rotational signatures, even at modest resolution, that are diagnostic of the aluminum methylene free radical.