Energy Epsilon Research Articles

Effect of inclination angle on the thermal-hydraulic characteristics and entropy generation of Al2O3–water nanofluid for in-tube turbulent flow

PurposeInclination angle has been reported to have an enhancing effect on the thermal-hydraulic characteristics and entropy of some thermal systems. Therefore, this paper aims to numerically investigate the effects of inclination angle, volume concentration and Reynolds number on the thermal and hydraulic characteristics and entropy generation rates of water-based Al2O3 nanofluids through a smooth circular aluminum pipe in a turbulent flow.Design/methodology/approachA constant heat flux of 2,000 Watts is applied to the circular surface of the tube. Reynolds number is varied between 4,000 and 20,000 for different volume concentrations of alumina nanoparticles of 0.5%, 1.0% and 2.0% for tube inclination angles of ±90o, ±60o, ±45o, ±30o and 0o, respectively. The simulation is performed in an ANSYS Fluent environment using the realizable kinetic energy–epsilon turbulent model.FindingsResults show that +45o tube orientation possesses the largest thermal deviations of 0.006% for 0.5% and 1.0% vol. concentrations for Reynolds numbers 4,000 and 12,000. −45o gives a maximum pressure deviation of −0.06% for the same condition. The heat transfer coefficient and pressure drop give maximum deviations of −0.35% and −0.39%, respectively, for 2.0% vol. concentration for Reynolds number of 20,000 and angle ±90o. A 95%–99.8% and 95%–98% increase in the heat transfer and total entropy generation rates, respectively, is observed for 2.0% volume concentration as tube orientation changes from the horizontal position upward or downward.Originality/valueResearch investigating the effect of inclination angle on thermal-hydraulic performance and entropy generation rates in-tube turbulent flow of nanofluid is very scarce in the literature.

A New Feature of the Efimov-Like Structure in the Hadron System: Long-Range Force as a Recoil Effect

On the three-body kinematics, we investigate the threshold behavior which appears not only at the three-body break-up threshold (3BT), but also at the quasi two-body threshold (Q2T) for the reactions: A+(BC)rightarrow A+B+C, and (ABC)rightarrow A+(BC), respectively. Recently, the author proposed a generalparticle {transfer} (GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a 1/r^n-type potential for long range. The long range part of the GPT potential for n=1 indicates an attractive Coulomb-like or a gravitation-like potential. While, n=2 indicates the Efimov-like potential between A and (BC). The three-body binding energy: E_n=epsilon +zeta _n with the two-body binding energy epsilon , and the separation energy zeta _n for (ABC)rightarrow A+(BC) satisfies E_n/E_{n+1}=zeta _n/zeta _{n+1}=const for epsilon =0 or the two-body scattering length: arightarrow infty (i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of E_n/E_{n+1}=(zeta _n+epsilon )/(zeta _{n+1}+epsilon )rightarrow 1 (const) for nrightarrow infty (with zeta _nrightarrow 0) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.

Modification of Coulomb law and energy levels of the hydrogen atom in a superstrong magnetic field

We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: \Phi(z) = e/|z| [ 1- exp(-\sqrt{6m_e^2}|z|) + exp(-\sqrt{(2/\pi) e^3 B + 6m_e^2} |z|) ]. The deviation from Coulomb's law becomes essential for B > 3\pi B_{cr}/\alpha = 3 \pi m_e^2/e^3 \approx 6 10^{16} G. In such superstrong fields, electrons are ultra-relativistic except those which occupy the lowest Landau level (LLL) and which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B > 3 \pi B_{cr}/\alpha, it substantially differs from the one obtained without accounting for the modification of the atomic potential.

On the Existence and Conditional Energetic Stability of Solitary Gravity-Capillary Surface Waves on Deep Water

This paper presents an existence and stability theory for gravity-capillary solitary waves on the surface of a body of water of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy epsilon subject to the constraint I = root 2 mu, where I is the wave momentum and 0 < mu << 1. Since epsilon and I are both conserved quantities a standard argument asserts the stability of the set D-mu of minimisers: solutions starting near D-mu remain close to D-mu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are modelled as solutions of the nonlinear Schrodinger equation with cubic focussing nonlinearity. We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of this model equation as mu down arrow 0.

Chaotic Dynamics and the Recurrence Spectra of the Rydberg Hydrogen Atom Near a Dielectric Surface

The classical electronic motion of the Rydberg hydrogen atom near a dielectric surface has been studied by using the Poincaré surfaces of section method and the closed orbit theory. The structure and evolution of the phase space as a function of the scaled energy is explored extensively by means of the Poincaré surfaces of section. The results suggest that when the scaled energy is less than the critical energy epsilon(s), the whole phase space structure is regular. However, when the energy is larger than epsilon(s), chaotic motions appear. The recurrence spectra of this system have also been calculated. The results show that, for a given scaled energy larger than the critical energy epsilon(s), when the dielectric constant alpha is small, the influence of the dielectric surface can be neglected and the number of closed orbits is very small. With the increase of the dielectric constant alpha, the effect of the dielectric surface becomes significant, the number of closed orbits increases, and there are more peaks in the recurrence spectra. When alpha = 1.0, the recurrence spectra approach the case of the Rydberg hydrogen atom near a metallic surface. This study provides a new method to explore the dynamic behavior of the Rydberg atom interacting with a dielectric surface.

On the accuracy of thermionic electron emission models. I. Electron detachment from SF6−

Detailed statistical rate calculations combined with electron capture theory and kinetic modeling for the electron attachment to SF(6) and detachment from SF(6)(-) [Troe et al., J. Chem. Phys. 127, 244303 (2007)] are used to test thermionic electron emission models. A new method to calculate the specific detachment rate constants k(det)(E) and the electron energy distributions f(E,epsilon) as functions of the total energy E of the anion and the energy epsilon of the emitted electrons is presented, which is computationally simple but neglects fine structures in the detailed k(det)(E). Reduced electron energy distributions f(E,epsilon/<epsilon>) were found to be of the form (epsilon/<epsilon>)(n) exp(-epsilon/<epsilon>) with n approximately = 0.15, whose shape corresponds to thermal distributions only to a limited extent. In contrast, the average energies <epsilon(E)> can be roughly estimated within thermionic emission and finite heat bath concepts. An effective temperature T(d)(E) is determined from the relation E - EA = <E(SF(6))(T(d))> + kT(d), where <E(SF(6))(T(d))> denotes the thermal internal energy of the detachment product SF(6) at the temperature T(d) and EA is the electron affinity of SF(6). The average electron energy is then approximately given by <epsilon(E)> = kT(d)(E), but dynamical details of the process are not accounted for by this approach. Simplified representations of k(det)(E) in terms of T(d)(E) from the literature are shown to lead to only semiquantitative agreement with the equally simple but more accurate calculations presented here. An effective "isokinetic" electron emission temperature T(e)(E) does not appear to be useful for the electron detachment system considered because it neither provides advantages over a representation of k(det)(E) as a function of T(d)(E), nor are recommended relations between T(e)(E) and T(d)(E) of sufficient accuracy.

Temperature effects in the mechanical desorption of an infinitely long lattice chain: Re-entrant phase diagrams

We consider the mechanical desorption of an infinitely long lattice polymer chain tethered at one end to an adsorbing surface. The external force is applied to the free end of the chain and is normal to the surface. There is a critical value of the desorption force f(tr) at which the chain desorbs in a first-order phase transition. We present the phase diagram for mechanical desorption with exact analytical solutions for the detachment curve: the dependence of f(tr) on the adsorption energy epsilon (at fixed temperature T) and on T (at fixed epsilon). For most lattice models f(tr)(T) displays a maximum. This implies that at some given force the chain is adsorbed in a certain temperature window and desorbed outside it: the stretched state is re-entered at low temperature. We also discuss the energy and heat capacity as a function of T; these quantities display a jump at the transition(s). We analyze short-range and long-range excluded-volume effects on the detachment curve f(tr)(T). For short-range effects (local stiffness), the maximum value of f(tr) decreases with stiffness, and the force interval where re-entrance occurs become narrower for stiffer chains. For long-range excluded-volume effects we propose a scaling f(tr) approximately T(1-nu)(T(c)-T)(nu/phi) around the critical temperature T(c), where nu=0.588 is the Flory exponent and phi approximately 0.5 the crossover exponent, and we estimated the amplitude. We compare our results for a model where immediate step reversals are forbidden with recent self-avoiding walk simulations. We conclude that re-entrance is the general situation for lattice models. Only for a zigzag lattice model (where both forward and back steps are forbidden) is the coexistence curve f(tr)(T) monotonic, so that there is no re-entrance.

The rotational spectrum and structure for the argon-cyclopentadienyl thallium van der Waals complex: Experimental and computational studies of noncovalent bonding in an organometallic π-complex

The rotational spectrum of a noble gas-organometallic complex was measured using a pulse molecular beam Fourier transform microwave spectrometer. Rotational transitions for the neutral argon-cyclopentadienyl thallium weakly bound complex were measured in the 4-9 GHz range. Analysis of the spectrum showed that the complex is a prolate symmetric-top rotor with C(5V) symmetry. The experimentally determined molecular parameters for Ar-C(5)H(5) (205)Tl are B=372.4479(3) MHz, D(J)=0.123(2) kHz, and D(JK)=0.45(2) kHz. For Ar-C(5)H(5) (203)Tl, B=373.3478(5) MHz, D(J)=0.113(3) kHz, and D(JK)=0.37(3) kHz. Using a pseudodiatomic model with Lennard-Jones potential yields an approximate binding energy of 339 cm(-1). The argon atom is located on the a-axis of the C(5)H(5)Tl monomer, directly opposite from the thallium metal atom. The measured separation distance between argon and the cyclopentadienyl ring is R=3.56 A. The overall size of the cluster is about 6 A, measuring from argon to thallium. Relatively small D(J) and D(JK) centrifugal distortion constants were observed for the complex, indicating that the structure of Ar-C(5)H(5)Tl is somewhat rigid. MP2 calculations were used to investigate the possible structures and binding energies of the argon-cyclopentadienyl thallium complex. Calculated, counterpoise corrected binding energies are evaluated at R=3.56 A for Ar-C(5)H(5)Tl range from 334 to 418 cm(-1). The experimental binding energy epsilon=339 cm(-1) for Ar-C(5)H(5)Tl falls within this range. The higher-level MP2/aug-cc-pVTZ-PP (thallium)/aug-cc-pVTZ(Ar, C, H) calculation with variable R yielded R(e)=3.46 A and binding energy of 535 cm(-1). Our estimated binding energy for argon-cyclopentadienyl thallium is very similar to the binding energy of argon-benzene. Calculations for the new van der Waals complexes, Ar(C(5)H(5)Tl)(2) and (C(5)H(5)Tl)(2), have been obtained, providing further information on the structures and bonding properties of previously observed cyclopentadienyl thallium polymer chains. The calculated intermolecular distance R(Tl-Cp)=3.05 A for the (CpTl)(2) chain subunit (Cp is cyclopentadienyl, C(5)H(5)) is slightly longer than the measured x-ray value R(M-Cp)(M=Tl)=2.75 A. The x-ray distance R(Tl-Tl)=5.5 A for the chain structure is almost identical to the calculated R(Tl-Tl)=5.51 A for the (C(5)H(5)Tl)(2) dimer.

Quantum Wire Hybridized With a Single-Level Impurity

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.

A study of the Fermi–Pasta–Ulam problem in dimension two

Continuing the previous work on the same subject, we study here different two-dimensional Fermi-Pasta-Ulam (FPU)-like models, namely, planar models with a triangular cell, molecular-type potential and different boundary conditions, and perform on them both traditional FPU-like numerical experiments, i.e., experiments in which energy is initially concentrated on a small subset of normal modes, and other experiments, in which we test the time scale for the decay of a large fluctuation when all modes are excited almost to the same extent. For each experiment, we observe the behavior of the different two-dimensional systems and also make an accurate comparison with the behavior of a one-dimensional model with an identical potential. We assume the thermodynamic point of view and try to understand the behavior of the system for large n (the number of degrees of freedom) at fixed specific energy epsilon=En. As a result, it turns out that: (i) The difference between dimension one and two, if n is large, is substantial. In particular (making reference to FPU-like initial conditions) the "one-dimensional scenario," in which the dynamics is dominated for a long time scale by a weakly chaotic metastable situation, in dimension two is absent; moreover in dimension two, for large n, the time scale for energy sharing among normal modes is drastically shorter than in dimension one. (ii) The boundary conditions in dimension two play a relevant role. Indeed, models with fixed or open boundary conditions give fast equipartition, on a rather short time scale of order epsilon(-1), while a periodic model gives longer equilibrium times (although much shorter than in dimension one).

Rotation and Diffusion of H2 in Hydrogen−Ice Clathrate by 1H NMR

A recently reported hydrogen-ice clathrate carries up to four H(2) in each large cage and one H(2) in each small cage. We report pulsed proton NMR line shape measurements on H(2)-D(2)O clathrate formed at 1500 bar and 250 K. The behavior of the two-pulse spin-echo amplitude with respect to the nutation angle of the refocusing pulse shows that intramolecular dipolar broadening, modulated by H(2) molecular reorientations, dominates the line width of the ortho-H(2). Dipolar interaction between H(2) guests and host D atoms explains the echo variation with the relative phases of the pulses. From 12 to 120 K, the line width varies as 1/T, demonstrating that the three sublevels of J = 1 are split by a constant energy, epsilon. The splitting arises from distortion in the otherwise high-symmetry cages from frozen-out D(2)O orientational disorder. Above 120 K, further line-narrowing signals the onset of H(2) diffusion from cage to cage. At the lowest temperature, 1.9 K, the spectrum has Pake powder doublet-like features; the doublet is not fully developed, indicating a broad distribution of order parameters and energies epsilon.

Random networks of fibres display maximal heterogeneity in the distribution of elastic energy

Above a small length scale, the distribution of local elastic energies in a material under an external load is typically Gaussian, and the dependence of the average elastic energy on strain defines the stiffness of the material. Some particular materials, such as granular packings, suspensions at the jamming transition, crumpled sheets and dense cellular aggregates, display under compression an exponential distribution of elastic energies, but also in this case the elastic properties are well defined. We demonstrate here that networks of fibres, which form uncorrelated non-fractal structures, have under external load a scale invariant distribution of elastic energy (epsilon) at the fibre-fibre contacts proportional to 1/epsilon. This distribution is much broader than any other distribution observed before for elastic energies in a material. We show that for small compressions it holds over 10 orders of magnitude in epsilon. In such a material a few 'hot spots' carry most of the elastic load. Consequently, these materials are highly susceptible to local irreversible deformations, and are thereby extremely efficient for damping vibrations.

Koopmans’ theorem in the ROHF method: Canonical form for the Hartree-Fock Hamiltonian

Since the classic work of Roothaan [Rev. Mod. Phys. 32, 179 (1960)], the one-electron energies of a ROHF method are known as ambiguous quantities having no physical meaning. Together with this, it is often assumed in present-day computational studies that Koopmans' theorem is valid in a ROHF method. In this work we analyze the specific dependence of orbital energies on the choice of the basic equations in a ROHF method which are the Euler equations and different forms of the generalized Hartree-Fock equation. We first prove that the one-electron open-shell energies epsilon(m) derived by the Euler equations can be related to the respective ionization potentials I(m) via the modified Koopmans' formula I(m)= -epsilon(m)f(m) where f(m) is an occupation number. As compared to this, neither the closed-shell orbital energies nor the virtual ones derived by the Euler equations can be related to the respective ionization potentials and electron affinities via Koopmans' theorem. Based on this analysis, we derive the new (canonical) form for the Hamiltonian of the Hartree-Fock equation, the eigenvalues of which obey Koopmans' theorem for the whole energy spectrum. A discussion of new orbital energies is presented on the examples of a free N atom and an endohedral N@C(60) (I(h)). The vertical ionization potentials and electron affinities estimated via Koopmans' theorem are compared with the respective observed data and, for completeness, with the respective estimates derived via a DeltaSCF method. The agreement between observed data and their estimates via Koopmans' theorem is qualitative and, in general, appears to possess the same accuracy level as in the closed-shell SCF.

Description of atomic burials in compact globular proteins by Fermi‐Dirac probability distributions

We perform a statistical analysis of atomic distributions as a function of the distance R from the molecular geometrical center in a nonredundant set of compact globular proteins. The number of atoms increases quadratically for small R, indicating a constant average density inside the core, reaches a maximum at a size-dependent distance R(max), and falls rapidly for larger R. The empirical curves turn out to be consistent with the volume increase of spherical concentric solid shells and a Fermi-Dirac distribution in which the distance R plays the role of an effective atomic energy epsilon(R) = R. The effective chemical potential mu governing the distribution increases with the number of residues, reflecting the size of the protein globule, while the temperature parameter beta decreases. Interestingly, betamu is not as strongly dependent on protein size and appears to be tuned to maintain approximately half of the atoms in the high density interior and the other half in the exterior region of rapidly decreasing density. A normalized size-independent distribution was obtained for the atomic probability as a function of the reduced distance, r = R/R(g), where R(g) is the radius of gyration. The global normalized Fermi distribution, F(r), can be reasonably decomposed in Fermi-like subdistributions for different atomic types tau, F(tau)(r), with Sigma(tau)F(tau)(r) = F(r), which depend on two additional parameters mu(tau) and h(tau). The chemical potential mu(tau) affects a scaling prefactor and depends on the overall frequency of the corresponding atomic type, while the maximum position of the subdistribution is determined by h(tau), which appears in a type-dependent atomic effective energy, epsilon(tau)(r) = h(tau)r, and is strongly correlated to available hydrophobicity scales. Better adjustments are obtained when the effective energy is not assumed to be necessarily linear, or epsilon(tau)*(r) = h(tau)*r(alpha,), in which case a correlation with hydrophobicity scales is found for the product alpha(tau)h(tau)*. These results indicate that compact globular proteins are consistent with a thermodynamic system governed by hydrophobic-like energy functions, with reduced distances from the geometrical center, reflecting atomic burials, and provide a conceptual framework for the eventual prediction from sequence of a few parameters from which whole atomic probability distributions and potentials of mean force can be reconstructed.

Near-Threshold Production ofϕMesons inppCollisions

The pp->pp phi reaction has been studied at the Cooler Synchrotron COSY-Juelich, using the internal beam and ANKE facility. Total cross sections have been determined at three excess energies epsilon near the production threshold. The differential cross section closest to threshold at epsilon=18.5 MeV exhibits a clear S-wave dominance as well as a noticeable effect due to the proton-proton final state interaction. Taken together with data for pp omega-production, a significant enhancement of the phi/omega ratio of a factor 8 is found compared to predictions based on the Okubo-Zweig-Iizuka rule.

Scaling behavior of an Anderson impurity close to the Mott-Anderson transition

The scaling behavior of Anderson impurity models each of which with a different site energy epsilon_i is examined close to the Mott-Anderson transition. Depending on the impurity energy epsilon_i, in the critical regime the site turns into a local magnetic moment, as indicated by a vanishing quasiparticle weight Z -> 0, or remains nearly doubly occupied or nearly empty, corresponding to Z -> 1. In this paper, we present the scaling behavior of Z as a function of the on-site energy epsilon_i and the distance t to the transition, and interpret our result in terms of an appropriate beta function beta(Z).

Condensed-history Monte Carlo simulation of the dosimetric distribution of electron microbeam

To evaluate the dose distributions of an electron microbeam and to help optimization of its design, the condensed-history (CH) Monte Carlo simulation algorithm implemented in the Geant4 toolkit was selected as an alternative to the conventionally used analog algorithm. Compared to the analog algorithm, the CH algorithm is cheaper and less limited by the lack of cross-sections. And, with a properly chosen production cut for secondaries, its accuracy for the problems of microdosimetry is satisfactory. In this work, calculations of the single-event (imparted energy epsilon) size distribution f (1)(epsilon) is described, for compartments in the Orlando electron micro beam. The results agree well with those obtained by use of the analog algorithm and reported in the literature. It is shown that substituting tissue with water in HeLa cells, and replacing Mylar with water of the same mass stopping power in the substrate, makes little difference. Additionally, the neighbor-to-target ratio of average event size R (NT) has been calculated as a function of the incident energy of the electrons. Comparison with analog results reported in the literature suggests that the average event size in neighbors, and hence the neighbor-to-target ratio, is sensitive to the selection of the energy threshold. Finally, the effect of finite beam radius on the event size distribution and the neighbor-to-target ratio has also been studied. All results presented suggest the condensed-history technique to provide an efficient and valuable alternative tool in the design of electron microbeams.

Effect of red cell clustering and anisotropy on ultrasound blood backscatter: a Monte Carlo study

When flowing at a low shear rate, blood appears hyperechogenic on ultrasound B-scans. The formation of red blood cell (RBC) aggregates that also alters blood viscosity is the microscopic mechanism explaining this acoustical phenomenon. In this study, Monte Carlo simulations were performed to predict how RBC clustering increases ultrasound scattering by blood. A bidimensional Gibbs-Markov random point process parameterized by the adhesion energy epsilon and an anisotropy index nu was used to describe RBC positions for a hematocrit H = 40%. The frequency dependence of the backscattering coefficient chi(f) was computed using Born approximation. The backscattering coefficient chi0 at 5 MHz and the spectral slopes n(x) and n(y) (chi alpha f(nx) or f(ny)) measured, respectively, when the insonification is parallel and perpendicular with the RBC cluster axis were then extracted. Under isotropic conditions, chi0 increased up to 7 dB with epsilon and n(x) = n(y) decreased from 4.2 to 3.4. Under anisotropic conditions, the backscattering was stronger perpendicularly to aggregate axis, resulting in n(x) < n(y). The anisotropy in scattering appeared more pronounced when epsilon or nu increased. These two dimensional results generally predict that low-frequency blood backscatter is related to cluster dimension, and higher-frequency properties are affected by finer morphological features as anisotropy. This numerically establishes that ultrasound backscatter spectroscopy on a large frequency range is pertinent to characterize in situ hemorheology.

Kinetic roughening of ion-sputtered Pd(001) surface: beyond the Kuramoto-Sivashinsky model.

We investigate the kinetic roughening of Ar+ ion-sputtered Pd(001) surface both experimentally and theoretically. In situ real-time x-ray reflectivity and in situ scanning tunneling microscopy show that nanoscale adatom islands form and grow with increasing sputter time t. Surface roughness W(t) and lateral correlation length xi(t) follow the scaling laws W(t) approximately t(beta) and xi(t) approximately t(1/z) with the exponents beta approximately 0.20 and 1/z approximately 0.20, for an ion beam energy epsilon=0.5 keV, which is inconsistent with the prediction of the Kuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying the coarse-grained continuum approach of the Sigmund theory to the order of O(inverted Delta(4),h(2)), where h is the surface height, and derive a new term of the form inverted Delta(2)(inverted Delta h)(2) which plays a decisive role in describing the observed morphological evolution of the sputtered surface.

The spin-unrestricted molecular Kohn–Sham solution and the analogue of Koopmans’s theorem for open-shell molecules

Spin-unrestricted Kohn-Sham (KS) solutions are constructed from accurate ab initio spin densities for the prototype doublet molecules NO(2), ClO(2), and NF(2) with the iterative local updating procedure of van Leeuwen and Baerends (LB). A qualitative justification of the LB procedure is given with a "strong" form of the Hohenberg-Kohn theorem. The calculated energies epsilon(isigma) of the occupied KS spin orbitals provide numerical support to the analogue of Koopmans' theorem in spin-density functional theory. In particular, the energies -epsilon(ibeta) of the minor spin (beta) valence orbitals of the considered doublet molecules correspond fairly well to the experimental vertical ionization potentials (VIPs) I(i) (1) to the triplet cationic states. The energy -epsilon(Halpha) of the highest occupied (spin-unpaired) alpha orbital is equal to the first VIP I(H) (0) to the singlet cationic state. In turn, the energies -epsilon(ialpha) of the major spin (alpha) valence orbitals of the closed subshells correspond to a fifty-fifty average of the experimental VIPs I(i) (1) and I(i) (0) to the triplet and singlet states. For the Li atom we find that the exact spin densities are represented by a spin-polarized Kohn-Sham system which is not in its ground state, i.e., the orbital energy of the lowest unoccupied beta spin orbital is lower than that of the highest occupied alpha spin orbital ("a hole below the Fermi level"). The addition of a magnetic field in the -z direction will shift the beta levels up so as to restore the Aufbau principle. This is an example of the nonuniqueness of the mapping of the spin density on the KS spin-dependent potentials discussed recently in the literature. The KS potentials may no longer go to zero at infinity, and it is in general the differences nu(ssigma)( infinity )-epsilon(isigma) that can be interpreted as (averages of) ionization energies. In total, the present results suggest the spin-unrestricted KS theory as a natural one-electron independent-particle model for interpretation and assignment of the experimental photoelectron spectra of open-shell molecules.