Classification of Novikov algebras

We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over $\mathbb{R }$ and $\mathbb{C }$ , as well as the classification of the 4-dimensional Novikov algebras over $\mathbb{C }$ whose associated Lie algebra is nilpotent. In particular this includes a list of all 4-dimensional commutative associative algebras over $\mathbb{C }$ .     

Specific Heat of K_{0.71}Na_{0.29}Fe_2As_2 at Very Low Temperatures

A commercially available calorimeter has been used to investigate the specific heat of a high-quality K $_{0.71}$ Na $_{0.29}$ Fe $_2$ As $_2$ single crystal. The addenda heat capacity of the calorimeter is determined in the temperature range $0.02 \, \mathrm{K} \le T \le 0.54 \, \mathrm{K}$ . The data of the K $_{0.71}$ Na $_{0.29}$ Fe $_2$ As $_2$ crystal imply the presence of a large $T^2$ contribution to the specific heat which gives evidence of $d$ -wave order parameter symmetry in the superconducting state. To improve the measurements, a novel design for a calorimeter with a paramagnetic temperature sensor is presented. It promises a temperature resolution of $\Delta T \approx 0.1 \, \mathrm{\mu K}$ and an addenda heat capacity less than $200 \, \mathrm{pJ/K}$ at $ T < 100 \, \mathrm{mK}$ .     

Measurements of Microstructural, Mechanical, Electrical, and Thermal Properties of an Al–Ni Alloy

The Al–7.5 wt% Ni alloy was directionally solidified upwards with different temperature gradients, $G$ ( $0.86\,\text{ K}~{\cdot }~ \text{ mm}^{-1}$ to $4.24\,\text{ K}~{\cdot }~\text{ mm}^{-1})$ at a constant growth rate, $V$ ( $8.34\,\upmu \text{ m}~{\cdot }~\text{ s}^{-1})$ . The dependence of dendritic microstructures such as the primary dendrite arm spacing ( $\lambda _{1}$ ), the secondary dendrite arm spacing ( $\lambda _{2}$ ), the dendrite tip radius ( $R$ ), and the mushy zone depth ( $d$ ) on the temperature gradient were analyzed. The dendritic microstructures in this study were also compared with current theoretical models, and similar previous experimental results. Measurements of the microhardness (HV) and electrical resistivity ( $\rho $ ) of the directionally solidified samples were carried out. Variations of the electrical resistivity ( $\rho $ ) with temperature ( $T$ ) were also measured by using a standard dc four-point probe technique. And also, the dependence of the microhardness and electrical resistivity on the temperature gradient was analyzed. According to these results, it has been found that the values of HV and $\rho $ increase with increasing values of $G$ . But, the values of HV and $\rho $ decrease with increasing values of dendritic microstructures ( $\lambda _{1}, \lambda _{2}, R,$ and $d$ ). It has been also found that, on increasing the values of temperature, the values of $\rho $ increase. The enthalpy of fusion ( $\Delta {H}$ ) for the Al–7.5 wt%Ni alloy was determined by a differential scanning calorimeter from a heating trace during the transformation from solid to liquid.     

Influence of pH and bath composition on properties of Ni–Fe alloy films synthesized by electrodeposition

Fe?CNi films were electrodeposited on ITO glass substrates from the electrolytes with different molar ratio of Ni $^{\boldsymbol{2+}}$ /Fe $^{\boldsymbol{2+}}$ and different pH values (2 $\boldsymbol{\cdot}$ 1, 2 $\boldsymbol{\cdot}$ 9, 3 $\boldsymbol{\cdot}$ 7 and 4 $\boldsymbol{\cdot}$ 3) at 25 $\boldsymbol{^\circ}$ C. The properties of Fe?CNi alloy films depend on both Ni $^{\boldsymbol{2+}}$ and Fe $^{\boldsymbol{2+}}$ concentrations in electrolyte and pH values. The content of Ni increases from 38% to 84% as the mole ratio of NiSO $_{\boldsymbol{4}}$ /FeSO $_{\boldsymbol{4}}$ increasing from 0 $\boldsymbol{\cdot}$ 50/0 $\boldsymbol{\cdot}$ 50 to 0 $\boldsymbol{\cdot}$ 90/0 $\boldsymbol{\cdot}$ 10 in electrolyte and slightly decreases from 65% to 42% as the pH values increase from 2 $\boldsymbol{\cdot}$ 1 to 4 $\boldsymbol{\cdot}$ 3. The X-ray diffraction analysis reveals that the structures of the films strongly depend on the Ni content in the binary films. The magnetic performance of the films shows that the saturation magnetization ( $\boldsymbol{M}_{\boldsymbol{\rm s}})$ decreases from 1775 $\boldsymbol{\cdot}$ 01 emu/cm $^{\boldsymbol{3}}$ to 1501 $\boldsymbol{\cdot}$ 46 emu/cm $^{\boldsymbol{3}}$ with the pH value increasing from 2 $\boldsymbol{\cdot}$ 1 to 4 $\boldsymbol{\cdot}$ 3 and the saturation magnetization ( $\boldsymbol{M}_{\boldsymbol{\rm s}})$ and coercivity ( $\boldsymbol{H}_{\boldsymbol{\rm c}})$ move up from 1150 $\boldsymbol{\cdot}$ 44 emu/cm $^{\boldsymbol{3}}$ and 58 $\boldsymbol{\cdot}$ 86 Oe to 2498 $\boldsymbol{\cdot}$ 88 emu/cm $^{\boldsymbol{3}}$ and 93 $\boldsymbol{\cdot}$ 12 Oe with the increase of Ni $^{\boldsymbol{2+}}$ concentration in the electrolyte, respectively.     

Molecular beam epitaxy of semipolar AlN(11\bar{2}2) and GaN(11\bar{2}2) on m-sapphire

We report on the plasma-assisted molecular-beam epitaxy of semipolar $\hbox{AlN}(11\bar{2}2)$ and GaN( $11\bar{2}2$ ) films on $(1\bar{1}00)$ m-plane sapphire. AlN deposited on m-sapphire settles into two main crystalline orientation domains, $\hbox{AlN}(11\bar{2}2)$ and $\hbox{AlN}(10\bar{1}0),$ whose ratio depends on the III/V ratio. Growth under moderate nitrogen-rich conditions enables to isolate the $(11\bar{2}2)$ orientation. The in-plane epitaxial relationships of $\hbox{AlN}(11\bar{2}2)$ on m-plane sapphire are $[11\bar{2}\bar{3}]_{\rm AlN} \vert \vert [0001]_{\rm sapphire}$ and $[1\bar{1}00]_{\rm AlN} \vert \vert [11\bar{2}0]_{\rm sapphire}.$ GaN deposited directly on m-sapphire results in ( $11\bar{2}2$ )-oriented layers with ( $10\bar{1}\bar{3}$ )-oriented inclusions. A ～100 nm-thick AlN( $11\bar{2}2$ ) buffer imposes the ( $11\bar{2}2$ )-orientation for the GaN layer grown on top. By studying the Ga-desorption on GaN( $11\bar{2}2$ ), we conclude that these optimal growth conditions corresponds to a Ga excess of one monolayer on the GaN( $11\bar{2}2$ ) surface.     

Linear complexity and correlation of a class of binary cyclotomic sequences

Let $p_1,p_2,\ldots ,p_n$ be distinct odd primes and let $e_1,e_2,\ldots ,e_n$ be positive integers. Based on cyclotomic classes proposed by Ding and Helleseth (Finite Fields Appl 4:140–166, 1998), a binary cyclotomic sequence of period $p_1^{e_{1}}p_{2}^{e_{2}}\ldots p_{n}^{e_n}$ is defined and denoted by $\underline{s_\Upsilon }$ . The linear complexity of $\underline{s_\Upsilon }$ is determined and is proved to be greater than or equal to $(p_1^{e_{1}}p_{2}^{e_{2}}\ldots p_{n}^{e_n}-1)/2$ . The autocorrelation function of $\underline{s_\Upsilon }$ is explicitly computed. Let $\ell \in \{1,2,\ldots ,n\}$ . We also explicitly compute the crosscorrelation function of $\underline{s_\Upsilon }$ and the Legendre sequence $\underline{L_{p_\ell }}$ with respect to $p_\ell $ . It is shown that $\underline{s_\Upsilon }$ and $\underline{L_{p_\ell }}$ have two-level or three-level crosscorrelation, and all their two-level crosscorrelation functions are determined.     

Hypersensitive Transition of Nd(III) Complexes in Liquids Detected by Pulsed-Laser-Induced Photoacoustic Spectroscopy

Laser-induced photoacoustic (PA) spectroscopy for the spectral measurements of extremely weak absorption such as a forbidden transition of lanthanide ions in liquids has been established. In spectroscopy, a pulsed Nd:YAG laser connected with a MOPO series optical parametric oscillator which emits a broad spectrum covering UV and visible regions is used as the excitation source, and the induced PA signals are detected by an optimized PA piezoelectric transducer. The absorption spectra of trivalent lanthanide ions ( $\text{ Pr}^{3+}, \text{ Ho}^{3+}$ , and $\text{ Nd}^{3+})$ in aqueous solutions have been obtained by the detection system with a detection-limit absorbance of $1.3\times 10^{-5}\,\text{ cm}^{-1}$ at room temperature. In addition, the effects of different binding environments on the band shapes and oscillator strengths of the hypersensitive transitions of $\text{ Nd}^{3+}$ ions, i.e., $\text{ Nd}(\text{ CH}_{3}\text{ COO})_{3}$ $\cdot $ $\text{ H}_{2}\text{ O}$ dissolved in $0.1\,{\text{ mol}} \cdot \text{ l}^{-1}$ acetic acid and $\text{ Nd(3-butanedione)}_{3}{\cdot } 2\text{ H}_{2} \text{ O}$ dissolved in triglycol compared with $\text{ NdCl}_{3}$ in $0.1\,{\text{ mol}}\cdot \text{ l}^{-1}$ hydrochloric acid, are observed. The results show that the chemical environment around the lanthanide ions has great impact on 4f–4f transitions, which is rationalized as the impact in terms of ligand (or solvent) special structures and coordination properties.     

On quasi-cyclic codes over {\mathbb{Z}_q}

Quasi-cyclic (QC) codes are a remarkable generalization of cyclic codes. Many QC codes have been shown to be best for their parameters. In this paper, some structural properties of QC codes over the prime power integer residue ring ${\mathbb{Z}_q}$ are considered. An l-QC code of length lm over ${\mathbb{Z}_q}$ is viewed both as in the conventional row circulant form and also as a ${\frac{\mathbb{Z}_q[x]}{\langle x^m-1 \rangle}}$ -submodule of ${\frac{GR(q,l)[x]}{\langle x^m-1 \rangle}}$ , where GR(q, l) is the Galois extension ring of degree l over ${\mathbb{Z}_q}$ . A necessary and sufficient condition for cyclic codes over Galois rings to be free is obtained and a BCH type bound for them is also given. A sufficient condition for 1-generator QC codes to be ${\mathbb{Z}_q}$ -free is given and a formula to evaluate their ranks is derived. Some distance bounds for 1-generator QC codes are also discussed. The duals of QC codes over ${\mathbb{Z}_q}$ are also briefly discussed.     

Structure and morphology of polar and semi-polar pyramidal surfaces coating wurtzite ZnO micro-wires

Wurtzite ZnO nano-pyramids grown by evaporation-deposition methods have been characterized using advanced electron microscopy. The basal and pyramidal planes of the nano-pyramids were identified as (0001) polar and $ \{ 20\bar{2}1\} $ semi-polar surfaces, respectively. The $ \{ 20\bar{2}1\} $ semi-polar surfaces were further faceted into $ \{ 10\bar{1}1\} $ semi-polar and $ \{ 10\bar{1}0\} $ non-polar surfaces. Surface area calculations revealed that approximately 65 % of the total surfaces of the as-grown nanostructures consisted of polar or semi-polar surfaces.     

Study of Glass-Transition Kinetics of Pb-Modified Se_{80}In_{20} System by Using Non-isothermal Differential Scanning Calorimetry

Glass-transition kinetics of $\mathrm{Se}_{80}\mathrm{In}_{20-\mathrm{x}}\mathrm{Pb}_{\mathrm{x}}$ ( $x =$ 0, 5, 10, and 15) chalcogenide glasses have been carried out at different heating rates by using differential scanning calorimeter (DSC) under the non-isothermal condition. The glass-transition temperature $T_{\mathrm{g}}$ and peak glass-transition temperature $T_{\mathrm{pg}}$ have been determined from DSC thermograms. The reduced glass temperature $T_{\mathrm{rg}}$ , total relaxation time $\tau _{T_{g}}$ thermal-stability parameters $K^{l}$ and $S$ , the activation energy of glass transition $E_{\mathrm{g}}$ , the fragility index $F_{\mathrm{i}}$ , and the average coordination number $\langle Z\rangle $ have been calculated on the basis of the experimental results. The temperature differences $(T_{\mathrm{c}}-T_{\mathrm{g}}), K_{\mathrm{gl}}, K^{l}, S$ , and $E_{\mathrm{g}}$ are found to be maxima for $\mathrm{Se}_{80}\mathrm{In}_{10}\mathrm{Pb}_{10}$ glass. This indicates that $\mathrm{Se}_{80}\mathrm{In}_{10}\mathrm{Pb}_{10}$ glass has the highest thermal stability and glass-forming ability in the investigated compositional range. These results could be explained on the basis of modification of the chemical bond formation due to incorporation of Pb in the Se–In glassy matrix.     

Evidence for One-Gap Superconductivity in Mg(B_{1-x}C_{x})_{2} Single Crystals at x=0.132 by Point-Contact Spectroscopy

We report the results of directional point-contact measurements in Mg(B $_{1-x}$ C $_{x})_{2}$ single crystals. The amplitudes of the gaps, $\Delta_{\pi}$ and $\Delta_{\sigma}$ , were determined for each C content by fitting the experimental low-temperature normalized conductance curves of our “soft” point contacts with the BTK model generalized to the two-band case. We found that, on increasing the carbon content, $\Delta_{\sigma}$ decreases almost linearly with $T_{c}$ and $\Delta_{\pi}$ slightly increases until, at $x=0.132$ (where $T_{c}=19$ K), they assume the same value $\Delta =3.2 \pm 0.9$ meV. This result is confirmed by the temperature and magnetic-field dependence of the conductance curves at this C content, which do not show any evidence of two distinct gap values. In particular, the Δ versus T curve follows very well a standard BCS curve, with a gap ratio $2\Delta /k_{B} T_{c}=3.9$ . These experimental findings are compared to the theoretical predictions of the two-band model in the Eliashberg formulation.     

Cryptanalysis of a key exchange protocol based on the endomorphisms ring End{(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})}

Climent et?al. (Appl Algebra Eng Commun Comput 22:91?C108, 2011) identified the elements of the endomorphisms ring End ${(\mathbb{Z}_p \times \mathbb{Z}_{p^2})}$ with elements in a set, E _p , of matrices of size 2?× 2, whose elements in the first row belong to ${\mathbb{Z}_{p}}$ and the elements in the second row belong to ${\mathbb{Z}_{p^2}}$ . By taking advantage of matrix arithmetic, they proposed a key exchange protocol using polynomial functions over E _p defined by polynomials in ${\mathbb{Z}[X]}$ . In this note, we show that this protocol is insecure; it can be broken by solving a set of 10 consistent homogeneous linear equations in 8 unknowns over ${\mathbb{Z}_{p^2}}$ .     

Exploratory Characterization of a Perfluoropolyether Oil as a Possible Viscosity Standard at Deepwater Production Conditions of 533 K and 241 MPa

DuPont’s perfluoropolyether oil Krytox $^{\textregistered }$ GPL 102 is a promising candidate for the high-temperature, high-pressure Deepwater viscosity standard (DVS). The preferred DVS is a thermally stable liquid that exhibits a viscosity of roughly 20  $\hbox {mPa} \cdot \hbox {s}$ at 533 K and 241 MPa; a viscosity value representative of light oils found in ultra-deep formations beneath the deep waters of the Gulf of Mexico. A windowed rolling-ball viscometer designed by our team is used to determine the Krytox $^{\textregistered }$ GPL 102 viscosity at pressures to 245 MPa and temperatures of 311 K, 372 K, and 533 K. At 533 K and 243 MPa, the Krytox $^{\textregistered }$ GPL 102 viscosity is $(27.2 \pm 1.3)\,\hbox {mPa} \cdot \hbox {s}$ . The rolling-ball viscometer viscosity results for Krytox $^{\textregistered }$ GPL 102 are correlated with an empirical 10-parameter surface fitting function that yields an MAPD of 3.9 %. A Couette rheometer is also used to measure the Krytox $^{\textregistered }$ GPL 102 viscosity, yielding a value of $(26.2 \pm 1)\,\hbox {mPa} \cdot \hbox {s}$ at 533 K and 241 MPa. The results of this exploratory study suggest that Krytox $^{\textregistered }\, \hbox {GPL}$ 102 is a promising candidate for the DVS, primarily because this fluoroether oil is thermally stable and exhibits a viscosity closer to the targeted value of 20 mPa $\cdot $ s at 533 K and 241 MPa than any other fluid reported to date. Nonetheless, further studies must be conducted by other researcher groups using various types of viscometers and rheometers on samples of Krytox GPL $^{\textregistered }$ 102 from the same lot to further establish the properties of Krytox GPL $^{\textregistered }$ 102.     

Full-Potential Calculation of Structural, Electronic, and Thermodynamic Properties of Fluoroperovskite \text{ CsMF}_{3} (M?=?Be and Mg)

The structural and electronic properties of the cubic fluoroperoveskite $\text{ CsBeF}_{3}$ and $\text{ CsMgF}_{3}$ have been investigated using the full-potential-linearized augmented plane wave method within the density functional theory. The exchange-correlation potential was treated with the local density approximation and the generalized gradient approximation. The calculations of the electronic band structures show that $\text{ CsBeF}_{3 }$ has an indirect bandgap, whereas $\text{ CsMgF}_{3}$ has a direct bandgap. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the effect of pressure $P$ and temperature $T$ on the lattice parameter, bulk modulus, thermal expansion coefficient, Debye temperature, and the heat capacity for $\text{ CsBeF}_{3}$ and $\text{ CsMgF}_{3}$ compounds are investigated for the first time.     

Rational formulas for traces in zero-dimensional algebras

We present a rational expression for the trace of the multiplication map Times _r : A → A in a finite-dimensional algebra ${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}$ in terms of the generalized Chow form of ${\mathcal{I}}$ . Here, ${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}$ is a zero-dimensional ideal, ${\mathbb {K}}$ is a field of characteristic zero, and r(x ₁,..., x _n ) a rational function whose denominator is not a zero divisor in A. If ${\mathcal {I}}$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.     

The theoretical calculation of the flow rate of granular matter from an inclined orifice

A theoretical calculation method for the flow rate of granular matter from an inclined orifice is discussed in this article and for the inclination angles at $\theta \le 90^{\circ }$ , a theoretical relation between the flow rate $Q$ and inclination angle $\theta $ is derived; and for the inclination angles at $\theta >90^{\circ }$ , a semi-theoretical relation is established. From the relations, we found that the ratio of the flow rate from a vertical orifice, $Q_{90}$ , to that from a horizontal orifice, $Q_{0}$ , is equal to the sine of the angle of repose $\theta _{\mathrm{r}}$ , i.e., $Q_{90} /Q_0 =\sin \theta _{\mathrm{r}} $ . The theoretical relations are tested by means of the experimental data and the results indicate that the theoretical calculating values are in good agreement with the experimental data over a wide range of the inclination angles. Therefore, the formula proposed in this article can be used for the theoretical calculation of the flow rate of granular matter from an inclined orifice. The relation $Q_{90} /Q_0 =\sin \theta _{\mathrm{r}}$ may be used as an alternative approach to obtaining $\theta _{\mathrm{r}}$ : measuring $Q_{90}$ and $Q_{0}$ , and then calculating $\theta _{\mathrm{r}} $ by using formula $\theta _{\mathrm{r}} =\arcsin (Q_{90} /Q_0 )$ .     

Determination of thermodynamic interactions of poly(l-lactide) and biphasic calcium phosphate/poly(l-lactide) composite by inverse gas chromatography at infinite dilution

Inverse gas chromatography at infinite dilution was applied to determine the thermodynamic interactions of poly(l-lactide) (PLLA) and the composite of biphasic calcium phosphate and PLLA (BCP/PLLA). The specific retention volumes, $ V_{\text{g}}^{0} $ , of 11 organic compounds of different chemical nature and polarity (non-polar, donor or acceptor) were determined in the temperature range of 308–378 K for PLLA and 308–398 K for BCP/PLLA. The weight fraction activity coefficients of test sorbates, $ \Omega_{1}^{\infty } $ , and the Flory–Huggins interaction parameters, $ \chi_{12}^{\infty } $ , were estimated and discussed in terms of interactions of the sorbates with PLLA and BCP/PLLA. Also, the partial molar free energy, $ \Delta G_{1}^{\infty } $ , the partial molar heat of mixing, $ \Delta H_{1}^{\infty } $ , the sorption molar free energy, $ \Delta G_{1}^{\text{S}} $ , the sorption enthalpy, $ \Delta H_{1}^{\text{S}} $ , and the sorption entropy, $ \Delta S_{1}^{\text{S}} $ , were analyzed. A different chromatographic behavior of the two investigated samples, PLLA and BCP/PLLA, was observed. The values of $ \Omega_{1}^{\infty } $ indicated n-alkanes, diethyl ether, tetrahydrofurane (THF), cyclohexane, benzene, dioxane (except for 338 K), and ethyl acetate (EtAc) (except for 338 K) as non-solvents, and chloroform (CHCl₃) as good solvent (except for 378 K) for PLLA. For BCP/PLLA, CHCl₃, EtAc (for 378 K), dioxane (except for 378 K), and THF were indicated as good solvents.     

Elastic Properties of Monoclinic \hbox {ZrO}_{2} at Finite Temperatures Via First Principles

The structural and elastic properties of orthorhombic $\hbox {ZrO}_{2}\,(m\hbox {-ZrO}_{2})$ as a function of temperature are investigated by the generalized gradient approximation (GGA) correction scheme in the framework of density functional theory (DFT) and the quasi-harmonic Debye model. The thirteen independent elastic constants of $m\hbox {-ZrO}_{2}$ at temperatures to 3200 K are theoretically investigated for the first time. It is found that with increasing temperature, all elastic constants change, especially $C_{35}\hbox { and }C_{25}$ change rapidly in the temperature range of 1400 K to 1600 K and 2200 K to 2600 K, respectively. We also obtain the bulk modulus $B$ , shear modulus $G$ , Young’s moduli $E$ , as well as Poisson’s ratio $\sigma $ of $m\hbox {-ZrO}_{2}$ at high temperatures. Our work suggests that it is very important to predict the melting properties of materials via the elastic constants at temperatures.     

Thermal Conductivity of Standard Sands. Part III. Full Range of Saturation

The thermal conductivity $(\lambda )$ ( λ ) of three unsaturated standard quartz sands (Ottawa C-109 and C-190, and Toyoura) was measured by a transient thermal-conductivity probe, at room temperature of approximately $25\,^{\circ }\text{ C }$ 25 ° C and at loose and tight compactions. The measurements were carried out at different degrees of saturation $(S_\mathrm{r})$ ( S r ) from dryness to full saturation. In general, a sharp $\lambda $ λ increase was observed at low $S_\mathrm{r}$ S r , followed by a moderate rise until full saturation. However, experiments on loosely compacted C-190 samples revealed $\lambda $ λ deviation from a general trend ( $\lambda $ λ vs $S_\mathrm{r})$ S r ) caused by water percolation. Alternatively, successful experiments were carried out on loosely packed unsaturated C-190 samples using 1 % agar gel. For loosely compacted C-109 and Toyoura, $\lambda $ λ data obtained from 1 % agar gel closely agreed with $\lambda $ λ data for water as a saturation medium. The measured data were used to verify a model by de Vries for unsaturated soils. The model largely underestimates experimental data at $S_\mathrm{r}<0.5$ S r < 0.5 and produces an overall root-mean-square error of about $0.2\, \text{ W }~{\cdot }~\text{ m }^{-1}~{\cdot }~\text{ K }^{-1}$ 0.2 W · m ? 1 · K ? 1 . Measured $\lambda $ λ data agreed with data by a steady-state technique (a guarded hot-plate apparatus) at dryness and full saturation and exceeded the steady-state data in the unsaturated region. However, TCP data can be considered more reliable due to a lower temperature increase during $\lambda $ λ measurements and a shorter testing time. Consequently, in the case of unsaturated soils, evaporation and migration of water and steam can be avoided.     

Nuclear Spin Relaxation Characteristic of Submonolayer ^3He Films in Nanochannels

In order to obtain information on dynamics of helium films in the nondegenerate fluid region, we have performed a pulsed-NMR experiment at 3.29 MHz on $^3$ He films adsorbed in straight 2.4 nm channels of FSM silicates down to 0.54 K. In general, the spin-lattice and spin-spin relaxation times $T_1$ and $T_2$ were explained in terms of the two-dimensional Bloembergen–Purcell–Pound model for dipolar relaxation. Temperature dependences of $T_1$ in submonolayer $^3$ He films show a minimum, indicating that the dipolar-field correlation time $\tau _\mathrm {c}$ is about $\omega ^{-1}=4.8\times 10^{-8}$ s. The temperature $T_\mathrm {min}$ of the $T_1$ minimum monotonically lowers with increasing coverage, suggesting that $^3$ He adatoms become more mobile at higher coverages. The low-dimensional property of $^3$ He adatoms is observed as the separation of $T_1$ and $T_2$ above $T_\mathrm {min}$ where $\omega \tau _\mathrm {c}<1$ . On the other hand, several features specific to films in the nanochannel geometry were also found. Especially, the temperature dependence of $T_2$ becomes very small just below $T_\mathrm {min}$ and shows a shoulder at lower temperatures. This anomaly has not been observed in $^3$ He adsorbed in wider pores or on flat surfaces, so that it is considered to be characteristic of $^3$ He films confined in narrow channels with a diameter of a few nm.