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Recent results of measurements of the Avogadro constant by the method of crystal silicon spheres in connection with the planned transition to a new definition of the basic SI unit, the mole, are discussed.

The role of the fundamental constants and of measurement data on the Planck and Avogadro constants, the kelvin, and the electrical charge in the planned transition to new definitions of the four SI base units (kilogram, mole, ampere, and kelvin) based on fixed values of these constants is discussed.

A class of multidimensional theories is identified in which the spatial and temporal variations in the gravitational constant and the fine structure constant have a common origin and are of the same magnitude. Arguments are presented in favor of the existence of these variations despite a lack of confirmed observational data on variations in the gravitational constant because of problems in constructing a unified theory of physical interactions and the well-known faint young Sun paradox. It is concluded that the gravitational constant probably depends nonlinearly on cosmological time.

Work on the redefinition of the kilogram and mole underway in many countries with experiments employing watt balances is analyzed. It is found that at present the reasons for the discrepancies in measurements of the Avogadro and Planck constants by different methods are not clear and that the required measurement accuracy has not been attained. Thus, studies with watt balances and crystalline silicon spheres must be continued in the framework of new projects.

Results of an analysis of the procedural and instrumental errors that unavoidably arise in measurement of the texture and shape parameters of a surface by means of the methods of three-dimensional interferometry with reference wave front and lateral shift interferometry are presented. It is noted that the errors in measurement of the current interference orders are responsible for the greatest contribution to the total procedural error, while the errors associated with measurement of the current coordinates and the shift are negligible. It is shown that the total error of the method of approximate integration is related to the interpolation error and depends on the state of the shape of the surface.

The mechanism of formation of the uncertainty budget of measurements of the parameters of the texture and form of a surface in the nanometric range with reference to the typical optical circuits of the Twyman–Green and Fizeau interferometers is considered. It is noted that in most of the well-known studies a differential (difference) method of measurement is implemented. Amplitude and amplitude-phase interference methods of coordinate measurement of the deviation of the form of a surface are considered.

Review materials and international procedural regulatory documentation devoted to methods of areal (zone) characterization of the topography and texture of a rough surface are analyzed. Questions related to the use of special filters designed to eliminate undesirable components of a measured surface are considered. The contemporary standardized approach to distinguishing between roughness and waviness on a primary (basic) surface is presented.

Selection of a fundamental physical constant for the purpose of redefinition of the updated SI base measurement unit according to the principle of concordance of dimensions of the constant and of the unit of measurement, when they either coincide or differ by a factor having the dimension of time, is proposed. A quantitative criterion for reconciling the new prototypes of the kilogram with its international prototype and a quantitative limitation of their instability are proposed. The possibility of preserving a relation between the definitions of the mole and the kilogram in the updated SI is considered. It is proposed that the kilogram and mole be redefined using a fixed value of the Avogadro constant, the kelvin, and the ampere, after, that is, the measurement accuracy of the Boltzmann constant has been improved and after closure of the “quantum triangle.”

A brief review of theoretical models explaining the variation in the fine structure constant α in space and time is given. A method is described for constructing models in which variations in α and other fundamental physical constants, including the gravitational constant G, follow from the dynamics of extra space-time dimensions in the framework of a multidimensional theory of gravitation that is nonlinear with respect to curvature. An explicit example of such a model is constructed for explaining the observed spatial and temporal variations in α.

We discuss the operating principle of a pyrosequencer, which is an instrument for sequential reading of the nucleotide sequence of DNA molecules in pyrophosphate sequencing (pyrosequencing). We formulate the basic principles of metrological support for DNA sequencing and we present the results of studies of the metrological characteristics of the GS FLX pyrosequencer. We list the major problems encountered in designing a system for metrological support of DNA sequencing.

Statistical errors of metrological control of the first kind (factually acceptable product rejected) and of statistical errors of the second kind (factually unacceptable product recognized as acceptable) are considered. The reasons for the occurrence of statistical errors of metrological control are analyzed. Formulas for estimating metrological control statistical errors of the first and second kind are presented. Approaches for increasing the reliability of metrological quality control of hydrocarbons shipped by pipeline are investigated mathematically.

A fragment of the DNA sequence of the pUC18 plasmid is proposed as a reference sequence for the calibration and metrological assurance of genome analyzers. This fragment consists of 271 nucleotide pairs and is obtained by a reference method. This sequence is optimal for determining the metrological characteristics of genome analyzers in light of its stability and the existence of several segments with repeating nucleotides. An example is given for the calculation of a genome analyzer characteristic, namely, the probability of error in measurement of the genome sequence.

One possible approach to the solution of questions of metrological assurance of complex measurement and control systems is set forth. A systems approach to the solution of the problem is proposed in order to eliminate the redundancy of state control in the operation of such systems and reduce the costs and period needed for placing such facilities into operation, especially at potentially hazardous industrial facilities. It is recommended that the CIPM MRA Contract signed in Paris in 1999 be used for facilities with foreign involvement.

The latest high-precision experimental results and theoretical calculations to determine the value of the fine-structure constant α are analyzed. These indicate a possible increase in its value by approximately 0.5·10−8α compared with the CODATA data (2006). It is shown that this shift in the value of α may play an important role in the new system of units, including the solution of the problem of matching the results of measurements of the Avogadro and Planck constants obtained by different methods (in the Avogadro project and by means of the watt balance).

The results of research to investigate mini-cells for reproducing the melting curves of gallium and indium in microprocessor-based temperature calibrators of the ATC and RTC series are presented. The results obtained reveal new possibilities for employing the melting curves of existing and new thermometer materials to improve the support facilities of precision thermometry.

Conditions for comparison of involute surface standards by the theme 314/UA/04 COOMET and their results are considered.

Some trends in research on the physics underlying metrology as the science of measurement are examined. The basic problems and the prospects for their solution are analyzed.

Numerical simulation of the profile restoration procedure for an optical surface with scattering of radiation by nanostructures of the type of single grooves or single protrusions as well as that of a periodic “comb-like” profile is performed. A comparison of the results of the simulation with observation data obtained with the use of a modified interference microscope (micro-interferometer) is performed. The effectiveness of numerical simulation of these procedures is confirmed.

Suggestions are analyzed pertaining to the transition to a new definition of the unit of thermodynamic temperature, which is planned by the International Committee on Weights and Measures for 2011, based on fixing the exact value of Boltzmann constant. It is demonstrated that, though it is correct and corresponds to the physical nature of the concept of “temperature”, this transition is not advisable in view of the present-day level of accuracy and reliability of determination of the value of Boltzmann constant.

The paper discusses possible signs of time variation in the constants for the extended standard model. Existing experimental constraints on the magnitude of the changes are given in order to allow for the possible effects on the metrological characteristics of primary standards for the units of physical quantities.

The constants in the extended standard model are considered, which includes gravitational interaction and massive neutrinos. The accuracy is compared in determining the coupling constants on various energy scales, and theoretical estimates are given for the possible time variations.

Some methods of determining the constants of the Standard Model, the values of the constants established at the present time, and the dependence of the coupling constants of the strong, electromagnetic and weak interactions on the characteristic energy of the process are presented. Possible generalizations of the Standard Model, which lead to a reduction in the number of fundamental constants, are considered.

Fundamental questions of contemporary metrology connected with redefinition of the basic units of physical quantities are discussed. Some new definitions of the kilogram, ampere, Kelvin, and mole are suggested and their consequences are analysed. The possibility of fixing some fundamental physical constants at the level of accuracy contemporary for 2011 is considered. Alongside the practical system of units, use of a fundamental (theoretical) system is proposed. The importance is noted of considering possible variations of physical constants for a fundamental system of units, whereas in practical metrology these variations are not currently essential.

The main versions of the redefinition for the international prototype kilogram are examined for best accuracy and transmitting the mass unit. It is concluded that it is most promising to use Avogadro’s number and the atomic mass unit in order to transfer to a new standard for the kilogram, i.e., to introduce an atomic kilogram.

Methodological aspects are considered for theoretical metrology and the principles for determining basic concepts. The basic concepts in metrology are determined operationally, with the meanings established during the performance of sequences of experimental operations. Differences are pointed out in the definition of the same concepts in metrology and in theoretical physics.

We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After a brief general exposition, we review in more detail the predicted corrections to Newton's law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein-Gauss-Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton's law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology., Comment: Brief review, 16 pages, 92 references. Some description and references added

Contemporary methods are presented for redefining the unit of mass standard, i.e., the kilogram prototype. The main tendencies in improving these methods in order to reduce the uncertainty of reproducing the unit of mass are discussed. It is noted that the use of precise values of a number of fundamental physical constants, primarily the Avogadro number, is important.

Contemporary methods are considered for storage and reproduction of the dimensions of basic SI units, i.e., length, time, and mass. The main trends are discussed for improving these methods in order to reduce reproduction errors for the dimensions of units. The importance of using results of theoretical calculations for microprocess characteristics and precise values for a number of fundamental physical constants is noted.

The paper discusses the scope for redefining the temperature measurement unit. Boltzmann's constant is naturally related to the temperature, and therefore the unit of temperature measurement can be an energy unit. Thermodynamic irreversibility in a dynamic system linked to a thermostat is discussed, and it is also shown to be desirable to use an energy unit for temperature.

The paper discusses the fundamental physical constants, the classification of them, the number of them, the definition accuracy, and the relationships to fundamental physical theories (interactions). Basic concepts are presented on gravitational relativistic metrology related to precision space-time measurements. The main attention is given to Newton’s gravitational constant G as regards the measurement of the absolute value and the possible variations in time and space as predicted by interaction union theories. Principles are presented for a proposed space experiment to measure G and its variations, whose implementation will enable one to improve on current data from appropriate laboratory experiments on Earth by 2–3 orders of magnitude.

Transverse and longitudinal magnetostriction of a large polycrystalline slab of Nb3Al superconductor was investigated by the strain gauge technique. At 4.2 K and in an external magnetic field of several Tesla the vertical width of transverse magnetostriction hysteresis loop was found to be of an order of 10−4. In a wide range of temperatures and external magnetic fields we observed the phenomenon of giant jumps of both transverse and longitudinal magnetostriction caused by thermomagnetic avalanches. The shapes of the magnetostriction hysteresis loops are also influenced by the phenomenon of the second maximum of the critical current density, called as a peak or fishtail effect. Experimental results can be understood in the framework of the model of the magnetostriction induced by pinning forces.

Electric S-brane solutions with two non-composite electric branes and a set of l scalar fields are considered. The intersection rules for branes correspond to Lie algebras A_2, C_2 and G_2. The solutions contain five factor spaces. One of them, M_0, is interpreted as our 3-dimensional space. It is shown that there exists a time interval where accelerated expansion of our 3-dimensional space is compatible with a small enough variation of the effective gravitational constant G(\tau). This interval contains \tau_0, a point of minimum of the function G(\tau). A special solution with two phantom scalar fields is analyzed and it is shown that in the vicinity of the point \tau_0 the time variation of G(\tau) (calculated in the linear approximation) decreases in the sequence of Lie algebras A_2, C_2 and G_2., Comment: 13 pages, LaTex, no figures

Some methods for the determination and the most precise values of constants of an extended Standard Model, which include the gravitation interaction and massive neutrinos, are presented. Accuracies of constants at different energy scales are compared and the possible manifestations of temporal variations of constants are considered. Theoretical estimations and obtained experimental bounds of variations are listed, that is important as for search of SM generalizations as to account for possible influence on metrological characteristics of measurement standards., Comment: 15 pages

We consider multidimensional gravity with a Lagrangian containing the Ricci tensor squared and the Kretschmann invariant. In a Kaluza-Klein approach with a single compact extra space of arbitrary dimension, with the aid of a slow-change approximation (as compared with the Planck scale), we build a class of spatially flat cosmological models in which both the observed scale factor $a(\tau)$ and the extra-dimensional one, $b(\tau)$, grow exponentially at large times, but $b(\tau)$ grows slowly enough to admit variations of the effective gravitational constant $G$ within observational limits. Such models predict a drastic change in the physical laws of our Universe in the remote future due to further growth of the extra dimensions., Comment: 5 pages, to be published in Grav. Cosmol