bluuebunny/crossref_metadata_2025 huggingface dataset:
Line load applied along generators of thin-walled circular cylindrical shells of finite length
Authors: Hoff N. J. , Kempner Joseph , Pohle Frederick V.
Published: December 2016

Donnell’s differential equations of the thin circular cylindrical shell are integrated in the case when the loads are radial forces or circumferential moments distributed sinusoidally along a generator. Closed form expressions are obtained for the displacements, internal moments, and the membrane stresses. In addition, loads distributed uniformly along a segment of a generator and concentrated loads are discussed and radial forces are combined into a longitudinal moment.
Effects of surface tension and viscosity on Taylor instability
Authors: Bellman Richard , Pennington Ralph H.
Published: December 2016

The model used is that of two fluids of infinite depth, with the interface initially in the form of a sine wave with amplitude small compared to wave length. The fluids are considered incompressible, and only the linear terms in the equations of hydrodynamics are used. The first four sections discuss the effects of surface tension and viscosity. The fifth gives a few numerical results to illustrate the main points of the preceding sections.
Two dimensional source flow of a viscous fluid
Authors: Levey H. C.
Published: December 2016

The steady two-dimensional source-type flow of a viscous heat-conducting perfect gas is investigated. The solutions of physical significance all contain shocks, and bounds are given for the shock-thickness in terms of the shock-strength and the Reynolds number of the flow. It is found that the entropy rises to a maximum within the shock, and this maximum does not disappear even when the viscosity tends to zero.
On the axially-symmetric steady wave propagation in elastic circular rods
Authors: Adem Julián
Published: December 2016

In the first part of this report we find an exact solution for the problem of steady wave propagation in an isotropic, elastic circular bar of infinite length, free of stress on its lateral surface and loaded by a harmonic body force, parallel to its axis, whose amplitude is a Dirac delta function. The solution of this problem gives at the same time the solution for a semi-infinite bar with a special prescribed load on its boundary plane.
On some effects of velocity distribution in electron streams
Authors: Yadavalli S. V.
Published: December 2016

Based on the Liouville theorem an integral equation is obtained for the solution of electron beam problems having a velocity spread. Assuming a rectangular velocity distribution (which is justified later) the integral equation is solved by Laplace Transforms to obtain the solution of the problems of small-signal velocity modulation in a drifting electron stream, and a drifting electron stream initially possessing full shot noise in each velocity class.
Closure waves in helical compression springs with inelastic coil impact
Authors: Morrison J. A.
Published: December 2016

This paper deals with the problem of spring surges taking into account coil closure. This may occur in many cases of compression springs subject to impact. Inelastic coil on coil impact conditions are assumed. The simple theory of spring surges is adopted wherein only the motion of the spring wire parallel to the axis of the spring is considered and the assumption made that each element of the spring satisfies the force-longitudinal strain relation of the whole spring, before coil closure occurs. The basic theory of coil closure with inelastic impact conditions has been given by Lee [1]

3

^{3}

. The spring is initially at rest and unstrained with one end fixed and the other (the impact end) is given an impulsive velocity and then either maintained at this velocity or decelerated at a constant rate. The case of a mass attached to the impact end is also considered. Conditions are obtained for which partial or complete closure of the spring occurs.
The solution of eigenvalue problems of integral equations by power series
Authors: Radok J. R. M.
Published: December 2016

The characteristic equations and eigensolutions of Fredholm integral equations of the second kind with symmetrical kernels of the homogeneous polynomial type are obtained by use of power series. The method is applied to the particular case of the kernel

|

x
−
y

|

\left | {x - y} \right |

and it is indicated that it may readily be extended to more general types of equations.
On the evaluation of indefinite integrals involving the special functions: development of method
Authors: Maximon L. C. , Morgan G. W.
Published: December 2016

The solution of a general second order linear partial differential equation in two variables by Laplace transforms is utilized to develop a method for the evaluation of a large class of indefinite integrals involving the special functions.
The decay of magneto-turbulence in the presence of a magnetic field and Coriolis force
Authors: Lehnert B.
Published: December 2016

The final period of decay of magneto-turbulence in an external, homogeneous magnetic field is considered and it is shown that it develops pronounced axisymmetric properties, turbulence elements with finite wave numbers in the direction of the field being damped strongly under normal physical conditions. The turbulence consists of aperiodic motions as well as wave motions. An introduction of an angular velocity, inclined to the field, destroys the axisymmetry and modifies the damping effects and periodicity. The influence of the magnetic field on the damping is counteracted by the Coriolis force. A linear stationary theory on the action of the field gives results consistent with those of the theory of decay. From the results of both theories an explanation is given of the observed inhibition of turbulence in mercury by a magnetic field.
The use of stability charts in the synthesis of numerical quadrature formulae
Authors: Gurk Herbert M.
Published: December 2016

A classification of quadrature formulae is made according to their stability chart characteristics. Methods are described for synthesizing formulae with such characteristics, emphasis being placed upon those methods used for formulae which are applicable in real-time simulation problems. The relations between the stability chart characteristics and computed results are also discussed.
Tensors associated with time-dependent stress
Authors: Cotter Barbara A. , Rivlin R. S.
Published: December 2016

It is assumed that six functional relations exist between the components of stress and their first

m
m

material time derivatives and the gradients of displacement, velocity, acceleration, second acceleration, . . . ,

(

n
−
1

)

\left ( {n - 1} \right )

th acceleration. It is shown that these relations may then be expressed as relations between the components of

m
+
n
+
2

m + n + 2

symmetric tensors if

n

m

n \> m

, and

2
m
+
2

2m + 2

symmetric tensors if

m

n

m \> n

. Expressions for these tensors are obtained.
Stress analysis in visco-elastic bodies
Authors: Lee E. H.
Published: December 2016

The analysis of stress and strain in linear visco-elastic bodies is considered when the loading is quasi-static so that inertia forces due to the deformation are negligible. It is shown that removal of the time variable by applying the Laplace transform enables the solution to be obtained in terms of an associated elastic problem. Thus the extensive literature in the theory of elasticity can be utilized in visco-elastic analysis. The operation of the transform on the prescribed boundary tractions and displacements and body forces may completely modify the spatial distribution in the associated problem. For proportional loading, in which the space and time variations of the prescribed quantities separate, the spatial distribution is maintained in the associated problem. A convenient method of treating a common case of non-proportional loading, moving surface tractions, is demonstrated. This work is compared with related approaches to this problem in the literature of visco-elastic stress analysis.
On perturbation methods involving expansions in terms of a parameter
Authors: Bellman Richard
Published: December 2016

It is shown by means of some examples from the theories of linear algebraic equations, linear integral equations and nonlinear differential equations that the effectiveness of the method of expanding a solution in a power series in terms of a parameter may in many cases be greatly increased by expanding in terms of a suitably chosen function of the parameter. This is particularly the case when the physical setting of the problem allows only positive values of the parameter to enter.
Temperature distribution in solids of variable thermal properties heated by moving heat sources
Authors: Grosh R. J. , Trabant E. A. , Hawkins G. A.
Published: December 2016

The temperature distribution in rods, plates, and infinite solids heated by moving plane, line, and point heat sources is obtained for the quasi-stationary state. The thermal properties of the solid can vary as a linear, parabolic, or some other convenient function of temperature as long as the thermal diffusivity of the material remains nearly constant.
Scattering of eletromagnetic waves from a random surface
Authors: Hoffman William C.
Published: December 2016

Suppose

Z

(

x
,
y

)

Z\left ( {x,y} \right )

is a real random process, continuous in the mean over a finite region

D
D

, and with mean value zero and covariance function

r

(

x
,
y
;

x
′

,

y
′

)

r\left ( {x,y;x’,y’} \right )

. As such

Z

(

x
,
y

)

Z\left ( {x,y} \right )

defines a random surface (provided certain differentiability conditions are satisfied). Then, by Karhunen’s theorem on the representation of a random function,

Z

(

x
,
y

)

Z\left ( {x,y} \right )

has an expansion in terms of an orthogonal process and the eigenfunctions and eigenvalues of the covariance function. Introducing this expression into the far-zone form of the Stratton-Chu solution of the electromagnetic field equations then leads to an approximate expression for the radiation scattered from the random surface, from which mean and covariance of the scattered field can be determined.
Statistical analysis of the flow of highway traffic through a signalized intersection
Authors: Newell G. F.
Published: December 2016

The following is a report on some calculations of the statistical distribution of delay times due to a fixed-time traffic signal on a single lane highway.
A note on the coincidence of some random functions
Authors: Weiss George H.
Published: December 2016

This paper deals with a system capable of randomly attaining two states “on” and “off". For convenience this system is pictured as a pulse train. The question is, what is the expected amount of time that

n
n

of such systems are in the same state simultaneously. The answer is shown to depend on the probability of a system being in a given state at a specified time. A formal solution for the Laplace transform of this probability is given.
Simple solutions of Saint-Venant torsion problem by using Tchebycheff polynomials
Authors: Abbassi Mohammed M.
Published: December 2016

By using Tchebycheff polynomials, various forms of the stress functions associated with torsion problems have been obtained. The method can be applied for various types of cross sections. It is well known that these problems can be solved by other methods, but the method presented here gives a simple and direct solution in many cases.
On uniqueness in the theory of plasticity
Authors: Drucker D. C.
Published: December 2016

The fundamental definitions of work-hardening and perfect plasticity have far reaching implications with respect to uniqueness of solution for elastic-plastic bodies. Satisfaction of the basic postulate, that in a cycle work cannot be extracted from the material and the system of forces acting upon it, guarantees an existing solution to be stable but not necessarily unique. Uniqueness follows for the usual linear relation between the increments or rates of stress and strain and also for combinations of such linear forms. Conversely, lack of uniqueness results for an elastic-perfectly plastic body when, for example, the maximum shearing stress criterion of yield is employed with the Mises flow rule.
A note on numerical differentiation
Authors: Miles John W.
Published: December 2016

Given the matrix

f
=
{

f
i

}

f = \{{f_i}\}

, representing

f

(
x
)

f\left ( x \right )

at the set of points

{

x
i

}

\{ {x_i}\}

, the

m
m

th derivatives of

f

(
x
)

f\left ( x \right )

at these points are expressed in terms of all of the

f
i

{f_i}

according to

f

(
m
)

=

C

−
1

A
m

C
f

{f^{\left ( m \right )}} = {C^{ - 1}}{A^m}Cf

, where A is the sum of the skew matrix

[

(

x
i

−

x
i

)

−
1

]

\left [ {{{\left ( {{x_i} - {x_i}} \right )}^{ - 1}}} \right ]

and the diagonal matrix formed by summing the terms in the corresponding rows of this skew matrix, and C is the diagonal matrix having as its elements the products of the elements in the corresponding rows of the skew matrix.
On the “bang-bang” control problem
Authors: Bellman R. , Glicksberg I. , Gross O.
Published: December 2016

Let

S
S

be a physical system whose state at any time is described by an

n
n

-dimensional vector

x

(
t
)

x\left ( t \right )

, where

x

(
t
)

x\left ( t \right )

is determined by a linear differential equation

d
z

/

d
t
=
A
z

dz/dt = Az

, with

A
A

a constant matrix. Application of external influences will yield an inhomogeneous equation,

d
z

/

d
t
=
A
z
+
f

dz/dt = Az + f

, where

f
f

, the “forcing term", represents the control. A problem of some importance in the theory of control circuits is that of choosing

f
f

so as to reduce

z
z

to 0 in minimum time. If

f
f

is restricted to belong to the class of vectors whose

i
i

th components can assume only the values

±

b
i

\pm {b_i}

, the control is said to be of the “bang-bang” type.
Wave propagation in rods of Voigt material and visco-elastic materials with three-parameter models
Authors: Morrison J. A.
Published: December 2016

The problem of an impulsively applied and subsequently maintained constant velocity at the end of a semi-infinite rod of Voigt material is considered and integral expressions are obtained for the velocity and stress distributions in the rod. Apart from a constant factor the stress distribution arising from an impulsively applied constant stress at the end of the rod is the same as the velocity solution above. The same problem is considered also for materials with three-parameter models. The stress distributions for both the case of constant applied stress and constant applied velocity are represented graphically for the materials considered, dimensionless co-ordinates being used.
General theory of elastic stability
Authors: Pearson Carl E.
Published: December 2016

Some general topics in elastic stability are discussed. In particular, attention is given to the relationship between adjacent-equilibrium-position and energy techniques, to the effects of non-linearity, and to the sensitivity of certain stability problems to the character of the loading.
Spherical, cylindrical and one-dimensional gas flows
Authors: Keller J. B.
Published: December 2016

The problem of spherical, cylindrical or planar flow of a polutropic gas has been formulated in Lagrangian variables, giving rise to a non-linear second order partial differential equation in two variables,

h
h

and

t
t

. A class of special solutions of this equation has been found by separation of variables, and these solutions depend upon an arbitrary function which is related to the arbitrary entropy distribution in the gas. By specializing this function solutions corresponding to the expansion into a vacuum of an isentropic or non-isentropic gas cloud have been obtained as well as solutions corresponding to the propagation of finite and of strong shocks in variable media.
Geometrical optics of angular stratified media
Authors: Sedney R.
Published: December 2016

Some aspects of the geometrical optics of angular stratified media are considered. A similarity property of the light paths enables one to draw some general conclusions about the behaviour of light rays traversing a cone. An application to the interferometric method of observing supersonic flows shows that a conical flow test is valid including the refraction effect.
Elastic-plastic torsion of circular ring sectors
Authors: Freiberger W.
Published: December 2016

The solution is presented to the problem of uniform torsion of circular ring sectors with circular cross section under the assumption of perfect plasticity. The elastic-plastic problem is solved by a semi-inverse method. When the entire ring is plastic a discontinuity of stress appears which may be regarded as the limiting case of an elastic core; such discontinuities have recently been discussed in the literature [1]. The solution for the discontinuous fully plastic stress distribution is exact, that for the elastic-plastic case approximate in the sense that it is found exactly for cross sections differing slightly from the circular. This difference is negligible for ratios of ring radius

R
R

to cross section radius

ρ
\rho

occurring in practical applications to helical springs of small pitch.
Notes on matrix theory. X. A problem in control
Authors: Bellman Richard
Published: December 2016

In the theory of control processes, it is important to be able to calculate

∫
0
∞

(

x
,
B
x

)

d
t

\smallint _0^\infty \left ( {x,Bx} \right )dt

without having to solve explicitly the differential equation

d
x

/

d
t
=
A
x
,

x

(
0
)

=
c

dx/dt = Ax, \\ x\left ( 0 \right ) = c

. A method for doing this is presented in this paper, generalizing one due to Anke for

n
n

th order linear differential equations.
Notes on control processes. I. On the minimum of maximum deviation
Authors: Bellman Richard
Published: December 2016

The functional equation technique of the theory of dynamic programming is applied to the problem of determining the minimum of the maximum deviation of a system from a preassigned state.
A suggested modification of noise theory
Authors: Keilson Julian
Published: December 2016

A class of stationary, equilibrium, Markoff processes is demonstrated all of which have the same equilibrium distribution,

W
0

(
x
)

{W_0}\left ( x \right )

, and correlation function

R

(
t
)

=

E
0

exp
⁡

(

−
t

/

τ
0

)

R\left ( t \right ) = {E_0}\exp \left ( { - t/{\tau _0}} \right )

differing from each other in the number of zero crossings of the system per second. The processes are described by an integral equation characterized by a parameter

γ
\gamma

. As

γ
\gamma

approaches 1, the integral equation passes over into the Fokker-Planck equation
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="tau 0 StartFraction partial-differential upper W Over partial-differential t EndFraction equals upper E 0 StartFraction partial-differential squared upper W Over partial-differential x squared EndFraction plus StartFraction partial-differential Over partial-differential x EndFraction left-parenthesis x upper W right-parenthesis">

τ
0

∂
W

∂
t

=

E
0

∂
2

W

∂

x
2

+

∂

∂
x

(

x
W

)

{\tau _0}\frac {{\partial W}}{{\partial t}} = {E_0}\frac {{{\partial ^2}W}}{{\partial {x^2}}} + \frac {\partial }{{\partial x}}\left ( {xW} \right )

. Since the number of zero crossings per second of the system becomes infinite as

γ
\gamma

goes to one, the degenerate nature of the Fokker-Planck process is made evident.
On the integration of non-linear parabolic equations by implicit difference methods
Authors: Rose Milton E.
Published: December 2016

The object of this paper is to investigate how solutions of mixed initial-boundary value problems for a certain class of non-linear parabolic equations may be obtained by solving suitable implicit difference equations on a rectangular lattice and taking the limit of such solutions as the mesh of the lattice tends to zero.
The bending of a work-hardening circular plate by a uniform transverse load
Authors: Boyce William E.
Published: December 2016

This paper contains an analysis of the bending moments and deflection of a work-hardening circular plate under the action of a uniformly distributed transverse load. A segment-wise linear yield condition and the associated flow rules are used in order to avoid the unsound features of total stress-strain laws while retaining much of their mathematical simplicity.
A new approach to the non-linear problems of FM circuits
Authors: Biot M. A.
Published: December 2016

Closed form expressions are developed for the output of a frequency modulation receiver for an arbitrary number of superposed input signals. This corresponds to problems of interference or disturbance due to scatter and multiple reflexions. It is also shown how the Fourier components of the output may be evaluated by methods more direct than the usual Fourier analysis.
The interaction of an acoustic wave and an elastic spherical shell
Authors: Mann-Nachbar P.
Published: December 2016

The effect of the impact of a plane pressure wave on an elastic spherical shell is considered, taking into account both the incident and diffracted waves. An infinite series (mode) solution is used and numerical results are obtained for the case of a steel shell in water. It is shown that a simple quasi-static system can be used to find a very good approximation for the stress. The total acceleration on initial impact is found exactly and seen to differ markedly from the accelerations associated with the lower vibrational modes.
The reflection coefficient of a surface of Rayleigh distributed impedance
Authors: Heaps H. S.
Published: December 2016

Formulas are obtained for the probability distribution

p

(
k
)

p\left ( k \right )

of the amplitude

k
k

of

(

z
−

c
2

)

2

(

z
+

c
1

)

−
2

{\left ( {z - {c_2}} \right )^2}{\left ( {z + {c_1}} \right )^{ - 2}}

in which

c
1

{c_1}

and

c
2

{c_2}

are real constants.

z
z

is a complex number of the form

c
+

z
1

c + {z_1}

where

c
c

is a complex constant and

z
1

{z_1}

is a complex variable of Gaussian distribution of amplitude and uniform distribution of phase (see Fig. 1).
One-dimensional diffusion with the diffusion coefficient a linear function of concentration: reduction to an equation of the first order
Authors: Parsons D. H.
Published: December 2016

The problem considered by Stokes

1

^{1}

, of one-dimensional diffusion from an initially sharp boundary between two semi-infinite columns of liquid, the diffusion constant being a linear function of concentration, is discussed. It is shown how the differential equation may be reduced to an equation of the first order. Some properties of the solution are investigated, and the method of obtaining numerical solutions is considered.
The application of limit analysis to the determination of the strength of butt joints
Authors: Shield R. T.
Published: December 2016

The technique of limit analysis is applied to determine upper and lower bounds for the tensile strength of a butt joint consisting of a thin layer of adhesive joining the parallel flats of two rigid adherends. The adhesive is assumed to be an elastic-perfectly plastic material which yields when the maximum shear stress reaches a critical value. The methods used apply to any joint with a convex area of cross-section. Particular application is made to joints whose cross-sections are circular, rectangular, or a polygon circumscribed about a circle.
Expansions of the irregular Coulomb function
Authors: Ham Frank S.
Published: December 2016

Convergent and asymptotic series in the energy are derived for an irregular Coulomb function appropriate to both attractive and repulsive potentials. The coefficients in these series are Bessel functions. For repulsive potentials the derivation yields series in agreement with those given by Breit and others. Some of the series for attractive potentials have been given by Kuhn. The present general derivation and some of the series are, however, new. Tables of the coefficients in the series for the attractive potentials for values of the parameters of interest in solid state energy band calculations have been prepared and are available.
Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems
Authors: Weston Vaughan H.
Published: December 2016

In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential equations in one variable, which are solvable by ordinary methods.
A weak momentum source in a uniform stream
Authors: Breach D. R.
Published: December 2016

The interaction of a momentum source with a viscous uniform stream is studied. Taken separately, each flow is described by an exact solution of the full Navier-Stokes equations. Their combined effect can be described in terms of two non-dimensional parameters related to the strength of the source and the distance from it. A perturbation solution for the case of a weak source is attempted and the initial terms are found. It is shown that the results are closely related to the Oseen expansion for viscous streaming past a spheroid and that when the momentum of the source opposes that of the stream a closed streamline of elliptical shape is formed.
Stability of Poiseuille flow in pipes, annuli, and channels
Authors: Joseph D. D. , Carmi S.
Published: December 2016

The value of

R
=
180

R = 180

which has been given by Orr [1] as a limit for sure stability of Hagen-Poiseuille flow is incorrect. A lower value,

R
=
82.88

R = 82.88

, can be associated with an eigenfunction possessing a first mode azimuthal variation

(

N
=
1

)

\left ( {N = 1} \right )

and no streamwise variation. This eigenfunction is obtained as an exact solution of the appropriate Euler equation. A yet lower value,

R
=
81.49

R = 81.49

, is associated with a spiral mode with

N
=
1

N = 1

and wave number

α
≈
1

\alpha \approx 1

. Corresponding results are obtained for Poiseuille flow between cylinders. For all but the very smallest radius ratios the smallest eigenvalue of Euler’s equation is assumed for the purely azimuthal disturbance. The mode shape for the pipe flow is consistent with the experimental situation as it is now understood [2], though the stability limit is much smaller than the experimental value

(

R
≈
2100

)

\left ( {R \approx 2100} \right )

. For the annulus, the variation of the energy limit with the radius ratio (from pipe flow to channel flow) is consistent with the experimentally observed stability limit. All the results of the energy analysis hold equally if the pipe is in rigid rotation about its axis. If the rotation is “fast” linear and energy results nearly coincide.
Buckling under axial compression of long cylindrical shells with random axisymmetric imperfections
Authors: Amazigo John C.
Published: December 2016

The buckling of long cylinders with homogeneous random axisymmetric geometric imperfections under uniform axial compression is studied by means of a modified truncated hierarchy technique. It is found that the buckling load of the cylinder depends only on the spectral density of the random imperfections. In particular, for small values of the standard deviation of the axisymmetric imperfection the buckling load depends only on the value of the spectral density at a specific wave number.
Dynamic thermal shock in hollow spheres
Authors: Zaker T. A.
Published: December 2016

A method is developed for the solution of problems of uncoupled dynamic thermoelasticity with arbitrarily prescribed spherically symmetric temperature fields. The technique is based on an integration theorem for hyperbolic initial-value problems, together with the construction of image temperature fields in regions outside the actual body so as to satisfy stress or displacement boundary conditions at surfaces.
The construction of difference approximations from a “sensitized functional"
Authors: Rigler A. K.
Published: December 2016

A technique from the calculus of variations is used to derive higher order difference approximations.
Two electromagnetic analogies for a hydrodynamic problem
Authors: Chambers LL. G.
Published: December 2016

It is shown that the equations governing long gravity waves on a rotating earth are the same as the electromagnetic equations in an isotropic plasma on the one hand and ferrites on the other under the influence of a magnetic field.
Jets of radiation
Authors: Synge J. L.
Published: December 2016

This paper deals with radiation (scalar, electromagnetic, or gravitational) produced by an extended source. The object is to construct a model source the radiation from which is concentrated in a jet of small angle with an assigned target direction. This is done by taking for the source an infinite train of high-frequency plane waves travelling in the target direction with the basic speed of propagation, the amplitude falling off exponentially with distance. The critical number, to be made large in this model, is the ratio

a

/

λ

a/\lambda

, where

a
a

is a typical radius of the source and

λ
\lambda

the wave length. However, it is also shown that a jet of scalar radiation may be obtained from a source which possesses no frequency but consists of a single shock wave.
A singular perturbation method. Part I
Authors: Fowkes N. D.
Published: December 2016

An approach to singular perturbation problems, introduced by Mahony [1] which arose out of the consideration of a problem involving a boundary layer is applicable to other singular perturbation problems. It lends itself particularly well to problems involving wave propagation, where “multiple scales” are involved. In this paper and the paper to follow, interest is centered around the equation
\[

ϵ
3

∇
2

ψ
−
g

(
x
)

ψ
=
0

{\epsilon ^3}{\nabla ^2}\psi - g\left ( x \right )\psi = 0

\]
, where

ϵ
\epsilon

is a small positive parameter and

g

(
x
)

g\left ( x \right )

is a bounded function of

x
x

which vanishes along simple closed curves in the solution domain. The one-dimensional case (the Langer turning point problem) is considered in this paper and it will be shown that the approach leads to exactly the same results as obtained by Langer and his associates using a “related equation” method.
Solution of the stress-equilibrium and compatability equations in the presence of body forces and arbitrary temperature fields
Authors: Childs Donald R.
Published: December 2016

We have solved the stress-equilibrium and compatibility equations in three dimensions in terms of a scalar stress function which satisfies a fourth order partial differential equation. The solution also includes operations on two integrals which exhibit the longitudinal and shear components explicitly. All possible relationships involving equilibrium and compatibility conditions result in the same fourth order differential equation involving time and space coordinates. For the static case this equation reduces to the biharmonic equation

∇
4

χ
=
0

{\nabla ^4}\chi = 0

.
Linear time-dependent fluid flow problems
Authors: Wadhwa Y. D. , Wineinger T. W.
Published: December 2016

A general method for solving the linear unsteady fluid flow problems through closed conduits has been given. The method is suitable for problems with or without initial conditions. The cases of flow through a circular pipe and a circular annular channel with arbitrary time-dependent pressure gradient have been solved to illustrate the method.
The neuron as a Lie group germ and a Lie product
Authors: Hoffman William C.
Published: December 2016

A basic Lie group derived earlier that describes the “constancies” of visual perception is extended to one more dimension to take into account the nonlinear flow of an afferent volley of nerve impulses through the layers of the visual cortex. One is then led, via the usual determination of the solutions of a Lagrange partial differential equation in terms of an associated Pfaffian system of ordinary differential equations, to a correspondence between neuron cell body, Lie group germ, and critical point of the system of ordinary differential equations governing the orbits. The local phase portraits of the latter bear a marked resemblance to one or the other of the neuron types defined by Sholl. Since “brains are as different as faces", the concept of structural stability plays an important role in analyzing the connectivity of the neural network. Finally, Lukasiewicz’s theory of parentheses is used to obtain a graph-theoretic representation of the Jacobi identity, which then serves to explain the branching of neuronal processes (dendrites).
Sub- and superharmonic synchronization in weakly nonlinear systems: Integral constraints and duality
Authors: Musa Samuel A. , Kronauer Richard E.
Published: December 2016

A forced system described by the differential equation:
\[

x
+
ϵ
f

(

x
,

x
′

)

+

ω
0
2

x
=
F
cos
⁡
ω
t

x + \epsilon f\left ( {x,x’} \right ) + \omega _0^2x = F\cos \omega t

\]
is considered for cases where

(

n

/

m

)

ω

\left ( {n/m} \right )\omega

is close to

ω
0

{\omega _0}

. (Here

m
m

and

n
n

are integers and

n

/

m
>
1

n/m > 1

denotes superharmonic while

n

/

m
>
1

n/m > 1

denotes subharmonics.) If the unforced system

(

F
=
0

)

\left ( {F = 0} \right )

is conservative, the forced system is shown to possess an integral constraint and the solution is reduced to quadratures, even though the force adds or removes energy from the oscillations. Furthermore, the sub- and superharmonic cases where the

n

/

m

n/m

ratios are inverse are shown to be intimately related, and results for one can be deduced from the other by appropriate interchange of variables.
Series transform solutions for Voigt transients
Authors: Clark George B. , Rupert Gerald B. , Jamison James E.
Published: December 2016

Equations for plane and spherical waves in a Voigt medium were investigated to find methods of solution by means of Laplace transforms for transient waves. One type of solution was found in the form of products of infinite series in both the

s
s

-plane and the

t
t

-plane.
On circularly-polarized nonlinear electromagnetic waves
Authors: Carroll M. M.
Published: December 2016

An exact solution of the nonlinear electromagnetic equations for a conservative nondispersive isotropic centro-symmetric dielectric is obtained, which has an especially simple form, i.e., a harmonic, circularly-polarized plane progressive wave. The normal incidence of such a wave at a plane interface is considered and also the propagation of such waves in a transversely isotropic, uniformly magnetized material.
On the contact problem of layered elastic bodies
Authors: Wu Ting-Shu , Chiu Y. P.
Published: December 2016

The contact problem of elastic bodies, each consisting of a finite layer of uniform thickness rigidly adhering to a half-plane, is investigated on the basis of the two-dimensional theory of elasticity. The materials of the layer and the half-plane in the contact body are isotropic and homogeneous, yet each of them may have distinct elastic properties. The mixed boundary value problem is reduced to a single Fredholm integral equation of the second kind where the unknown variable is a fictitious surface deformation, through which the contact pressure can easily be obtained.
Means, variances, and covariances for laser beam propagation through a random medium
Authors: Schmeltzer Robert A.
Published: December 2016

Wave propagation in a random continuous medium is studied by solving the stochastic wave equation with a random function for the refractive index coefficient. By the application of the Rytov transformation, an equivalent spatial form of the nonlinear Riccati equation is obtained which is then solved by means of an iteration scheme. The statistical properties of the propagated wave are then computed for the case of a coherent focused source with a Gaussian amplitude distribution. These formulas contain, as limiting sub-cases, the results of previous analyses for the spherical and plane wave. More generally, they describe the propagation of a laser beam.
Generalized aerodynamic forces on a flexible plate undergoing transient motion
Authors: Dowell Earl H.
Published: December 2016

The aerodynamic forces on a flexible plate embedded in a rigid half-space, undergoing arbitrary temporal and spatial motion are determined.
Multi-mode surface wave diffraction by a right-angled wedge
Authors: Morgan R. C. , Karp S. N. , Karal Jr.
Published: December 2016

This paper extends the phenomenological theory of multi-mode surface wave diffraction to a right-angled wedge configuration. The solution to a two-mode problem is obtained under the edge condition
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript j equals 0 Overscript 2 Endscripts StartAbsoluteValue StartFraction partial-differential Superscript j Baseline u Over partial-differential x Superscript j Baseline EndFraction EndAbsoluteValue equals 0 left-parenthesis r Superscript minus left-bracket 1 plus h right-bracket Baseline right-parenthesis comma 0 less-than-or-equal-to h greater-than 2 slash 3">

∑

j
=
0

2

|

∂
j

u

∂

x
j

|

=
0

(

r

−

[

1
+
h

]

)

,
0
≤
h
>
2

/

3

\sum \limits _{j = 0}^2 {\left | {\frac {{{\partial ^j}u}}{{\partial {x^j}}}} \right | = 0\left ( {{r^{ - \left [ {1 + h} \right ]}}} \right ),0 \le h > 2/3}

\]
as

r
→
0

r \to 0

. It is conjectured that the same procedure may be used to construct the solution to the corresponding

N
N

-mode problem under the edge condition
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript j equals 0 Overscript upper N Endscripts StartAbsoluteValue StartFraction partial-differential Superscript j Baseline u Over partial-differential x Superscript j Baseline EndFraction EndAbsoluteValue equals 0 left-parenthesis r Superscript minus left-bracket left-parenthesis 2 upper N minus 1 right-parenthesis slash 3 plus h right-bracket Baseline right-parenthesis comma 0 less-than-or-equal-to h less-than-or-equal-to 2 slash 3">

∑

j
=
0

N

|

∂
j

u

∂

x
j

|

=
0

(

r

−

[

(

2
N
−
1

)

/

3
+
h

]

)

,
0
≤
h
≤
2

/

3

\sum \limits _{j = 0}^N {\left | {\frac {{{\partial ^j}u}}{{\partial {x^j}}}} \right |} = 0\left ( {{r^{ - \left [ {\left ( {2N - 1} \right )/3 + h} \right ]}}} \right ),0 \le h \le 2/3

\]
as

r
→
0

r \to 0

.
System identification and prediction—An algorithm using a Newtonian iteration procedure
Authors: Goodman Theodore R.
Published: December 2016

A mathematical technique, especially suitable for programming on a high speed digital computer, is presented for identifying a complete dynamic system having unknown parameters when data concerning one variable of the system is available.
Transverse electric and magnetic effects
Authors: Carroll Michael M. , Rivlin Ronald S.
Published: December 2016

The non-linear electromagnetic constitutive equations, for an isotropic material possessing a center of symmetry, are used to predict the possibility of certain new effects.
Application of conservation laws to the asymptotic properties of hypersonic flow
Authors: Richardson J. M.
Published: December 2016

The conservation laws involving mass, momentum, and energy are utilized for the derivation of a set of exact relations between the drag force on a body moving at hypersonic speeds through air and certain integral properties of the wake at great distances downstream. The above integral properties involve the surface integrals of the deviation of the hydrodynamical variables from their ambient values. The surface in question is a plane perpendicular to the wake axis. Explicitly, the relations state that all of the surface integrals just defined are proportional to the drag force with proportionality factors that are given functions of the ambient values of the hydrodynamical field variables. The results are valid if the plane cutting the wake is sufficiently far downstream that the deviations of the field variables are small relative to their ambient values everywhere on this plane and if irreversible processes are negligible there.
The initial vibrations of a spinning shell
Authors: Rath P. C. , Vasudevan R.
Published: December 2016

In this paper, we have studied the initial angular motion of a spinning shell with an overturning and yawing moment and shown that the frictional effects provided by the yawing moment change the initial rosette motion of the shell to one with a non-zero minimum yaw.
Viscous MHD flow about a spherical magnetic quadrupole
Authors: O’Brien Vivian
Published: December 2016

The perturbation velocity field and the perturbation magnetic field due to the first-order interaction of the slow flow field of a conductive viscous fluid with an aligned quadrupole magnet have been calculated. The drag increase can be computed from the perturbation stream function alone with an economy of effort compared to previous calculations for magnetized bodies.
On diakoptics: Tearing an arbitrary system
Authors: Spillers W. R.
Published: December 2016

Kron’s techniques of tearing and k-partitioning are discussed as they apply to large linear systems of an arbitrary nature and tearing is discarded as inefficient. It is shown that decreasing the size of the sub-units in k-partitioning increases its efficiency; carried to the limit, this reduction results in a Gaussian elimination scheme. Finally, the optimum application of k-partitioning is presented as a linear programming problem.
On the saint Venant problem for a nonhomogeneous elastic materi
Authors: Schile R. D. , Sierakowski R. L.
Published: December 2016

The problem considered is the deformation of a cylindrical or prismatical bar, loaded by forces and moments applied at the ends, in which the elastic “constants” are arbitrary functions of two variables. The solution is formulated in terms of the six Beltrami stress functions and it is shown that two of these are sufficient to satisfy both compatibility and the boundary conditions.
Eigenvalue branching configurations and the Rayleigh-Ritz procedure
Authors: Thompson J. M. T.
Published: December 2016

A general theory of elastic post-buckling, applicable to a wide class of structural eigenvalue problems, is developed in generalized coordinates. Attention is restricted to the initial post-buckling path of the structural system on a plot of the load against the critical principal coordinate, and exact first-order solutions for the path are presented. These solutions are compared with the predictions of the non-linear Rayleigh-Ritz analysis in which the linear buckling mode is employed as the assumed form, and theorems concerning the results of this analysis are established.
On the scattering of electromagnetic wabes by a dielectric cylinder
Authors: Streifer William , Kodis Ralph E.
Published: December 2016

The scattering of

E
E

-polarized cylindrical electromagnetic waves by an infinitely long dielectric cylinder is investigated. For small incident wavelength the slowly converging series solution is converted to a sum of integrals. An expansion is performed so that the integrals may be divided into two classes depending on the relative locations of source and observation points. Those in the first class have points of stationary phase and an asymptotic evaluation gives contributions which are identified as those of geometric optics. The remaining integrals are evaluated as residue sums. A plot of normalized back-scattering cross section vs. normalized radius for

n
=
.4

n = .4

is given.
Isothermal squeeze films
Authors: Langlois W. E.
Published: December 2016

A derivation is presented of the equation governing the pressure in a thin, flat film of ideal gas under isothermal conditions, when the surfaces bounding the film are in relative normal and tangential motion. When tangential motion is absent, the pressure equation reduces to a nonlinear heat equation, which admits of very few closed-form solutions. Various approximation methods are discussed, and two problems involving small periodic variation of the gap between parallel plates are solved by a perturbation method for a film in which fluid inertia is negligible.
On the folding of a viscoelastic medium with adhering layer under compressive initial stress
Authors: Biot M. A. , Ode H.
Published: December 2016

The exact solution is given for the folding by compression of a viscoelastic layer embedded in a viscoelastic medium, under the assumption that there is perfect adherence between layer and medium. This solution agrees closely with the earlier result obtained by Biot which was based on the assumption that layer and medium could slip over each other.
Minimum weight design and the theory of plastic collapse
Authors: Foulkes J.
Published: December 2016

This paper examines the problem of assigning economical sections to the members of a structure whose geometrical form is given. The criterion of failure is taken to be that of the plastic theory of collapse, and the criterion of minimum weight is employed to determine the best design. A geometrical analogue of the equations involved is used to clarify their significance, and such proofs as there are in the text, are cast into geometrical terms. A method of solution is suggested at the end of the paper, but the primary concerns of the paper are the general features of the problem.
Untangling ciliary access and enrichment of two rhodopsin-like receptors using quantitative fluorescence microscopy reveals cell-specific sorting pathways
Authors: Geneva Ivayla I. , Tan Han Yen , Calvert Peter D.
Published: December 2016

Resolution limitations of optical systems are major obstacles for determining whether proteins are enriched within cell compartments. Here we use an approach to determine the degree of membrane protein ciliary enrichment that quantitatively accounts for the differences in sampling of the ciliary and apical membranes inherent to confocal microscopes. Theory shows that cilia will appear more than threefold brighter than the surrounding apical membrane when the densities of fluorescently labeled proteins are the same, thus providing a benchmark for ciliary enrichment. Using this benchmark, we examined the ciliary enrichment signals of two G protein–coupled receptors (GPCRs)—the somatostatin receptor 3 and rhodopsin. Remarkably, we found that the C-terminal VxPx motif, required for efficient enrichment of rhodopsin within rod photoreceptor sensory cilia, inhibited enrichment of the somatostatin receptor in primary cilia. Similarly, VxPx inhibited primary cilium enrichment of a chimera of rhodopsin and somatostatin receptor 3, where the dual Ax(S/A)xQ ciliary targeting motifs within the third intracellular loop of the somatostatin receptor replaced the third intracellular loop of rhodopsin. Rhodopsin was depleted from primary cilia but gained access, without being enriched, with the dual Ax(S/A)xQ motifs. Ciliary enrichment of these GPCRs thus operates via distinct mechanisms in different cells.
Improved seismic profiling by minimally invasive multimodal surface wave method with standard penetration test source (MMSW-SPT)
Authors: Lin Shibin , Ashlock Jeramy C.
Published: December 2016

Surface waves propagating in layered media inherently possess multimodal dispersion characteristics. However, traditional surface wave testing methods employing measurements at the free surface usually capture only a single apparent dispersion curve, especially when using short geophone arrays common to near surface and geotechnical-scale investigations. Such single-mode or fragmented multimode apparent dispersion curves contain only a fraction of the possible dispersion information, thus limiting the accuracy of inverted profiles. To enable more robust measurement of higher Rayleigh-wave modes, a recently developed hybrid minimally invasive multimodal surface wave method is combined herein with the widely used geotechnical standard penetration test (SPT), which is employed as a practical and ubiquitous downhole source. Upon superimposing surface wave dispersion data for a range of SPT impact depths within the soil, higher modes can be measured more consistently and reliably relative to traditional non-invasive testing methods. As a result, misidentification of multiple dispersion modes can be practically eliminated, significantly improving the accuracy and certainty of inversion results.